# Mathematical Model for Energy and Exergy-Based Simulation of Triangular Solar Energy Extractor for Air Heating Applications

Authors: C. Ramesh; M. Vijayakumar; L. Jeyanthi; P. L. Rupesh; A. Kanchana; P. R. Jyothi Sankar; V. S. Sajith; Neha Munjal; Habtewolde Ababu Birhanu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In the present work, the thermal and exergy efficiency of the equilateral triangular duct solar air heater is analytically investigated and its performance is improved by attaching an inclined wire rib over the absorber surface. Using triangular ducts improves the operating flow conditions up to the Reynolds number of 35000. The thermal model of solar air heater is solved by using an iterative procedure by code developed in MATLAB. The analysis considers the roughness parameters that roughness pitch (P)-to-height (e) ratio (P/e) of 4 to 16, roughness height (e)-to-hydraulic diameter (Dh) ratio (e/Dh) of 0.021 to 0.043, and rib inclination angle (α) of 30 to 75°. While increasing the Reynolds number from 2000 to 35000, the inclined rib roughened triangular duct solar air heater thermal performance is increased and attains the maximum value of 83.61% and the effective thermal efficiency of 80.26%. The maximum exergy efficiency of 2.62% is obtained at the Reynolds number value of 1864. It improves the thermal performance by 14.2% as compared with the rectangular rib roughened triangular duct solar air heater. The optimum value of roughness parameters is P/e of 12, e/D of 0.042, and α of 75°. The air heater is useable to attain the temperature rise parameter ranges from 0.001 to 0.03 K·m2/W.


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## Body

## 1. Introduction

Industries in developing countries are unsustainable because of the rapid escalation in the emission of greenhouse gases [1]. Therefore they are formulating their new energy policy to encourage eco-friendly energy usage for sustainable development. The researchers and economists identified the potential of solar thermal technologies specifically for industries for sustainable operations and production of low carbon emissions [2]. Among the industrial solar heat production devices, the flat plate solar air heaters are applicable for low temperature heating processes with an operating temperature range of 60 to 85°C [3].The thermal performance improvement in rectangular duct solar air heaters is achieved by incorporating the techniques like artificial roughness, jet impingement, fins, and baffles [4]. The thermal performance enhancement techniques raise fluid friction and improve the pumping power consumption. The researchers also utilized novel roughness shapes such as winglike tabulators [5], trapezoidal louvered winglets with wavy grooves [6], and double pass [7] arrangements to maximize the thermos hydraulic performance of rectangular duct solar air heater. These techniques effectively improve the heat transfer rate with a penalty of higher consumption in pumping power. Then it is identified that usage of triangular flow passages lowers the pressure drop and minimizes the consumption of pumping power [8]. The triangular ducts can integrate with artificial roughness and can produce a better performance as compared with conventional ducts. The influence of apex angle and dimple roughness on heat transfer and frictional characteristics of triangular air heater was experimentally investigated by Goel et al. and revealed that an apex angle of 60° makes the system more efficient [9]. Kumar et al. improved the thermohydraulic features of triangular duct channels by incorporating semicircular ribs and concluded that lower pitch distance and higher roughness height values improved the system performance by 2.2 times as compared with conventional system [10]. The provision of the rounded corner and straight ribs on triangular channels are investigated by Kumar et al. who observed the performance augmentation by 2.48 times at the Reynold number of 18000 and the relative roughness pitch value of 12 [11]. The researchers also investigated the aspect ratio of straight ribs suitable for triangular channels and concluded that providing the aspect ratio rib roughness values of 4.0 improves the hydraulic performance parameter by 1.89 times as compared with earlier studies [12].Bharadwaj et al. [13] experimentally analyzed the heated triangular duct by using inclined rib roughness and suggested formulating a correlation between energy transfer and frictional factors as a function of inclined rib roughness parameters. Singh [14] uses recycling and discrete V ribs on TDSAH and concluded that the maximum thermohydraulic performance of the system was 71% at the hydraulic diameter of 0.06 m with a temperature rise parameter of 0.004 kW/m2. Kumar et al. [15] also investigated the roughened triangular airflow channels by using CFD analysis for the roughness profiles of elliptical, rectangular, and circular ribs. While comparing the results, it is concluded that the rectangular ribs have superior performance that yields around 1.89 times improvement in thermohydraulic performance [16]. Kumar et al. [17] further carried out a thermal performance investigation in this field by varying the radius of curvature (Rc) of the duct and identified that Rc of 0.33 h provides the enhancement by 21 to 25%. Jain et al. [18] incorporated broken inclined ribs on equilateral triangular ducts and carried out the numerical analysis and revealed that relative gap positions with a value of 0.25 provide the thermohydraulic performance parameter of 2 for the Reynolds number ranging from 4000 to 8000.Nidhul et al. [19] carried out an exegetic performance of TDSAH with the integration of V-shaped rib roughness for the Reynolds number ranges from 5000 to 20000 and concluded that an effective rib angle of 45° yields the maximum exergetic performance of the collector of 2.3%. Misra et al. [20] modified this V shape design with multiple gaps and carried out the investigation numerically for roughness pitch and angle of attack varies from 8 to 14 and 45 to 60°, respectively. Among these conditions, roughness pitch of 10 and angle of attack of 45 formulate better turbulence with a minimum formulation of eddy viscosity. Nidul et al. [21] carried out exergetic performance using an analytical model for straight rectangular ribs and concluded that the enhancement in thermal and exergy efficiency by 36 and 17% for the rib aspect ratio of 4. Kumar et al. [22] compared the exergetic performance of semicircular and square straight ribs and resulted that semicircular ribs enhance the performance by 26%.The analytical and experimental investigations available in triangular duct solar air heaters have been summarized in Table1. However, it was noted that heat transfer and friction factor analysis were considered for the analysis of artificially roughened TDSAH and less work is conveyed on the first law, effective thermal and exergy based analysis. From the table, it was noticed that exergy based performance analysis was considered for the roughness shaped of straight rectangular, semicircular, and V ribs. These designs result in lower enhancements of thermal performance on SAH.Table 1
Particulars of reported research on artificially roughened triangular duct solar air heater.
Roughness designHeat transfer and friction factor analysisFirst law based energy and effective thermal performanceSecond law based exergy analysisDimple shapeGoel et al. [9]✕✕Straight semi-circular ribKumar et al. [10]Kumar et al. [22]Kumar et al. [22]Straight circular ribKumar et al. [11]✕✕Straight rectangular ribKumar et al. [12]✕Nidhul et al. [21]Inclined circular ribBharadwaj et al. [13]✕✕Inclined broken square ribJain et al. [18]✕✕V ribNidhul et al. [19]✕Nidhul et al. [19]V rib with multiple gapMisra et al. [20]✕✕The literature studies also recognized that the influence of artificial roughness with inclined circular ribs is not investigated based on its thermohydraulic and exergetic performance. There is very lesser analysis carried out for triangular air heaters to evaluate its realistic performance on exergy basis. The objective of this work is to improve the performance of solar air heater and investigate the effective thermal and exergetic performance by using inclined circular ribs on triangular duct solar air heaters. The configuration is stated as an inclined rib roughened triangular duct solar air heater (IRTDSAH). During this analysis, the influence of roughness pitch (P) to height (e) ratio (P/e), roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh), and rib inclination angle (α) on effective thermal and exergy efficiency is investigated to identify its optimum values.


## 2. Theoretical Analysis

The inclined rib roughened triangular duct solar air heater is illustrated in Figure1(a). Three identical size plates that are to be considered backplates and absorber plates create the airflow path for the air heater. The triangular channel is covered by insulation at the bottom and sides and a transparent glass cover at the top to minimize heat losses. The inclined wire ribs are attached at the bottom of the absorber plate to act as a tabulator for improving the convection current. The details of the inclined wire ribs and the operating parameters are described in Figure 1(b). The inclined rib attached over the absorber plate breaks the sublayer formulation, and the pitch between the plates and its inclination angle supports flow separation in upstream and flow reattachment in downstream conditions.Figure 1
(a) Inclined rib roughened triangular duct solar air heater. (b) Roughness details.
(a)(b)


## 3. Energy-Based Performance of IRTDSAH

### 3.1. Thermal Efficiency

The real usability of IRTDSAH is calculated by considering the quantity of thermal energy flowing inwards to the system through the glass cover and the amount of heat that bring back to the ambient.It is evaluated by considering the assumption that the roughened absorber plate is working at a mean temperature of Twf and a surrounding temperature of Tas [23].(1)Qu1=FRACIατ−ULTwf−Tas.In the above equation,Tf is given by the following:(2)Twf=Twfi+Twfo2.The rise in enthalpy of outlet air describes the energy gained by the working fluid evaluated using the relation as follows:(3)Qu1=mwfCpfTwfo−Twfi.Heat removal factorFR from the roughened absorber plate is stated as follows [21]:(4)FR=mwfCpfTwfo−TwfiACIτα−ULTwf−Tas.The thermal performance of IRTDSAH can be calculated by using the equation stated by Hottel-Whiler-Bliss by using the parameters that cumulative heat loss coefficientUL and heat removal factor FR. It is stated as follows [24]:(5)ηth=Qu1IAC=FRIτα−ULTwf−TsaI.Heat removal factorFR in terms of collector efficiency factor is stated as follows:(6)FR=mCpULAc1−expULApF′mCp.


### 3.2. Effective Thermal Efficiency

The effective thermal efficiency indicates the performance of IRTDSAH by considering the pumping power losses consumed by the system. It is evaluated by using the equation (7), which consists of efficiency of blower (ηB), efficiency of motor (ηm), efficiency of transmission (ηT), and power plant (ηP) [25].(7)ηEE=Qu1IAC−PmIACηBηmηTηP.


### 3.3. Exergy Analysis

Exergy refers to the conversion of available energy into useful energy or work, and so exemplifies the compactness of the solar air heater. Exergy efficiency can also be stated as useful work that a system may produce with respect to the ambient, and it is defined as follows [26]:(8)ηex=EuEsun,where Eu represents useful exergy output from RTDSAH and Esun exergy input to the system from the Sun. It can be evaluated using the relation as follows [26]:(9)E.sun=AcI1−43TfoTsun+13TfoTsun4.Equation (10) evaluates the irreversibility produced by loss of pressure and energy transfer to the air in the system. It is evaluated as follows:(10)Eu.=Qu1−m..CpTo.lnTfoTfi−mTo.ΔPρfTfi,where ∆P is the pressure drop that happens across the solar air heater path.The entropy values describe the energy destruction from the solar air heater that is not able to convert as useful heat with respect to corresponding operating conditions and ambient temperature. It is evaluated using the following equation:(11)Entropy=Esun−EuTa.


### 3.4. Analytical Procedure

The energy and exergy analysis of IRTDSAH was evaluated by considering assumptions as follows [27].(1)
The energy and exergy investigations are carried out at the 1D-steady state model.(2)
There is a negligible temperature drop that happens across the components of IRTDSAH.(3)
The joints of the air heater are leak-proof.(4)
The variation in convective heat transfer is coefficient across the length of the collector or negligible.(5)
Energy transfer that happens in the axial direction of the collector is only considered for evaluate the outlet temperature of air.The thermal modeling procedure to evaluate the energy and exergetic performance of IRTDSAH is described below.Step 1: The design parameters of inclined wire roughness and surrounding and operating conditions of SAH are taken from Table2.Step 2: It is assumed that the air sucked from the surroundings to the inlet of the SAH is in thermal equilibrium with ambient air temperature. Therefore, the rise in temperature at the outlet (Tfo) of the air is evaluated by the following:(12)Tfo=Tfi+ΔT.Here ΔT represents the rise in temperature of air from the absorber surface. It is used to evaluate the rise in temperature (ΔT/I) [18, 19, 28].(13)ΔT=ΔTI×I.Step 3: Then equations (10)–(12) are used to evaluate the thermophysical properties of air [25].(14)μ=0.181×10−4Twf2930.735,(15)Cp=0.1006×104Twf2930.0155,(16)k=0.275×10−3Twf2930.086.Step 4: The mean temperature of the absorber surface is estimated by using the equation as follows [26]:(17)Tap=Tfo+Tfi2+10.Step 5: The wasted heat losses through the top cover, back insulations, and side cover of the IRTDSAH due to convection are named as overall heat loss that is evaluated by using the relation [18, 19].(18)Ul=Ut+Ub+Ue.In the above relation (18), Ub, Ut and Ue represent bottom, top, and side losses that happen in the SAH. The top loss of the SAH is influenced by the parameters of wind velocity, glass, and absorber plate temperature. Akhtar and Mullick correlation describes the top loss as follows [22]:(19)Ut=σTap2+Tgc2Tap+Tgc1/εap+1/εgc−1+kNulL1+σεgTap2+Tgc2Tgc+Ta+hw−1+tgckgc.The terms in equation (16) are evaluated using the relations as follows:(20)Tgc=FlTap+cTas1+FlNul=1+1.441−1708Racosβ+1−1708sin1.8β1.6Racosβ+Racosβ58300.33−1Fl=12×10−8Tas+0.2Tap3+hw−1+0.3Lg6×10−8εap+0.028×Tap+0.5Tas3+0.6L1−0.2Tap−Tascosβ0.25−1c=Tsky/Tas+hw/3.51+hw/3.5Ts=0.0522×Ta1.5.The edge and bottom losses from the system are evaluated using the relation as follows [21]:(21)Ub=kiδi,Ue=tekiδi×3a1/2×aH.Step 6: The useful energy gain from the IRTDSAH is given by the following:(22)Qu1=AcIτα−ULTap−Tas.Step 7: The mass flow rate that happens in the IRTDSAH is evaluated by the following equations [21]:(23)m˙=Qu1CpΔT,(24)Re=m˙DhμAcs.Step 8: Then the convective heat transfer coefficient of IRTDSAH is calculated based on the Nusselt number correlation that incorporates the relation between the nondimensional inclined wire roughness design parameters is as follows [13]:(25)Nu=0.0031Re1.0972Pe1.0832α600.0792eDh0.3585×exp−0.1908lnα602×exp−0.246lnPe2,hc=NukaDh.Step 9: The plate efficiency factor F′ is calculated by using the value of convective heat transfer coefficient valuehc and the heat loss coefficient value of UL by using the relation shown below [21]:(26)Fι=hchc+UL.Step 10: The outlet temperature based heat gain value (Qu2) is calculated using the equation as mentioned below [21, 22]:(27)Qu2=FRAcIτα−ULTfo−Tfi.Step 11: Then, the deviation betweenQu2 and Qu1 is evaluated. If the difference between the heat gain values is more than 0.01%, then the mean plate temperature of the IRTDSAH is recalculated and resubstituted by equations (22) and (28). The procedure is repeated from the sequence of steps 4 to Step 10 up to the attainment of convergence [26].(28)Tap=Tas+Iατ−Qu2/ACUL.Once the convergence is achieved, then the energy efficiency of the SAH is evaluated using equation (5).Step 12: The frictional flow resistance occurred by the inclined rob roughness is evaluated by using the correlations, and the pump power requirement for propelling the air is given by the following [13]:(29)fr=11.845Re−0.693Pe1.1389α600.0418eDh0.3365×exp−0.1686lnα602×exp−0.2644lnPe2.Step 13: The evaluated friction factor from equation (29) is substituted in equation (30) to estimate the pressure drop (ΔP) and loss of pumping power (Pm) that occurs in IRTDSAH [27].(30)ΔP=4frLv2ρ2Dh,(31)Pm=mΔPρ.Table 2
Typical value of design and operating conditions.
Design and operating parametersValueLength (L) and width (W) of the duct1.5 mThickness (δi) of insulation0.06 mGlass transparent cover thickness (tg)0.004 mThermal conductivity value of insulation (ki)0.04 W/mKThermal conductivity value of glass cover (kg)0.75 W/mKRadiation of intensity (I)1000 W/m2Atmospheric temperature (Ta)300 KTemperature rise parameter (ΔT/I)0.002–0.03 K·m2/WReynolds number (Re)2000–35000Relative roughness height (e/Dh)0.021–0.043Relative roughness pitch (P/e)4–16Inclination angle of arc (α)30–75°The effective thermal efficiency based performance of the IRTDSAH is evaluated by using the relation stated in equation (7).


## 3.1. Thermal Efficiency

The real usability of IRTDSAH is calculated by considering the quantity of thermal energy flowing inwards to the system through the glass cover and the amount of heat that bring back to the ambient.It is evaluated by considering the assumption that the roughened absorber plate is working at a mean temperature of Twf and a surrounding temperature of Tas [23].(1)Qu1=FRACIατ−ULTwf−Tas.In the above equation,Tf is given by the following:(2)Twf=Twfi+Twfo2.The rise in enthalpy of outlet air describes the energy gained by the working fluid evaluated using the relation as follows:(3)Qu1=mwfCpfTwfo−Twfi.Heat removal factorFR from the roughened absorber plate is stated as follows [21]:(4)FR=mwfCpfTwfo−TwfiACIτα−ULTwf−Tas.The thermal performance of IRTDSAH can be calculated by using the equation stated by Hottel-Whiler-Bliss by using the parameters that cumulative heat loss coefficientUL and heat removal factor FR. It is stated as follows [24]:(5)ηth=Qu1IAC=FRIτα−ULTwf−TsaI.Heat removal factorFR in terms of collector efficiency factor is stated as follows:(6)FR=mCpULAc1−expULApF′mCp.


## 3.2. Effective Thermal Efficiency

The effective thermal efficiency indicates the performance of IRTDSAH by considering the pumping power losses consumed by the system. It is evaluated by using the equation (7), which consists of efficiency of blower (ηB), efficiency of motor (ηm), efficiency of transmission (ηT), and power plant (ηP) [25].(7)ηEE=Qu1IAC−PmIACηBηmηTηP.


## 3.3. Exergy Analysis

Exergy refers to the conversion of available energy into useful energy or work, and so exemplifies the compactness of the solar air heater. Exergy efficiency can also be stated as useful work that a system may produce with respect to the ambient, and it is defined as follows [26]:(8)ηex=EuEsun,where Eu represents useful exergy output from RTDSAH and Esun exergy input to the system from the Sun. It can be evaluated using the relation as follows [26]:(9)E.sun=AcI1−43TfoTsun+13TfoTsun4.Equation (10) evaluates the irreversibility produced by loss of pressure and energy transfer to the air in the system. It is evaluated as follows:(10)Eu.=Qu1−m..CpTo.lnTfoTfi−mTo.ΔPρfTfi,where ∆P is the pressure drop that happens across the solar air heater path.The entropy values describe the energy destruction from the solar air heater that is not able to convert as useful heat with respect to corresponding operating conditions and ambient temperature. It is evaluated using the following equation:(11)Entropy=Esun−EuTa.


## 3.4. Analytical Procedure

The energy and exergy analysis of IRTDSAH was evaluated by considering assumptions as follows [27].(1)
The energy and exergy investigations are carried out at the 1D-steady state model.(2)
There is a negligible temperature drop that happens across the components of IRTDSAH.(3)
The joints of the air heater are leak-proof.(4)
The variation in convective heat transfer is coefficient across the length of the collector or negligible.(5)
Energy transfer that happens in the axial direction of the collector is only considered for evaluate the outlet temperature of air.The thermal modeling procedure to evaluate the energy and exergetic performance of IRTDSAH is described below.Step 1: The design parameters of inclined wire roughness and surrounding and operating conditions of SAH are taken from Table2.Step 2: It is assumed that the air sucked from the surroundings to the inlet of the SAH is in thermal equilibrium with ambient air temperature. Therefore, the rise in temperature at the outlet (Tfo) of the air is evaluated by the following:(12)Tfo=Tfi+ΔT.Here ΔT represents the rise in temperature of air from the absorber surface. It is used to evaluate the rise in temperature (ΔT/I) [18, 19, 28].(13)ΔT=ΔTI×I.Step 3: Then equations (10)–(12) are used to evaluate the thermophysical properties of air [25].(14)μ=0.181×10−4Twf2930.735,(15)Cp=0.1006×104Twf2930.0155,(16)k=0.275×10−3Twf2930.086.Step 4: The mean temperature of the absorber surface is estimated by using the equation as follows [26]:(17)Tap=Tfo+Tfi2+10.Step 5: The wasted heat losses through the top cover, back insulations, and side cover of the IRTDSAH due to convection are named as overall heat loss that is evaluated by using the relation [18, 19].(18)Ul=Ut+Ub+Ue.In the above relation (18), Ub, Ut and Ue represent bottom, top, and side losses that happen in the SAH. The top loss of the SAH is influenced by the parameters of wind velocity, glass, and absorber plate temperature. Akhtar and Mullick correlation describes the top loss as follows [22]:(19)Ut=σTap2+Tgc2Tap+Tgc1/εap+1/εgc−1+kNulL1+σεgTap2+Tgc2Tgc+Ta+hw−1+tgckgc.The terms in equation (16) are evaluated using the relations as follows:(20)Tgc=FlTap+cTas1+FlNul=1+1.441−1708Racosβ+1−1708sin1.8β1.6Racosβ+Racosβ58300.33−1Fl=12×10−8Tas+0.2Tap3+hw−1+0.3Lg6×10−8εap+0.028×Tap+0.5Tas3+0.6L1−0.2Tap−Tascosβ0.25−1c=Tsky/Tas+hw/3.51+hw/3.5Ts=0.0522×Ta1.5.The edge and bottom losses from the system are evaluated using the relation as follows [21]:(21)Ub=kiδi,Ue=tekiδi×3a1/2×aH.Step 6: The useful energy gain from the IRTDSAH is given by the following:(22)Qu1=AcIτα−ULTap−Tas.Step 7: The mass flow rate that happens in the IRTDSAH is evaluated by the following equations [21]:(23)m˙=Qu1CpΔT,(24)Re=m˙DhμAcs.Step 8: Then the convective heat transfer coefficient of IRTDSAH is calculated based on the Nusselt number correlation that incorporates the relation between the nondimensional inclined wire roughness design parameters is as follows [13]:(25)Nu=0.0031Re1.0972Pe1.0832α600.0792eDh0.3585×exp−0.1908lnα602×exp−0.246lnPe2,hc=NukaDh.Step 9: The plate efficiency factor F′ is calculated by using the value of convective heat transfer coefficient valuehc and the heat loss coefficient value of UL by using the relation shown below [21]:(26)Fι=hchc+UL.Step 10: The outlet temperature based heat gain value (Qu2) is calculated using the equation as mentioned below [21, 22]:(27)Qu2=FRAcIτα−ULTfo−Tfi.Step 11: Then, the deviation betweenQu2 and Qu1 is evaluated. If the difference between the heat gain values is more than 0.01%, then the mean plate temperature of the IRTDSAH is recalculated and resubstituted by equations (22) and (28). The procedure is repeated from the sequence of steps 4 to Step 10 up to the attainment of convergence [26].(28)Tap=Tas+Iατ−Qu2/ACUL.Once the convergence is achieved, then the energy efficiency of the SAH is evaluated using equation (5).Step 12: The frictional flow resistance occurred by the inclined rob roughness is evaluated by using the correlations, and the pump power requirement for propelling the air is given by the following [13]:(29)fr=11.845Re−0.693Pe1.1389α600.0418eDh0.3365×exp−0.1686lnα602×exp−0.2644lnPe2.Step 13: The evaluated friction factor from equation (29) is substituted in equation (30) to estimate the pressure drop (ΔP) and loss of pumping power (Pm) that occurs in IRTDSAH [27].(30)ΔP=4frLv2ρ2Dh,(31)Pm=mΔPρ.Table 2
Typical value of design and operating conditions.
Design and operating parametersValueLength (L) and width (W) of the duct1.5 mThickness (δi) of insulation0.06 mGlass transparent cover thickness (tg)0.004 mThermal conductivity value of insulation (ki)0.04 W/mKThermal conductivity value of glass cover (kg)0.75 W/mKRadiation of intensity (I)1000 W/m2Atmospheric temperature (Ta)300 KTemperature rise parameter (ΔT/I)0.002–0.03 K·m2/WReynolds number (Re)2000–35000Relative roughness height (e/Dh)0.021–0.043Relative roughness pitch (P/e)4–16Inclination angle of arc (α)30–75°The effective thermal efficiency based performance of the IRTDSAH is evaluated by using the relation stated in equation (7).


## 4. Results and Discussion

The inclined rib roughened triangular duct solar air heater is analytically investigated and the influence of roughness pitch (P) to height (e) ratio (P/e), roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh), and rib inclination angle (α) on thermal, effective and exergy efficiency of the IRTDSAH are presented in following sections.


### 4.1. Effect of Rib Roughness Angle (α) on Thermal Performance of IRTDSAH

The wire ribs are mounted on the IRTDSAH absorber plate with the inclination of angleα varies from 30° to 75°, and its effects on the thermal effective thermal and exergy efficiency are shown in Figures 2–7.Figure 2
Impact of rib roughness angle (α) and Reynolds number on the thermal efficiency of IRTDSAH.Figure 3
Impact of rib roughness angle (α) and rise in temperature parameter on thermal efficiency of IRTDSAH.Figure 4
Impact of rib roughness angle (α) and Reynolds number on the effective thermal efficiency of IRTDSAH.Figure 5
Impact of rib roughness angle (α) and rise in temperature parameter on the effective thermal efficiency of IRTDSAH.Figure 6
Impact of rib roughness angle (α) and reynolds number on exergy efficiency of IRTDSAH.Figure 7
Impact of rib roughness angle (α) and rise in temperature parameter on exergy efficiency of IRTDSAH.Figure2 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on the thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. While increasing the Reynolds number from 2000 to 35000, the thermal efficiency of IRTDSAH improved by a maximum of 52.8% to 83.8% for the rib inclination angle (α) value of 75°. While decreasing the value of α decreases the thermal performance of IRTDSAH due to the production of thermally dead zones.Figure3 reveals the impact of rib roughness angle (α) ranging from 30 to 75° on the thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The thermal efficiency values were found to increase with the increase in α. The maximum thermal efficiency value found in the analysis is 83.61% at α = 75°. Comparatively at a higher angle of attack, the thermal efficiency is higher because of effective flow reattachment in the boundary layer.Figure4 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on the effective thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The effective efficiency values found increases up to the critical Reynolds Number as shown in Table 3. The maximum effective efficiency value found in the analysis is 80.26% in α = 75° at 17534 Reynolds number. For the same Reynolds number with α = 30° the effective efficiency is 79.94%, while the trend gets reversed at higher Reynolds numbers (>25000) that α = 30° yields better performance due to offering lesser flow resistance and consumption of lower pumping power. At a higher Reynolds Number, the pressure drop increases due to the turbulent flow nature of the air. Due to this reason, there is a dip in effective efficiency after the 17528 Reynolds Number. Comparatively, at a higher angle of attack, the effective efficiency is higher, which is evident.Table 3
Critical Reynolds number based on different values ofα.
S. noα (°)Maximum effective efficiency (%)Reynolds number13079.941946924580.131955136080.241752847580.2617534Figure5 reveals the impact of rib roughness angle (α) ranging from 30 to 75° on the effective thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The effective efficiency values found increase up to the critical value of rising in temperature parameter as shown in Table 4. The maximum effective efficiency value found in the analysis is 80.26% at α = 75°. Comparatively, at a higher angle of attack, the effective efficiency is higher.Table 4
Influence ofα on the rise in temperature parameter.
S. nα (°)∆T/I for maximum effective efficiencyMaximum effective efficiency (%)1300.004579.942450.00580.133600.00580.244750.00580.26Figure6 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on exergy efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12.The exergy efficiency values were found to increase up to the critical value of the Reynolds number, as shown in Table5. The maximum exergy efficiency value found in the analysis is 2.87% at α = 75° at Re of 1864, and a further rise in Re > 1864 reduces the exergy efficiency. Comparatively, at operating the air heater lower angle of attack declines the second law efficiency of the system due to higher exergy losses and destructions at a lower Reynolds number. At the system operated at a Reynolds number >20000, it produces a negative value of exergy efficiency for all the values of α due to the rise in internal exergy destruction parameter such as fluid friction occurring between absorber plate and working fluid.Table 5
Critical reynolds number based on different values ofα.
S. nα (°)Maximum exergy efficiency (%)Reynolds number1302.5618212452.7818013602.8518534752.871864Figure7 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on exergy efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The exergy efficiency values were found to increase with the increase in ∆T/I and α till ∆T/I = 0.03 K·m2/W. The maximum exergy efficiency value found in the analysis is 2.87% at α = 75°. Comparatively, at a higher angle of attack, the exergy efficiency is higher. It is observed that at higher ∆T/I, the exergy efficiency value increases.


### 4.2. Effect of Roughness Height (e)-to-Hydraulic Diameter (Dh) Ratio (e/Dh) on Thermal Performance of IRTDSAH

The wire ribs are mounted on the IRTDSAH absorber plate with roughness height to diameter ratio (e/Dh) varying from 0.021 to 0.042, and its effects on the thermal effective thermal and exergy efficiency are shown in Figures 8–14.Figure 8
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) and Reynolds number on the thermal efficiency of IRTDSAH.Figure 9
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) and rise in temperature parameter on thermal efficiency.Figure 10
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on effective thermal efficiency of IRTDSAH.Figure 11
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) and rise in temperature parameter on the effective thermal efficiency of IRTDSAH.Figure 12
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on the effective thermal efficiency of IRTDSAH.Figure 13
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on exergy thermal efficiency of IRTDSAH.Figure 14
Impact of roughness pitch (p) to height (e) ratio (p/e) and Reynolds number on the thermal efficiency of IRTDSAH.Figure8 reveals the rib roughness height (e) to hydraulic diameter (Dh) ratio ranging from 0.021 to 0.043 on the thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 0.75° and P/e = 12.The maximum thermal efficiency value found in the analysis is 83.8% ate/Dh  = 0.043. While increasing the Reynolds number from 2000 to 35000, the thermal efficiency of IRTDSAH improved by a maximum of 53.1% to 83.8% for the rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) value of 0.043. While decreasing the value of e/Dh decreases the thermal performance of IRTDSAH due to the poor formulation, secondary flow reattachment points at the downward part of IRTDSAH.Figure9 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio from 0.021 to 0.043 on the thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The thermal efficiency values were found to increase with the increase in e/Dh. The maximum thermal efficiency value found in the analysis is 83.61% at e/Dh = 0.043. Comparatively, at higher relative roughness height, the thermal efficiency is higher because of the effective breaking of thermal barrier formulated in fluid boundaries.Figure10 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) ranges from 0.021 to 0.043 on effective thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The effective efficiency values found increase up to the critical Reynolds Number, as shown in Table 6. The maximum effective efficiency value found in the analysis is 80.26% in e/ Dh  = 0.043 at 17534 Reynolds number. For the same Reynolds number with e/ Dh  = 0.021, the effective efficiency is 79.76%, while the trend gets reversed at higher Reynolds numbers (>25000) that e/ Dh  = 0.021 yield better performance due to offering lesser flow resistance and consumption lower pumping power. At a higher Reynolds number, the pressure drop increases due to the increment in roughness size increasing the pressure drop. Due to this reason, there is a dip in effective efficiency after the 17534 Reynolds Number. Comparatively, at higher relative roughness height, the effective efficiency is higher, which is evident.Table 6
Critical Reynolds number based on different values ofe/Dh.
S. ne/DhMaximum effective efficiency (%)Reynolds number10.02179.762193720.03280.071950330.04380.2617534Figure11 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) ranging from 0.021 to 0.043 on the effective thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The effective efficiency values found increase up to the critical value of rising in temperature parameter as shown in Table 7. The maximum effective efficiency value found in the analysis is 80.26% at e/Dh = 0.043. Comparatively, at higher roughness height, the effective efficiency is higher.Table 7
Influence ofe/Dh on temperature parameter.
S. ne/Dh∆T/I for maximum effective efficiencyReynolds number10.0210.0042193720.0320.00451950330.0430.00517534Figure12 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on the exergy efficiency of IRTDSAH while flowing air at the Reynolds number from 2000 to 35000 and maintaining other roughness parameters that are constant, i.e., α = 75° and P/e = 12. The exergy efficiency values found to increase up to the critical value of the Reynolds number, as shown in Table 8. The maximum exergy efficiency value found in the analysis is 2.87% at e/Dh = 0.043 and at Re of 1864, and a further rise in Re > 1864 reduces the exergy efficiency. Comparatively, at operating the air heater lower rib roughness height (e) to hydraulic diameter (Dh) ratio declines the second law efficiency of the system due to higher exergy losses and destructions at a lower Reynolds number. At the system operated at a Reynolds number >20000, it produces a negative value of exergy efficiency for all the values of e/Dh due to the rise in internal exergy destruction parameters such as fluid friction occurs between absorber plate and working fluid.Table 8
Critical Reynolds number based on different values ofe/Dh.
S. ne/DhMaximum exergy efficiency (%)Reynolds number10.0212.35185020.0322.66177430.0432.871864Figure13 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) ranging from 0.021 to 0.043 on exergy efficiency of IRTDSAH, while producing hot air with a rise in temperature parameter value ranges from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The exergy efficiency values were found to increase with the increase in ∆T/I and α till ∆T/I 0.03 K·m2/W. The maximum exergy efficiency value found in the analysis is 2.87% at e/Dh = 0.043. Comparatively, at higher e/Dh the exergy efficiency is higher. It is observed that at higher ∆T/I the exergy efficiency value increases.


### 4.3. Effect of Roughness Pitch (P)-to-Height (e) Ratio (p/e) on Thermal Performance of IRTDSAH

The wire ribs are mounted on the IRTDSAH absorber plate with roughness pitch (p) to height (e) ratio (p/e) varies from 4 to 16, and its effects on the thermal effective thermal and exergy efficiency are shown in Figures 13–17.Figure 15
Impact of roughness pitch (p) to height (e) ratio (p/e) and rise in temperature parameter on the thermal efficiency of IRTDSAH.Figure 16
Impact of rib roughness pitch (p) to height (e) ratio (p/e) and Reynolds number on the effective thermal efficiency of IRTDSAH.Figure 17
Impact of rib roughness pitch (p) to height (e) ratio (p/e) and rise in temperature parameter on the effective thermal efficiency of IRTDSAH.Figure14 reveals the impact of rib roughness pitch (p) to height (e) ratio (p/e) ranging from 4 to 16 on the thermal efficiency of IRTDSAH while flowing of air at the Reynolds number from 2000 to 35000 and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and α = 75°. While increasing the Reynolds number from 2000 to 35000, the thermal efficiency of IRTDSAH improved by a maximum of 53.1% to 83.8% for the rib roughness pitch (p) to height (e) ratio (p/e) value of 12. While increasing or decreasing the value of P/e value of 12 decreases the thermal performance of IRTDSAH due to the formulation of sluggish boundary layers.Figure15 exemplifies the impact of roughness pitch (p) to height (e) ratio (p/e) on the thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and α = 75°. The thermal efficiency values were found to increase with the increase in p/e value up to 12 and achieving the maximum thermal efficiency value of 83.61%. Comparatively providing the p/e of 12 improves the thermal efficiency because of the increase in reattachment points in the boundary layer and enriching the local heat transfer coefficients.Figure16 rib roughness pitch (p) to height (e) ratio (p/e) ranges from 4 to 16 on the effective thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 75° and e/Dh = 0.043. The effective efficiency values found increase up to the critical Reynolds Number, as shown in Table 9. The maximum effective efficiency value found in the analysis is 80.26% in P/e = 12 at the Reynolds number of 17534.Table 9
Critical Reynolds number based on different values ofP/e.
S. nP/eMaximum effective efficiency (%)Reynolds number1480194692880.11752231280.221753441680.1719527For the same Reynolds number withP/e = 4, the effective efficiency is 80%, while the trend gets reversed at higher Reynolds numbers (>25000) that P/e = 4 yield better performance due to offering of lesser flow resistance and consumption of lower pumping power. At a higher Reynolds number, the frictional resistance increases due to the increment in the number of elements, increasing the pressure drop. Due to this reason, there is a dip in effective efficiency after the 17534 Reynolds Number.Figure17 reveals the impact rib roughness pitch (p) to height (e) ratio (p/e) ranges from 4 to 16 on the effective thermal efficiency of IRTDSAH, while producing hot air with a rise in temperature parameter value ranges from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and e/D = 0.043. The effective efficiency values found increase up to the critical value of rise in temperature parameter as shown in Table 10. The maximum effective efficiency value found in the analysis is 80.26% at P/e = 12.Table 10
Influence ofP/e on temperature parameter.
S. nP/e∆T/I for maximum effective efficiencyReynolds number140.004519469280.005175223120.005175344160.004519527Figure18 reveals the impact of rib roughness pitch (p) to height (e) ratio (p/e) on the exergy efficiency of IRTDSAH while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 75° and e/Dh = 0.042. The exergy efficiency values were found to increase up to the critical value of the Reynolds number, as shown in Table 11. The maximum exergy efficiency value found in the analysis is 2.87% at P/e = 12 at the Re of 1864 and a further rise in Re > 1864 reduces the exergy efficiency.Figure 18
Impact of rib roughness pitch (p) to height (e) ratio (p/e) and Reynolds number on the effective thermal efficiency of IRTDSAH.Table 11
Critical Reynolds number based on different values ofP/e.
S. nP/eMaximum exergy efficiency (%)Reynolds number142.541878282.6318643122.8718434162.721759Figure19 reveals the impact rib roughness pitch (p) to height (e) ratio (p/e) ranging from 4 to 16 on exergy efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., α = 75° and e/D = 0.043. The exergy efficiency values were found to increase with the increase in ∆T/I and α till ∆T/I 0.03 K·m2/W. The maximum exergy efficiency value found in the analysis is 2.87% at e/Dh = 0.043. Comparatively, at higher p/e up to 12, the exergy efficiency is higher.Figure 19
Influence of rib roughness pitch (p) to height (e) ratio (p/e) on the rise in temperature parameter on exergy thermal efficiency of IRTDSAH.


### 4.4. Entropy Generation

The influence ofe/Dh value on entropy generation is described in Figure 20. From the figure, it is observed that the e/Dh value of 0.043 produces a lower value of entropy for the Re ranging from 2000 to 6000. Then increase in flow rate rise value of entropy generation and the maximum value destruction occurs during the operating condition that consists of the e/Dh value of 0.021.Figure 20
Influence of rib roughness height (e) ratio to hydraulic diameter (e/Dh) and Reynolds number on entropy generation of IRTDSAH.


## 4.1. Effect of Rib Roughness Angle (α) on Thermal Performance of IRTDSAH

The wire ribs are mounted on the IRTDSAH absorber plate with the inclination of angleα varies from 30° to 75°, and its effects on the thermal effective thermal and exergy efficiency are shown in Figures 2–7.Figure 2
Impact of rib roughness angle (α) and Reynolds number on the thermal efficiency of IRTDSAH.Figure 3
Impact of rib roughness angle (α) and rise in temperature parameter on thermal efficiency of IRTDSAH.Figure 4
Impact of rib roughness angle (α) and Reynolds number on the effective thermal efficiency of IRTDSAH.Figure 5
Impact of rib roughness angle (α) and rise in temperature parameter on the effective thermal efficiency of IRTDSAH.Figure 6
Impact of rib roughness angle (α) and reynolds number on exergy efficiency of IRTDSAH.Figure 7
Impact of rib roughness angle (α) and rise in temperature parameter on exergy efficiency of IRTDSAH.Figure2 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on the thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. While increasing the Reynolds number from 2000 to 35000, the thermal efficiency of IRTDSAH improved by a maximum of 52.8% to 83.8% for the rib inclination angle (α) value of 75°. While decreasing the value of α decreases the thermal performance of IRTDSAH due to the production of thermally dead zones.Figure3 reveals the impact of rib roughness angle (α) ranging from 30 to 75° on the thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The thermal efficiency values were found to increase with the increase in α. The maximum thermal efficiency value found in the analysis is 83.61% at α = 75°. Comparatively at a higher angle of attack, the thermal efficiency is higher because of effective flow reattachment in the boundary layer.Figure4 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on the effective thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The effective efficiency values found increases up to the critical Reynolds Number as shown in Table 3. The maximum effective efficiency value found in the analysis is 80.26% in α = 75° at 17534 Reynolds number. For the same Reynolds number with α = 30° the effective efficiency is 79.94%, while the trend gets reversed at higher Reynolds numbers (>25000) that α = 30° yields better performance due to offering lesser flow resistance and consumption of lower pumping power. At a higher Reynolds Number, the pressure drop increases due to the turbulent flow nature of the air. Due to this reason, there is a dip in effective efficiency after the 17528 Reynolds Number. Comparatively, at a higher angle of attack, the effective efficiency is higher, which is evident.Table 3
Critical Reynolds number based on different values ofα.
S. noα (°)Maximum effective efficiency (%)Reynolds number13079.941946924580.131955136080.241752847580.2617534Figure5 reveals the impact of rib roughness angle (α) ranging from 30 to 75° on the effective thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The effective efficiency values found increase up to the critical value of rising in temperature parameter as shown in Table 4. The maximum effective efficiency value found in the analysis is 80.26% at α = 75°. Comparatively, at a higher angle of attack, the effective efficiency is higher.Table 4
Influence ofα on the rise in temperature parameter.
S. nα (°)∆T/I for maximum effective efficiencyMaximum effective efficiency (%)1300.004579.942450.00580.133600.00580.244750.00580.26Figure6 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on exergy efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12.The exergy efficiency values were found to increase up to the critical value of the Reynolds number, as shown in Table5. The maximum exergy efficiency value found in the analysis is 2.87% at α = 75° at Re of 1864, and a further rise in Re > 1864 reduces the exergy efficiency. Comparatively, at operating the air heater lower angle of attack declines the second law efficiency of the system due to higher exergy losses and destructions at a lower Reynolds number. At the system operated at a Reynolds number >20000, it produces a negative value of exergy efficiency for all the values of α due to the rise in internal exergy destruction parameter such as fluid friction occurring between absorber plate and working fluid.Table 5
Critical reynolds number based on different values ofα.
S. nα (°)Maximum exergy efficiency (%)Reynolds number1302.5618212452.7818013602.8518534752.871864Figure7 reveals the impact of rib roughness angle (α) ranges from 30 to 75° on exergy efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and P/e = 12. The exergy efficiency values were found to increase with the increase in ∆T/I and α till ∆T/I = 0.03 K·m2/W. The maximum exergy efficiency value found in the analysis is 2.87% at α = 75°. Comparatively, at a higher angle of attack, the exergy efficiency is higher. It is observed that at higher ∆T/I, the exergy efficiency value increases.


## 4.2. Effect of Roughness Height (e)-to-Hydraulic Diameter (Dh) Ratio (e/Dh) on Thermal Performance of IRTDSAH

The wire ribs are mounted on the IRTDSAH absorber plate with roughness height to diameter ratio (e/Dh) varying from 0.021 to 0.042, and its effects on the thermal effective thermal and exergy efficiency are shown in Figures 8–14.Figure 8
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) and Reynolds number on the thermal efficiency of IRTDSAH.Figure 9
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) and rise in temperature parameter on thermal efficiency.Figure 10
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on effective thermal efficiency of IRTDSAH.Figure 11
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) and rise in temperature parameter on the effective thermal efficiency of IRTDSAH.Figure 12
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on the effective thermal efficiency of IRTDSAH.Figure 13
Impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on exergy thermal efficiency of IRTDSAH.Figure 14
Impact of roughness pitch (p) to height (e) ratio (p/e) and Reynolds number on the thermal efficiency of IRTDSAH.Figure8 reveals the rib roughness height (e) to hydraulic diameter (Dh) ratio ranging from 0.021 to 0.043 on the thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 0.75° and P/e = 12.The maximum thermal efficiency value found in the analysis is 83.8% ate/Dh  = 0.043. While increasing the Reynolds number from 2000 to 35000, the thermal efficiency of IRTDSAH improved by a maximum of 53.1% to 83.8% for the rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) value of 0.043. While decreasing the value of e/Dh decreases the thermal performance of IRTDSAH due to the poor formulation, secondary flow reattachment points at the downward part of IRTDSAH.Figure9 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio from 0.021 to 0.043 on the thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The thermal efficiency values were found to increase with the increase in e/Dh. The maximum thermal efficiency value found in the analysis is 83.61% at e/Dh = 0.043. Comparatively, at higher relative roughness height, the thermal efficiency is higher because of the effective breaking of thermal barrier formulated in fluid boundaries.Figure10 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) ranges from 0.021 to 0.043 on effective thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The effective efficiency values found increase up to the critical Reynolds Number, as shown in Table 6. The maximum effective efficiency value found in the analysis is 80.26% in e/ Dh  = 0.043 at 17534 Reynolds number. For the same Reynolds number with e/ Dh  = 0.021, the effective efficiency is 79.76%, while the trend gets reversed at higher Reynolds numbers (>25000) that e/ Dh  = 0.021 yield better performance due to offering lesser flow resistance and consumption lower pumping power. At a higher Reynolds number, the pressure drop increases due to the increment in roughness size increasing the pressure drop. Due to this reason, there is a dip in effective efficiency after the 17534 Reynolds Number. Comparatively, at higher relative roughness height, the effective efficiency is higher, which is evident.Table 6
Critical Reynolds number based on different values ofe/Dh.
S. ne/DhMaximum effective efficiency (%)Reynolds number10.02179.762193720.03280.071950330.04380.2617534Figure11 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) ranging from 0.021 to 0.043 on the effective thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The effective efficiency values found increase up to the critical value of rising in temperature parameter as shown in Table 7. The maximum effective efficiency value found in the analysis is 80.26% at e/Dh = 0.043. Comparatively, at higher roughness height, the effective efficiency is higher.Table 7
Influence ofe/Dh on temperature parameter.
S. ne/Dh∆T/I for maximum effective efficiencyReynolds number10.0210.0042193720.0320.00451950330.0430.00517534Figure12 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) on the exergy efficiency of IRTDSAH while flowing air at the Reynolds number from 2000 to 35000 and maintaining other roughness parameters that are constant, i.e., α = 75° and P/e = 12. The exergy efficiency values found to increase up to the critical value of the Reynolds number, as shown in Table 8. The maximum exergy efficiency value found in the analysis is 2.87% at e/Dh = 0.043 and at Re of 1864, and a further rise in Re > 1864 reduces the exergy efficiency. Comparatively, at operating the air heater lower rib roughness height (e) to hydraulic diameter (Dh) ratio declines the second law efficiency of the system due to higher exergy losses and destructions at a lower Reynolds number. At the system operated at a Reynolds number >20000, it produces a negative value of exergy efficiency for all the values of e/Dh due to the rise in internal exergy destruction parameters such as fluid friction occurs between absorber plate and working fluid.Table 8
Critical Reynolds number based on different values ofe/Dh.
S. ne/DhMaximum exergy efficiency (%)Reynolds number10.0212.35185020.0322.66177430.0432.871864Figure13 reveals the impact of rib roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh) ranging from 0.021 to 0.043 on exergy efficiency of IRTDSAH, while producing hot air with a rise in temperature parameter value ranges from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and P/e = 12. The exergy efficiency values were found to increase with the increase in ∆T/I and α till ∆T/I 0.03 K·m2/W. The maximum exergy efficiency value found in the analysis is 2.87% at e/Dh = 0.043. Comparatively, at higher e/Dh the exergy efficiency is higher. It is observed that at higher ∆T/I the exergy efficiency value increases.


## 4.3. Effect of Roughness Pitch (P)-to-Height (e) Ratio (p/e) on Thermal Performance of IRTDSAH

The wire ribs are mounted on the IRTDSAH absorber plate with roughness pitch (p) to height (e) ratio (p/e) varies from 4 to 16, and its effects on the thermal effective thermal and exergy efficiency are shown in Figures 13–17.Figure 15
Impact of roughness pitch (p) to height (e) ratio (p/e) and rise in temperature parameter on the thermal efficiency of IRTDSAH.Figure 16
Impact of rib roughness pitch (p) to height (e) ratio (p/e) and Reynolds number on the effective thermal efficiency of IRTDSAH.Figure 17
Impact of rib roughness pitch (p) to height (e) ratio (p/e) and rise in temperature parameter on the effective thermal efficiency of IRTDSAH.Figure14 reveals the impact of rib roughness pitch (p) to height (e) ratio (p/e) ranging from 4 to 16 on the thermal efficiency of IRTDSAH while flowing of air at the Reynolds number from 2000 to 35000 and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and α = 75°. While increasing the Reynolds number from 2000 to 35000, the thermal efficiency of IRTDSAH improved by a maximum of 53.1% to 83.8% for the rib roughness pitch (p) to height (e) ratio (p/e) value of 12. While increasing or decreasing the value of P/e value of 12 decreases the thermal performance of IRTDSAH due to the formulation of sluggish boundary layers.Figure15 exemplifies the impact of roughness pitch (p) to height (e) ratio (p/e) on the thermal efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., e/Dh = 0.043 and α = 75°. The thermal efficiency values were found to increase with the increase in p/e value up to 12 and achieving the maximum thermal efficiency value of 83.61%. Comparatively providing the p/e of 12 improves the thermal efficiency because of the increase in reattachment points in the boundary layer and enriching the local heat transfer coefficients.Figure16 rib roughness pitch (p) to height (e) ratio (p/e) ranges from 4 to 16 on the effective thermal efficiency of IRTDSAH, while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 75° and e/Dh = 0.043. The effective efficiency values found increase up to the critical Reynolds Number, as shown in Table 9. The maximum effective efficiency value found in the analysis is 80.26% in P/e = 12 at the Reynolds number of 17534.Table 9
Critical Reynolds number based on different values ofP/e.
S. nP/eMaximum effective efficiency (%)Reynolds number1480194692880.11752231280.221753441680.1719527For the same Reynolds number withP/e = 4, the effective efficiency is 80%, while the trend gets reversed at higher Reynolds numbers (>25000) that P/e = 4 yield better performance due to offering of lesser flow resistance and consumption of lower pumping power. At a higher Reynolds number, the frictional resistance increases due to the increment in the number of elements, increasing the pressure drop. Due to this reason, there is a dip in effective efficiency after the 17534 Reynolds Number.Figure17 reveals the impact rib roughness pitch (p) to height (e) ratio (p/e) ranges from 4 to 16 on the effective thermal efficiency of IRTDSAH, while producing hot air with a rise in temperature parameter value ranges from 0.001 to 0.03 K·m2/W, and maintaining other roughness parameters are constant, i.e., α = 75° and e/D = 0.043. The effective efficiency values found increase up to the critical value of rise in temperature parameter as shown in Table 10. The maximum effective efficiency value found in the analysis is 80.26% at P/e = 12.Table 10
Influence ofP/e on temperature parameter.
S. nP/e∆T/I for maximum effective efficiencyReynolds number140.004519469280.005175223120.005175344160.004519527Figure18 reveals the impact of rib roughness pitch (p) to height (e) ratio (p/e) on the exergy efficiency of IRTDSAH while flowing of air at the Reynolds number from 2000 to 35000, and maintaining other roughness parameters are constant, i.e., α = 75° and e/Dh = 0.042. The exergy efficiency values were found to increase up to the critical value of the Reynolds number, as shown in Table 11. The maximum exergy efficiency value found in the analysis is 2.87% at P/e = 12 at the Re of 1864 and a further rise in Re > 1864 reduces the exergy efficiency.Figure 18
Impact of rib roughness pitch (p) to height (e) ratio (p/e) and Reynolds number on the effective thermal efficiency of IRTDSAH.Table 11
Critical Reynolds number based on different values ofP/e.
S. nP/eMaximum exergy efficiency (%)Reynolds number142.541878282.6318643122.8718434162.721759Figure19 reveals the impact rib roughness pitch (p) to height (e) ratio (p/e) ranging from 4 to 16 on exergy efficiency of IRTDSAH while producing hot air with a rise in temperature parameter value ranging from 0.001 to 0.03 K·m2/W and maintaining other roughness parameters are constant, i.e., α = 75° and e/D = 0.043. The exergy efficiency values were found to increase with the increase in ∆T/I and α till ∆T/I 0.03 K·m2/W. The maximum exergy efficiency value found in the analysis is 2.87% at e/Dh = 0.043. Comparatively, at higher p/e up to 12, the exergy efficiency is higher.Figure 19
Influence of rib roughness pitch (p) to height (e) ratio (p/e) on the rise in temperature parameter on exergy thermal efficiency of IRTDSAH.


## 4.4. Entropy Generation

The influence ofe/Dh value on entropy generation is described in Figure 20. From the figure, it is observed that the e/Dh value of 0.043 produces a lower value of entropy for the Re ranging from 2000 to 6000. Then increase in flow rate rise value of entropy generation and the maximum value destruction occurs during the operating condition that consists of the e/Dh value of 0.021.Figure 20
Influence of rib roughness height (e) ratio to hydraulic diameter (e/Dh) and Reynolds number on entropy generation of IRTDSAH.


## 5. Conclusion

In the present work, circular wire ribs attached over an absorber plate in an inclined manner act as an artificial roughness for a triangular duct solar air heater. The analytical model is used to evaluate the optimum dimensions of the roughness dimensions relative roughness height of 0.021–0.043, relative roughness pitch of 4–16 and inclination angle of the arc of 30 to 75°. From the analytical results, it is concluded that(i)
While increasing the roughness pitch (P) to height (e) ratio (P/e), roughness height (e) to hydraulic diameter (Dh) ratio (e/Dh), rib inclination angle (α), and mass flow rate improve the thermal performance of the system. It is also noticed that the exergy performance of IRTDSAH decreases with the increase in Reynolds number > 1864(ii)
The maximum thermal efficiency of 83.61% is obtained atP/e of 12, e/D of 0.042, and α of 75°. It is founded that the thermal efficiency is increased with the rise in all these parameters and obtains its maximum value at Re of 35000(iii)
The effective thermal efficiency attains its maximum value of 80.26% at the Re of 17543 with the roughness parameters ranges ofP/e of 12, e/D of 0.042, and α of 75°(iv)
The maximum exergy efficiency of 2.62% is attained at the Re of 1864 at the optimized operating conditions. The air heater can produce a rise in temperature value 0.005 to 0.03 K·m2/W as compared with other systems. The exergy based parameter optimization yields more accurate results to fix the roughness parameters



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