# A shield based thermoelectric converter system with a thermosyphonic heat sink for utilization in wood-stoves

Vikram Bhattacharjee, Debanjan Chatterjee, Permual Raman

► To cite this version:

Vikram Bhattacharjee, Debanjan Chatterjee, Permual Raman. A shield based thermoelectric converter system with a thermosyphonic heat sink for utilization in wood-stoves. ICAER 2015, Indian Institute of Technology,Mumbai, Sep 2015, Mumbai, India. hal-01492936

HAL Id: hal-01492936

https://hal.science/hal-01492936

Submitted on 20 Mar 2017

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A shield based thermoelectric converter system with a thermosyphonic heat sink for utilization in wood-stoves

Vikram Bhattacharjee<fnref n="1" />*, Debanjan Chatterjee<fnref n="2" />, Permual Raman<fnref n="3" />

## Abstract

The Thermoelectric Power Generators (TEG) are solid state devices which utilize temperature gradients to produce electrical energy. In domestic wood-stoves, these devices have carved out a niche for themselves and can be used for generation of electricity in rural areas. This paper presents the design of a shield based thermoelectric power generation system consisting of a thermosyphonic heat sink, for utilization in wood stoves. The average current density of the TEG module improved by 28.3% and 22.3% when compared to the conventional plate-fin heat sink based converter system and a simple single loop thermosyphonic heat sink based converter system respectively. The converter system achieved a maximum power output of 3.2 Watts along with a maximum conversion efficiency of 5.05 % which was higher than the conventional heat sink based module systems in wood burning stoves. An optimal shield thickness of 6 cm reduced the steady state hot side temperature below the permissible limit and an optimal coolant velocity of 8 m/sec ensured efficient removal of heat from the cold side of the generator.

Keywords: Thermoelectric Power Generator; thermosyphonic heat sink; shield; wood-stoves; conversion efficiency

## 1. Introduction

According to WHO around 3 billion people are utilizing simple biomass as a source of fuel for domestic cooking at present [1]. Rural areas, where wood is the main source, domestic wood-fired stoves are being heavily used. In addition to the climatic conditions the rural homes also suffer from uneven distribution of reliable electrical power supply from the grids. As a solution to these problems researchers have investigated the concept of modelling and reconstructing these systems with integration of converter systems utilizing thermoelectric generators for power generation purposes [2-11]. Nuwayhid et al.[2] studied the performance characteristics of a low cost stove top thermoelectric power generator where the evaluation led to the design of Peltier modules to produce maximum power for different utilities. In [3] a small scale electricity generation system was achieved using biomass cook stoves. The prototype produced a total power of 5.9 W and the electricity was utilized to power a 3.3 V Lithium Ion battery. Lertsatithanakorn [4] designed a biomass cook-stove combined with a TEG which gave a net power output of 2.4 Watts. A conversion efficiency of 3.2% enabled the system to light up a low power incandescent bulb. Jiang et al. utilized a TEG system in a plat-flame micro combustor burning dimethyl ether and giving an output power of 2 Watts with a conversion efficiency of 1.25 %. The system sustained a stable premixed flame and achieved a low wall temperature thereby reducing heat loss from the combustion system [5]. In [6] a Bi₂Te₃ based TEG system consisting of 8 modules was used in a biomass gasifier for improved waste heat recovery, giving a maximum power output of 6.1 Watts. A rice husk gasifier coupled with a TEG system on the gasifier wall was tested in [7] where at a temperature difference of 60 °C the output power of the system was 3.9 W along with a conversion efficiency of 2.01%. In [8] a TEG powered wood-stove was designed where the cold side was coupled to a loop-type thermosyphonic heat sink using water as a coolant. The system generated a total output power of 3 W making the system commercially viable for low power applications. A domestic wood stove fitted to a TEG unit working under natural convection produced a power output of 4.2 W. It was deduced that the use of multiple modules with a single heat sink reduces the power output when compared to that of a single module due to reduced temperature difference between the hot and the cold sides of the unit [9]. In [10] a performance evaluation was carried out to study a forced draft clean combustion cook-stove where the power output of the TEG was 4.5 Watts with a temperature difference of 240 °C. Killander et al. [11] designed a cook stove consisting of two Hi-ZHZ modules whose cold side was maintained by a cooling fan. A DC-DC converter was used to step up the output voltage of the TEG and the stove produced a net power output of 10 Watts. Based on the literature review it can be deduced that the performance of the thermoelectric generators in wood stoves is mainly dependent on the following factors like the temperature difference between the hot and the cold sides of the TEG and the design of the heat sink. However, the conventional heat sink based TEG-wood stoves suffer from reduced

<footnote n="1">¹Departmental of Chemical Engineering, Jadavpur University, Kolkata, India</footnote>

<footnote n="2">²Departmental of Electrical Engineering, Jadavpur University, Kolkata, India</footnote>

<footnote n="3">³The Energy and Resources Institute, New Delhi, India</footnote>

<footnote>* Corresponding Author. Tel: (+91) 8583008108, E-mail: vikramju65@gmail.com</footnote>
conversion efficiencies due to reduced temperature differences between the hot and cold sides as a result of increased hot side temperatures above the recommended limit for a generator and inefficient heat dissipation through the fins from its cold side. Hence the objective of this study is to present the design of a new shield based thermoelectric converter system coupled with a single loop thermosyphonic heat sink design for utilization in wood stoves where the additional conductive resistance of the shield would prevent the overheating and damage of the module by maintaining the hot side temperature within the permissible limit and the high specific heat intake of the water in the thermosyphonic heat sink would ensure efficient heat removal from its cold side. The research methodology and the design optimization strategy have been presented in this paper.

**Nomenclature**

TEG Thermoelectric Power Generator

$T_{\text{cold}}$ Cold side temperature (K)

$T_{\text{hot}}$ Hot side temperature (K)

$A_{\text{TEG}}$ TEG surface Area (m²)

$k_{\text{gas}}$, $k_{\text{rod}}$, $k_{\text{rod}}$, $k_{\text{stove}}$, $k_{\text{air}}$, $k_{\text{TEG}}$ Thermal Conductivity of geometry(W m⁻¹ K⁻¹)

$P$ Output Power (Watts)

$A$ Contact area of a thermocouple (m²)

$L_c$ Thickness of solder (mm)

$n$ Electrical Contact Parameter

$N$ Number of thermocouples

$r$ Contact parameter of the module (dimensionless)

$L$ Length of a thermocouple (m)

$x,y,z$ Cartesian Coordinates

$\vec{J}$ Current Density (Am⁻²)

$k_{\text{absorption}}$ Gas absorption Coefficient (m⁻¹)

$k_{\text{scattering}}$ Gas scattering Coefficient (m⁻¹)

$\varphi_{\text{extinction}}$ Extinction Coefficient (m⁻¹)

$C_{\text{p,gas}}$, $C_{\text{p,TEG}}$ Specific Heat Capacity (J kg⁻¹ K⁻¹)

$\bar{T}$ Mean of hot and cold side temperature (K)

**Greek Symbols**

$\alpha$ Seebeck Coefficient (V K⁻¹)

$\eta$ Conversion Efficiency

$\rho_{\text{TEG}}$ Density of TEG material (kg m⁻³)

$\Re_{\text{TEG}}$ Electrical Resistivity (Ω m)

$\varphi_{\text{extinction}}$ Extinction Coefficient

$e_{\text{amb}}$ Surface Emissivity
## 2. Thermoelectricity

### 2.1 Background

Thermoelectric Effect was first discovered by Seebeck [12] in the year 1822. The “Seebeck Effect” principle states that when a temperature difference is maintained across the junctions of two dissimilar metals, a voltage is generated. Thermoelectric Modules, also called the Thermoelectric Power Generators are a combination of a pair of n and p type semiconductors which are combined electrically in series and thermally in parallel and are alternately arranged to ensure unidirectional career transport. The negative loading of the n type elements and the positive loading of the p type elements finally constitute the electrical power output from the system. The whole assembly is supported by two ceramic plates for mechanical support. Having a high thermal conductivity, ceramic allows efficient heat transfer from the hot to the cold side thereby ensuring a high conversion efficiency of the module.

### 2.2 Module Parameters

The principle parameters that determine the performance of a thermoelectric power generator are the net output power, the maximum conversion efficiency and the hot and cold side temperatures of the TEG unit. The maximum conversion efficiency, theoretical maximum power output, the voltage and the output current can be determined on basis of the contact resistances and are given by (1) and (2) respectively [13].

$$ \eta = \frac{T_{\text{hot}} - T_{\text{cold}}}{T_{\text{hot}}} \left\{ \left( 1 + \frac{2rL_c}{L} \right)^2 \left( 2 - 0.5 \left( \frac{T_{\text{hot}} - T_{\text{cold}}}{T_{\text{hot}}} \right) + \frac{4}{ZT} \left( \frac{L+n}{(L+2rL_c)^2} \right) \right) \right\}^{-1} \quad (1) $$

$$ P = \frac{\alpha^2 NA(T_{\text{hot}} - T_{\text{cold}})^2}{2\rho (L+n) \left(1 + \frac{2rL_c}{L}\right)^2} \quad (2) $$

Typically the value of $L_c$, n, and r, are constants for a module and depending on the material Bi-Te and the temperature difference used and were taken from [13]. Here $L_c$ = 0.8 mm and $\alpha$ = 2.1226* 10⁻⁴ V K⁻¹, n=0.1 mm, r=0.2, and L=1.2 mm and $\rho$ = 2.07 * 10⁻³ Ω cm. and Z= 2.75 * 10⁻³ K⁻¹.

## 3. Experimental Setup

### 3.1 Converter System Design

The Thermoelectric Converter System consisting of a single module was designed in a manner such that the hot side of the TEG unit is not directly exposed to the incoming heat energy from the source. Rather it was attached to an 15 cm cylindrical copper rod which is in direct contact with the heat source. There exists a shield between rod and the hot side of the TEG. The shield adds an additional conductive resistance to the system and hence lowers the hot side temperature below the permissible value and prevents the damage of the module due to sudden outburst of heat energy from the source. The cold side was attached to a single loop thermosyphonic system with water as the coolant. Cold water at 13 °C flowed from the reservoir whose volume was kept constant at 2 litres from an external water supply. The cooling system was a stainless steel box having dimensions 10 cm x 10 cm x 5 cm. The TEG was supported in a small socket on the surface of the coolant chamber and the rod and the shield assembly was supported by the help of Magnetic Sockets as shown in the Figure 1. The chamber had two openings on one pair of its opposite faces. Both the openings were provided with valves and pipes for the passage and control of the coolant flow velocity. In this study a Bi₂Te₃ TEG module having dimensions 30 mm x 30mm x 3.3 mm was selected. The maximum hot side and cold side temperature of the module was 300°C and 30°C respectively. The value of thermal conductivity, the Seebeck coefficient and the electrical conductivity for the material were taken from [14].
<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic of the Converter System</figcaption></figure>

## 3.2 Stove Geometry

The chamber had a squared opening (4cm x 4cm) at the bottom for the entry of air inside the system. Wood pieces (of dimensions 1.5 inch x 1.75 inch) were used for ignition inside the combustion chamber. Initially a total of 250 gm. of wood chips occupied $\frac{1}{3}rd$ of the chamber volume. The chamber was made to operate in batch mode and wood was added eventually when the temperature dropped. The cylindrical rod of the converter system was inserted into the chamber through a hole (1 cm I.D). The length of the rod inside the chamber was 10 cm. The temperature was measured by the help of three standard temperature sensors attached to the display. Air was forced into the chamber via a 5 V blower from beneath through a narrow opening to ensure efficient combustion. A similar 5V fan was attached as a load with the TEG whose RPM was measured and controlled throughout the experiment. The experimental setup has been shown in the following Figure 2.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Stove Geometry</figcaption></figure>

## 3.3 Conventional Heat Sink Designs for performance assessment

The performance of the converter was compared with the performance of a two conventional heat sink designs. In the first design the coolant chamber was replaced with a aluminium based rectangular plate-fin heat sink having a fixed number of fins. The second design was a simple single loop thermosyphonic system with no shield in between the hot side and the stove wall. The dimensions of the coolant chamber in a simple single loop thermosyphonic system was similar to that in the proposed design. The material properties for the stove geometry and the converter system designs were taken from [15] and the instruments used during the experiment have been tabulated below along with their respective specifications in Table 1 and Table 2 respectively.
<table><caption>**Table 1**
Instrument Specifications</caption><thead><tr><th>Instruments used</th><th>Measurement</th><th>Makers Name</th><th>Resolution</th><th>Unit</th><th>Accuracy</th></tr></thead><tbody><tr><td>Digital thermometer</td><td>Temperature</td><td>CIE305</td><td>0.10</td><td>°C</td><td>0.10</td></tr><tr><td>Multimeter</td><td>V/A</td><td>MecoV</td><td>0.01</td><td>V</td><td>±0.05</td></tr><tr><td>Multimeter</td><td>V/A</td><td>MecoV</td><td>0.01</td><td>A</td><td>±1.10</td></tr><tr><td>Tachometer</td><td>Speed</td><td>Techmark</td><td>1</td><td>RPM</td><td>±0.05</td></tr><tr><td>Digital Balance</td><td>Weight<br>Of fuel</td><td>Sunshine<br>Instruments</td><td>1.00</td><td>g</td><td>Auto calibration</td></tr></tbody></table>

<table><caption>**Table 2**
Parameters of the stove [23].</caption><thead><tr><th>Components</th><th>Material of Construction</th><th>Thermal Conductivity<br>W m<sup>-1</sup> K<sup>-1</sup></th><th>Notation</th></tr></thead><tbody><tr><td>Stove</td><td>Stainless Steel</td><td>16.300</td><td>k<sub>stove</sub></td></tr><tr><td>Coolant Box</td><td>Aluminium</td><td>204.300</td><td>--</td></tr><tr><td>Cylindrical Rod</td><td>Copper</td><td>385.000</td><td>k<sub>rod</sub></td></tr><tr><td>Coolant</td><td>Water</td><td>0.563</td><td>k<sub>coolant</sub></td></tr><tr><td>Shield</td><td>Iron</td><td>71.800</td><td>k<sub>shield</sub></td></tr></tbody></table>

# 4. Mathematical Modelling

## 4.1 Guiding Equations

In order to estimate its analytical performance, a mathematical analysis of the converter system was carried out by defining the flow and energy equations with appropriate boundary conditions for its different components. Inside the stove the flow of the inlet air was modelled using the Reynolds-Averaged Navier Stokes equations [16] including the k-ε turbulent model [17]. The equations of conjugate heat transfer (3-9) involved viscous effects and the effect on the temperature profile of the flue gas due to heat generation from the heat source inside the chamber.

$$ \rho \frac{\delta \mathbf{u}}{\delta t} + \rho(\mathbf{u} \cdot \nabla)\mathbf{u} = \nabla \cdot (-\mathbf{P}\mathbf{I} + (\boldsymbol{\mu} + \boldsymbol{\mu}_t) \left(\nabla \mathbf{u} + (\nabla \mathbf{u})^T - \frac{2}{3}(\boldsymbol{\mu} + \boldsymbol{\mu}_t)(\nabla \cdot \mathbf{u})\mathbf{I} - \frac{2}{3}\rho k \mathbf{I}\right) + \mathbf{F} \quad (3) $$

$$ \rho \frac{\delta \mathbf{k}}{\delta t} + \rho(\mathbf{u} \cdot \nabla)\mathbf{k} = \nabla \cdot \left( \left( \mu + \frac{\mu_t}{\sigma_k} \right) \nabla \mathbf{k} \right) + P_r - \rho \in \quad (4) $$

$$ \rho \frac{\delta \mathbf{u}}{\delta t} + \nabla \cdot (\rho \mathbf{u}) = 0 \quad (5) $$

$$ \rho \frac{\delta \epsilon}{\delta t} + \rho(\mathbf{u} \cdot \nabla)\epsilon = \nabla \cdot \left( \left( \mu + \frac{\mu_t}{\sigma_k} \right) \nabla \epsilon \right) + 1.44 \frac{\epsilon}{k} P_r - 1.92 \rho \frac{\epsilon^2}{k} \quad (6) $$

$$ \mu_t = 0.09 \rho \frac{k^2}{\epsilon} \quad (7) $$
$$P_r = \mu_t \left[ (\nabla \mathbf{u} : (\nabla \mathbf{u} + (\nabla \mathbf{u})^T)) - \frac{2}{3} (\nabla \cdot \mathbf{u})^2 \right] - \frac{2}{3} \rho k \nabla \cdot \mathbf{u} \quad (8)$$

$$\rho_{gas} C_{p,gas} \frac{\delta T}{\delta t} + \rho_{gas} C_{p,gas} \mathbf{u} \cdot \nabla T_{gas} = \nabla \cdot (k_{gas} \nabla T_{gas}) + q_{gen} \quad (9)$$

where $\mu_t$ represents the undamped kinematic viscosity, $k$ represents the turbulent kinetic energy and $\in$ is the turbulent dissipation rate. The terms $k_{gas}$ along with $\rho_{gas}$ represent the thermal conductivity and the density of the fluid respectively. $q_{gen}$ is the heat generation term which has been modelled as a non exhaustive heat source dependent on the source temperature and the production coefficient. Radiative heat transfer between ambient and a flame was previously modelled in [18] which considered the radiative transfer equation (Eq.(10)) for a gray medium incorporating the effects due to the phenomenon of scattering, absorption and emission. Given by (11) the heat generation $q_{gen}$ inside the volume is a function of the average intensity $H(r,s)$ of the scattered radiation where $k_{absorption}$ and $k_{scattering}$ represent the coefficients describing absorption and scattering respectively. $\varphi_{extinction}$ represents the overall extinction coefficient and is expressed as the sum of the scattering and the absorption coefficients and can be expressed by Eq.(11).

$$s \cdot \nabla H(r, s) = -\varphi_{extinction} H(r, s) + q_{gen} \quad (10)$$

$$q_{gen} = \frac{k_{absorption}}{\pi} \sigma T_{source}^4 + \frac{k_{scattering}}{4\pi} \int H(r, s) d\Omega \quad (11)$$

The governing equations which determine the performance parameters of the TEG are dependent on its current density and the heat transfer through the material. The thermal conductivity, the specific heat capacity along with the density of the material of construction of the TEG, determine its performance and hence were taken into account in the analysis.

The governing equation of the TEG at unsteady state is a three dimensional form which can be represented considering energy balance and current conservation [19]. They have been elucidated below as follows.

$$\rho_{TEG} C_{p,TEG} \frac{\delta T_{TEG}}{\delta t} + \nabla \cdot \vec{q} = \dot{q} \quad (17)$$

$$\nabla \cdot \vec{J} = 0 \quad (18)$$

Where $\vec{q}$, $\dot{q}$ and $\vec{J}$ represent the heat flux, the heat generation and the current density respectively. The heat flux is related to the current density and the electric field intensity vector by the equations (19) and (20) respectively.

$$\nabla \cdot \vec{q} = \alpha T_{TEG} \vec{J} - k_{TEG} \nabla T_{TEG} \quad (19)$$

$$\vec{J} = \frac{1}{\Re_{TEG}} (\vec{E} - \alpha \nabla T_{TEG}) \quad (20)$$

Where $\vec{E}=-\nabla\Omega$ and $\Omega$ being the scalar electric potential with $\Re_{TEG}$ and $k_{TEG}$ being the electrical resistivity and the thermal conduction of the material of construction of the TEG respectively. Substitution of the (19) into (17) gives the final form of the governing equation which has been used for the determination of the temperature profiles and the scalar potential in each of the three phases of the experiment.

$$\nabla \cdot (k_{TEG} \nabla T_{TEG} - \alpha T_{TEG} \vec{J}) + \dot{q}_{TEG} = \rho_{TEG} C_{p,TEG} \frac{\delta T_{TEG}}{\delta t} \quad (21)$$
The heat generation is dependent on power loss due Joule Heating and therefore the final equation giving the temperature profile of the TEG is given by (22).

$$ \nabla \cdot (k_{TEG} \nabla T_{TEG} - \alpha T_{TEG} \vec{J}) + \rho_{TEG} \vec{J}^2 = \rho_{TEG} C_{p,TEG} \frac{\delta T_{TEG}}{\delta t} \quad (22) $$

Where the specific heat capacity of the thermoelectric material varies with temperature according to the Equation (23) [20].

$$ C_{p,TEG} = 108.06 + 0.0553 T_{TEG} \quad (23) $$

# 6. Results & Discussion

## 6.1 Steady State temperature Differences

The proposed system reduced the maximum hot side temperature of the TEG below the permissible limit of 573 K to 542 K where as the conventional plate-fin and the simple thermosyphonic heat sink system with no shield recorded a maximum hot side temperature of 584 K and 575 K respectively. The proposed system recorded a maximum temperature difference of 250 K which is comparatively higher than the conventional plate-fin heat sink and the simple thermosyphonic systems which recorded a maximum temperature difference of 195 K and 228 K respectively.

## 6.2 Selection and assessment of variable parameters for optimum module performance

### 6.2.1 Effect on variation of inserted length on turbulent energy dissipation

Arrow Surface: Vorticity field Surface: Turbulent dissipation rate (m²/s³)

<figure><img src="image_4.png" /><figcaption>Fig.3. Distribution Of The Turbulence Energy Dissipation Rate Inside The Flow Field</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig.4. Variation of the Turbulent Energy Dissipation Rate (m² s⁻³) and maximum hot side temperature of the TEG with inserted length</figcaption></figure>

Figure 3. shows the distribution of the turbulence energy dissipation rate inside the flow field. As predicted by the k-ε turbulent model and the imposed boundary conditions near the wall, the magnitude of the turbulent energy dissipation rate increases near the inserted rod as a result of shear provided by the surface of the rod structure inside the geometry. From the figure it can be inferred that the energy dissipation rate from the fluid reaches a maximum value of 844 m²s⁻³ in regions near the wall in which the rod is attached. Therefore magnitude of heat flux travelling through the rod and ultimately falling on the hot side of the TEG through the shield will vary directly with the length of the part of rod inserted inside the geometry. However increasing the length of the inserted portion will increase proximity of the TEG hot side with the wall of the stove and will lead to the overheating of the device. Thus to avoid overheating and to allow optimum module performance, the length of the inserted portion was chosen accordingly based on optimized rates of turbulent energy dissipation and the maximum hot side temperature of the module. Figure 4. shows the variation of the turbulent dissipation rate and maximum hot side temperature with increasing length of the converter. It is evident from the figure that at a length of 8 cm the average turbulent dissipation energy is high and the maximum hot side temperature is below the allowable limit of 573 K. Hence the said geometric length was chosen and kept constant during the experiment.

### 6.2.2 Effect on variation of shield thickness for optimum module performance

<figure><img src="image_6.png" /><figcaption>Fig.5. Variation of Heat Flux through Shield at different shield thicknesses.</figcaption></figure>

The above histogram in Figure 5. shows the variation of the magnitude of the conductive heat flux flowing normal to the surface of the shield into the TEG and the total radiative heat loss from the faces of the shield. At various shield thicknesses, increasing the shield thickness increases the conductive resistance along the thickness of the
shield and the flow of the heat flux is mainly along the directions which offer lower resistance due to conduction. The conductive heat flux flowing normal to the faces excluding those parallel to the walls of the TEG is thus manifested as radiation loss into the ambient. In the figure the hot side temperature of the TEG corresponding to the conductive heat flux falling on the hot side is above the maximum allowable limit up to a shield thickness of 3 cm but gradually decreases as the shield thickness increases and the radiation loss increases. However since the chief mode of heat transfer from the shield to the TEG is in the form of conduction, increasing the additional conductive resistance drastically will reduce the power output of the generator. Hence the shield thickness should be based on the optimized rates of conductive and radiative heat transfer to simultaneously prevent module overheating and ensure efficient module performance.

### 6.2.3 Effect on variation of flow rate on boundary convective flux

<figure><img src="image_7.png" /><figcaption>Fig.6.Variation of Convective Heat Flux from TEG cold side at different coolant flow velocities.</figcaption></figure>

Figure 6. describes the variation of the boundary convective flux from the cold side of the TEG at different flow velocities through the chamber. The figure shows that the convective heat flux from the cold side increases gradually when the coolant velocity is gradually increased from 5 to 10 m/sec but the magnitude of the boundary convective flux from the TEG cold side becomes more or less constant at a coolant flow velocity of 9-10 m/sec. A higher coolant velocity requires larger reservoir heights and demands material costs on piping. Therefore based on the availability of water storage space and optimization of material costs, the height of the reservoir should be judiciously chosen for achieving effective heat removal at optimum flow rates.

<figure><img src="image_8.png" /><figcaption>Fig.7.Variation of TEG Output Power as a function of shield thickness</figcaption></figure>
Figure 7. shows the variation of the maximum output power of the TEG with shield thickness at various coolant flow velocities. In the figure the power output initially increases with increasing thickness and after reaching a maximum the power output starts decreasing with further increase in the shield thickness. The power output is minimum in the absence of shield due to overheating of the TEG hot side. As the shield thickness increases the efficiency of the module increases due to increased temperature difference between its two sides and finally starts decreasing as the conductive flux entering the module decreases with an increase in the conductive resistance of the shield. When the thickness is constant the maximum output power also increases with an increase in the coolant flow velocity till it reaches a value of 9 m/sec. Figure 6. shows that the convective heat flux removed from the cold side of the TEG becomes constant beyond a magnitude of 9 m/sec and hence the maximum power output of the TEG remains constant at 3.2 Watts as the coolant flow rate is increased further. A shield thickness of 6 cm was chosen taking into consideration the material cost and the optimized heat transfer rates in order to achieve successful prevention of overheating of the side exposed to incoming heat flux, and a coolant flow velocity of 8 m/sec was considered in the design for ensuring optimal performance of the TEG unit.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Comparison of the variation of Conversion Efficiency with Temperature Difference in two converter systems</figcaption></figure>

Calculated using Eq. (1), Figure 8. describes the variation of the conversion efficiencies for the three systems which shows that due to higher temperature differences, the module in the proposed system, having a maximum efficiency of 5.1% at a temperature difference of 250 K, reached a higher maximum conversion efficiency of 5.05% when compared to the other two systems which recorded efficiencies upto a maximum of 0.75% and 3.5% respectively. The process parameters have been tabulated below in Table 3.

<table><caption>Table 3
Tabulation of the input parameters of the model</caption><thead><tr><th>Components</th><th>Symbol</th><th>Value</th><th>Reference</th></tr></thead><tbody><tr><td><strong>Forced Convection</strong></td><td></td><td></td><td></td></tr><tr><td>Medium:Air</td><td></td><td></td><td></td></tr><tr><td>Ambient Temperature (K)</td><td>T<sub>0</sub></td><td>300</td><td></td></tr><tr><td>Velocity (ms<sup>-1</sup>)</td><td></td><td>5</td><td></td></tr><tr><td><strong>Surface to Surface Radiation</strong></td><td></td><td></td><td></td></tr><tr><td>Emissivity</td><td>e<sub>amb</sub></td><td>0.80</td><td>[21]</td></tr><tr><td>Stefan-Boltzmann Constant<br>(W m<sup>-2</sup> K<sup>-4</sup>)</td><td>σ</td><td>5.670373*10<sup>-8</sup></td><td>[22]</td></tr><tr><td>Thermal conductivity of TEG<br>material</td><td>k<sub>TEG</sub></td><td>1.20</td><td>[23]</td></tr><tr><td>Absorption Coefficient (m<sup>-1</sup>)</td><td>k<sub>absorption</sub></td><td>0.50</td><td>[24]</td></tr><tr><td>Scattering Coefficient (m<sup>-1</sup>)</td><td>k<sub>scattering</sub></td><td>0.01</td><td>[24]</td></tr></tbody></table>
<figure><img src="image_10.png" /><figcaption>Fig.9 Surface Plot for Steady State Distribution of Current Intensity in the TEG using three different systems</figcaption></figure>

Figures 9(a),9(b) and 9(c) show the variation of the steady state current density inside the TEG in the three cases. The current density is maximum at the center of the module due to the concentration of the conductive heat flux from the rod and it gradually decreases away from the center. Comparatively the first case shows a maximum current density of 2.08×10⁴ Am⁻² and a minimum of 243 Am⁻² where as it increases to a maximum of 2.79×10⁴ Am⁻² and 2.55×10⁴ Am⁻² and a minimum of 175 Am⁻² and 96.8 Am⁻² in the second and the third case respectively. Due to higher hot side temperatures the maximum current intensity in the conventional heat sink designs, is greater than that of the proposed system but the reduced temperature differences and low conversion efficiencies gradually minimize the current intensity in larger sections of the module. Due to the increased temperature difference between the two sides of the TEG the average intensity increased by 28.3% when the shield based thermosyphonic converter system is used in place of the conventional plate-fin heat sink system and by 22.3% when the shield was added to a single open loop thermosyphonic system.

## Conclusion

A shield based thermosyphonic converter system was designed for power generation in wood stoves. The additional conductive resistance of the shield reduced the hot side temperature below the maximum allowable temperature for the hot side and prevented module overheating while the thermosyphonic system helped in the efficient removal of the heat energy from the cold side. The performance of the converter was studied for utilization in a wood stove consisting of a heat source and was compared to that of a conventional rectangular plate-fin heat sink based thermoelectric converter system and a simple single loop thermosyphonic heat sink based system. It was observed that the proposed system showed an appreciable increase in the maximum conversion efficiency and an increase in the average current density by 28.3% and 22.3% respectively. The maximum power output of the system was 3.2 Watts with a maximum conversion efficiency of 5.05% making the design viable for low power applications.

## Acknowledgements

The authors would like to acknowledge the technical staff of The Energy and Resources Institute, New Delhi, India, for conducting the study.
References

[1]. WHO Report on biomass consumption. Source:http://www.who.int/mediacentre/factsheets/fs292/en/.(cited:17.01.2015)

[2]. R.Y. Nuwayhid, D.M. Rowe, G. Min. Low cost stove-top thermoelectric generator for regions with unreliable electricity supply. Renew Energy 2003; 28(2):205-222.

[3]. S.M. O'Shaughnessy, M.J. Deasy, C.E. Kinsella, J.V. Doyle, A.J. Robinson. Small scale electricity generation from a portable biomass cookstove: Prototype design and preliminary results. Appl Energy 2013; 102: 374-385.

[4]. C. Lertsatitthanakorn.Electrical performance analysis and economic evaluation of combined biomass cook stove thermoelectric (BITE) generator. Bioresource Technology 2006;8:1670-1674.

[5]. L.Q. Jiang, D.Q. Zhao, C.M. Guo, X.H. Wang, Experimental study of a plat-flame micro combustor burning DME for thermoelectric power generation, Energy Conversion and Management, Volume 52, Issue 1, January 2011, Pages 596-602, ISSN 0196-8904, Available from: http://dx.doi.org/10.1016/j.enconman.2010.07.035.

[6]. Hsiao-Kang Ma, Ching-Po Lin, How-Ping Wu, Chun-Hao Peng, Chia-Cheng Hsu. Waste heat recovery using a thermoelectric power generation system in a biomass gasifier. Appl Therm Engg; Available online 5 October 2014: ISSN 1359-4311. Available from: http://www.sciencedirect.com/science/article/pii/S1359431114008424

[7]. C. Lertsatitthanakorn, J. Jamradloedluk, M. Rungsiyopas, Study of Combined Rice Husk Gasifier Thermoelectric Generator, Energy Procedia, Volume 52, 2014, Pages 159-166, ISSN 1876-6102, http://dx.doi.org/10.1016/j.egypro.2014.07.066.

[8]. Nuwayhid RY, Hamade R. Design and testing of a locally made loop-type thermosyphonic heat sink for stove-top thermoelectric generators. Renewable Energy 2005;30:1101-16.

[9]. R. W. Nuwayhid, A. Shihadeh and N. Ghaddar. Development and Testing of a Domestic Woodstove Thermoelectric Generator with Natural Convection cooling. Energy Convers Mgmt 2005;46 (9-10):1631-1643.

[10]. Perumal Raman, Narasimhan K. Ram, Ruchi Gupta. Development, design and performance analysis of a forced draft clean combustion cookstove powered by a thermo electric generator with multi-utility options. Energy 2014; 69:813-825.

[11]. Killander A, Bass JC. A stove-top generator for cold areas. In: Proceedings of the 15th international conference on thermoelectrics; 1996 Mar 26-29; New York, USA. New York: IEEE; 1996.

[12]. Riffat SB, Ma Xiaoli. Thermoelectrics: A review of present and potential applications. Appl Therm Engg 2003; 23: 913-935.

[13]. C. Lertsatitthanakorn.Electrical performance analysis and economic evaluation of combined biomass cook stove thermoelectric (BITE) generator. Bioresource Technology 2006;8:1670-1674.

[14]. Thermal Conductivity, Seebeck Coefficient. Melcor Corp.. Thermoelectric Engineering Handbook. Trenton, N.J. Available From: http://www.melcor.com/handbook.html.

[15]. Thermal conductivity of metals, Available from: http://en.wikipedia.org/wiki/List_of_thermal_conductivities.

[16]. RANS model, Available from:http://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equations.

[17]. The k-ε turbulent model Available from :http://en.wikipedia.org/wiki/K-epsilon_turbulence_model.

[18]. Keramida, E. P., et al. Radiative heat transfer in natural gas-fired furnaces. International Journal of Heat and Mass Transfer 43.10 (2000): 1801-1809.

[19]. Bongkyun Jang, Seungwoo Han, Jeong-Yup Kim. Optimal design for micro-thermoelectric generators using finite element analysis. Microelectron Eng 2011; 88(5):775-778.

[20]. H Landolt, R Börnstein.O Madelung.K H Hellwege.Wolfgang Pies.Alarich Weiss.Gerhard Pieper.Landolt-Börnstein numerical data and functional relationships in science and technology. Group 3, Crystal and solid state physics. Vol. 7, Crystal structure data of inorganic compounds. Berlin : Springer, 1985. ISBN: 3540139303 9783540139300.

[21]. Howell RJ, Siegel R, Menguc MP. Thermal radiation heat transfer. 5th ed. Boca Raton: CRC Press Taylor and Francis; 2010.

[22]. Stefan Boltzmann Coefficient, Available from: http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann constant.

[23]. Thermal Conductivity of Bi₂Te₃, Available from: http://en.wikipedia.org/wiki/Bismuth_telluride.

[24]. N.S. Wilkes, P.W. Guilbert, C.M. Shepherd, S. Simcox, The application of HARWELL-FLOW3D to combustion models, AERE-R13508, in: Atomic Energy Authority Report, Harwell, UK, 1989.