esa-sceva/satcom-chunk-collection huggingface dataset:
_Appl. Sci._**2014**, \(4\), 318-330; doi:10.3390/app4030318  
_Applied sciences_  
**ISSN 2076-3417**  
www.mdpi.com/journal/applsci  
High-Energy, Multicolor Femtosecond Pulses from the Deep Ultraviolet to the Near Infrared Generated in a Hydrogen-Filled Gas Cell and Hollow Fiber  
**[PERSON] 1, [PERSON] 1-* and [PERSON] 1,2**  
1 Department of Applied Chemistry, Graduate School of Engineering, Kyushu University,  
744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan;  
E-Mails: [EMAIL_ADDRESS] (K.M.); [EMAIL_ADDRESS] (T.I.)  
2 Division of Optoelectronics and Photonics, Center for Future Chemistry, Kyushu University,  
744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan  
* Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS];  
Tel.: +81-92-802-2886; Fax: +81-92-802-2888.  
_Received: 4 April 2014; in revised form: 29 May 2014 / Accepted: 13 June 2014 / Published: 1 July 2014_  
**Abstract:** We investigate four-wave mixing in hydrogen gas using a gas cell and a hollow fiber for the generation of high-energy, multicolor femtosecond (fs) optical pulses. Both a hydrogen-filled gas cell and hollow fiber lead to the generation of multicolor fs pulses in a broad spectral range from the deep ultraviolet to the near infrared. However, there is a difference in the energy distribution of the multicolor emission between the gas cell and the hollow fiber. The hydrogen-filled gas cell generates visible pulses with higher energies than the pulses created by the hollow fiber. We have generated visible pulses with energies of several tens of microjoules. The hydrogen-filled hollow fiber, on the other hand, generates ultraviolet pulses with energies of a few microjoules, which are higher than the energies of the ultraviolet pulses generated in the gas cell. In both schemes, the spectral width of each emission line supports a transform-limited pulse duration shorter than 15 fs. Four-wave mixing in hydrogen gas therefore can be used for the development of a light source that emits sub-20 fs multicolor pulses in a wavelength region from the deep ultraviolet to the near infrared with microjoule pulse energies.  
**Keywords:** multicolor laser; ultrashort optical pulses; four-wave mixing; high-order sideband generation
## 3 Materials and Methods
### Semi-Quantitative Gene Expression Analysis  
The Qiagen Plant Total RNA Miniprep Kit was used to extract total RNA from fresh tissue (Qiagen Inc., Germantown, MD, USA). The RNA quantity was checked using Picodrop (Picodrop Ltd., Cambridge, UK). The amount of total RNA was calculated at 260 nm, and an A260:A280 ratio in the range of 1.8-2.0 was selected for further investigation. An iScript cDNA synthesis kit (Bio-Rad Laboratories, Inc., Pleasanton, CA, USA) was used for single-stranded cDNA synthesis. Five technical triplicates and three biological duplicates were used in the experiment. Then, 0.2 M gene-specific forward primers and reverse primers (0.5 uL each), Taqman-polymerase master mix (2X), reaction buffer (12 uL), and nuclease-free water (NFW) (10 uL), resulting in a reaction volume of 25 uL, were used in the semi-quantitative RT-qPCR analysis. The PCR reaction in the thermocycler (Applied Biosystems VeritiPro Thermal Cyler, Applied Biosystems, Thermo Fisher Scientific, Waltham, MA, USA) was carried out as follows: (1) denaturation at 94 \({}^{\circ}\)C for 3 min; (2) 30 cycles of 94 \({}^{\circ}\)C for 30 s, annealing at 57 \({}^{\circ}\)C for 45 s, and extension at 72 \({}^{\circ}\)C for 10 min. The PCR products were examined on a 1.5% agarose gel. The band intensity was quantified in ImageJ 1.51 K ([[http://imagej.nih.gov/ij](http://imagej.nih.gov/ij)]([http://imagej.nih.gov/ij](http://imagej.nih.gov/ij)), accessed on 21 May 2022) densitometric software.  
Primer Designing  
Primers for the candidate genes were designed using Primer-BLAST v3 software from NCBI, namely, Cu/Zn superoxide dismutase 1 (_Cu/Zn-SOD_), ascorbate peroxidase (_APX_), GDP-L-galactose phosphorylase (_GGP_), and trehalose-6-phosphate synthase (_TPS_) (Table 5), which were then custom synthesized by Sigma. To normalize the data, glyceraldehyde-3-phosphate dehydrogenase (_GAPDH_) was used as the internal reference gene.
###### Abstract  
The combustion characteristics of nanofluid fuels have been widely investigated, but rare studies on the atomization were reported. Atomization is an imperative and crucial step to improve the combustion performance of nanofluid fuels, and the secondary breakup of droplets is an important segment for atomization to produce uniform fine droplets and distribute nanoparticles in each droplet. This paper firstly presents the secondary breakup characteristics of single electrified Al/n-decane nanofluid fuel droplets and revealed the mechanism of the secondary breakup. The results demonstrated that fine droplets could be produced in the electrostatic field and Al nanoparticles were distributed in each droplet. Before the breakup, the single electrified droplets experienced surface charge transportation, deformation, and Taylor cone formation. A gradient of the electric field deformed the droplet to produce the Taylor cone. As the Taylor cones were stabilized, the fluid was extruded from the tips of stable Taylor cones to produce jet filament parallel to the electric field direction and correspondingly broke up into fine sub droplets. At the nanoparticle concentration range of 1.0-10 mg/mL, the minimum average diameter of breakup sub droplets could achieve ~55.4 \(\upmu\)m at 6.0 mg/mL. The Al nanoparticle concentration had a significant effect on the breakup performance by influencing the physical properties and charging. The order of the Charge-to-Mass ratio magnitude was 10\({}^{-7}\)-\(10^{-5}\) C/kg. Furthermore, the secondary breakup mechanism of single electrified nanofluid fuel droplets in the uniform electrostatic field was revealed by analyzing the droplet surface charge, deformation, Taylor cone formation, and nanoparticle concentration effect.  
**Keywords:** secondary breakup; single electrified droplet; electrostatic atomization; nanofluid fuel; concentration effect
# Dynamic Workload Management System in the Public Sector: A Comparative Analysis
## 4 Experimental Results
### Comparing Algorithms
#### 4.1.6 SVM Results  
The Support Vector Machine (SVM) model provided average performance in predicting the target values, with moderate error rates and a reasonable correlation between actual and predicted values. The model shows a balanced approach to handling the training, testing, and validation datasets.  
Figure 11(a) shows SVM's training performance, with a clear relationship between actual and predicted values. Figure 11(b) illustrates the testing performance, highlighting the model's predictive accuracy, while Figure 11(c) depicts the validation phase, demonstrating SVM's ability to generalize well to new data.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Metric** & **Training** & **Testing** & **Validation** \\ \hline Mean Squared Error (MSE) & 1194.496 & 2404.466 & 2589.089 \\ Root Mean Squared Error (RMSE) & 34.561 & 49.035 & 50.883 \\ Mean Absolute Error (MAE) & 26.167 & 36.749 & 36.897 \\ Median Absolute Error (MedAE) & 19.792 & 26.250 & 28.546 \\ Mean Squared Logarithmic Error (MSLE) & 0.003 & 0.006 & 0.007 \\ Root Mean Squared Logarithmic Error (RMSLE) & 0.055 & 0.077 & 0.081 \\ Mean Bias Deviation (MBD) & \(-\)0.173 & \(-\)6.595 & 2.575 \\ Mean Absolute Percentage Error (MAPE—Validation) & 4.07\% & 5.74\% & 5.73\% \\ Huber Loss (Validation) & 25.671 & 36.254 & 36.402 \\ Angle between Perfect Fit and Best Fit (degrees) & 34.165 & 29.025 & 27.121 \\ C-index & 0.90 & 0.88 & 0.87 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Bagged Decision Tree analysis.  
Figure 11: Bagged Decision Tree Time Factor performance.  
The model's performance, as reflected by RMSE 54.21 and other metrics, suggests that it may benefit from further optimization to improve its predictive accuracy.  
The SVM algorithm showed a balanced performance, effectively handling linear and non-linear relationships within the data. It offered a solid alternative by maximizing the margin between classes, crucial for clear decision boundaries. SVM's versatility and robustness were notable; however, it struggled with large datasets due to its computational intensity. Additionally, the model required careful parameter tuning and selecting an appropriate kernel function to achieve optimal results. Despite these challenges, SVM provided a reliable and consistent performance across various metrics, as seen in Table 8.
# Nanotechnology, Nanomedicine, and the Kidney
## 5 Nanotechnology for Renal Therapy  
A diverse range of diseases injure kidneys. Injury can be the result of direct damage or as a secondary effect. Nanotechnology aims to broaden the therapy options to treat kidney damage or delay chronic injury and thereby prevent end-stage renal disease.  
Therapeutic approaches can be divided into technologies that are used to (i) deliver drugs specifically to the kidney or kidney compartments, (ii) improve current renal replacement therapies, or (iii) promote the regeneration of renal tissue after injury.
# Xanthone Derivatives and Their Potential Usage in the Treatment of Telangiectasia and Rosacea
## 2 Xanthone Derivatives and Their Vascular Activity
### Sealing Blood Vessel Activity  
One of the intriguing therapeutic potentials of xanthone derivatives lies in their ability to modulate vascular function, particularly when connected with sealing blood vessels. The integrity of blood vessels is crucial for maintaining proper cardiovascular health, as disruptions in their structure or function can lead to various pathological conditions, including hemorrhaging, thrombosis, and atherosclerosis, and connections with the skin, including telangiectasia and rosacea.  
Research has increasingly elucidated the mechanisms by which various xanthone derivatives exert their vascular sealing effects. These mechanisms often involve interactions with key molecular targets involved in vascular homeostasis, such as endothelial cells, smooth muscle cells, and inflammatory mediators. For instance, xanthone derivatives have been shown to enhance endothelial barrier function by regulating the expression of tight junction proteins and inhibiting the production of pro-inflammatory cytokines [26].
## 3 Results
### Phytoplankton and Ciliate Dynamics
On the 10 th July, total biovolumes reached similar values to pre-storm conditions (338.51 mm\({}^{3}\)-m\({}^{-3}\)). In turn, on the 24 th July, total biovolume reached maximum values of 535.49 mm\({}^{3}\)-m\({}^{-3}\) coinciding with Dinophyta (_Gymnodinium_ sp. and _Ceratum_ sp.) and cyanobacteria (_Woronichinia naegeliana_ and _Anabaena flos-aquae_) biovolume increases to 113.38 mm\({}^{3}\)-m\({}^{-3}\) (21.17%) and 104.29 mm\({}^{3}\)-m\({}^{-3}\) (19.47%), respectively (Figure 6A). In contrast to what was observed on the 26 th June, with similar total biovolumes at different depths (Figure 7, 26 th June intermediate), on the 24 th July (post-storm period), phytoplankton cells were more concentrated within the first top 6 m from the surface, representing a decrease from 535.49 to 254.63 mm\({}^{3}\)-m\({}^{-3}\) of total biovolume at 12 m and to 67.97 mm\({}^{3}\)-m\({}^{-3}\) at 25 m, respective to the 6 m integrated water sample taken on the same sampling day. Despite the lower biovolumes recorded at the bottom layers relative to the top 6 m layer, the bottom layers were highly dominated by ciliates and Cryptophyta taxa (Figure 7, 24 th July post-storm). On the 7 th August, cyanobacteria reached their maximum biovolume, corresponding to 210.46 mm\({}^{3}\)-m\({}^{-3}\), an unprecedentedly high value for this lake [10], and this was mainly a consequence of large aggregates of _Woronichinia naegeliana_. In turn, from late July onwards, the Shannon diversity index increased again to a maximum value of 2.65 for the study period on the 3 rd September (Figure 6A). Figure 6: (**A**) Biovolumes (mm\({}^{3}\cdot\)m\({}^{-3}\)) of different phytoplankton phyla and ciliates from 6 m integrated water samples and Shannon diversity index (H\({}^{\prime}\)) and (**B**) biomass (ug DW-L\({}^{-1}\)) of different zooplankton taxa and chlorophyll \(a\) recorded in Lough Feeagh between April and October 2018. Dotted red lines indicate the Storm Hector event and solid red lines indicate when the Feeagh water column returned to more stable stratification conditions.
## 4 Results and Analysis
### The Inversion Results of FPAR  
The annual FY-FPARs for the five research areas of grassland, cropland, shrub, broadleaf forest, and needleleaf forest were inverted successfully based on the inversion strategy from the FY-3C data.  
The seasonal variation of FYgrass-FPAR in the HulunBer grassland study area was distinct (Figure 5a). The FPAR values for the whole year showed a general trend of rising first and then decreasing. In addition, there was a large degree of spatial loss in January-February and November-December. This loss was due to the low temperatures in these months, and the inversion of FPAR was affected by snow or other atmospheric factors.  
The seasonal variation of FYcropland-FPAR in the Shangqiu cropland study area was clearer (Figure 5b). The high value period of FPAR was in July and August, located in the west of the Shangqiu Research Area, while the low value period of FPAR was in February, June, and October. This annual distribution seemed to indicate a resurgence that met the growth curve of the two seasonal crops.  
The seasonal variation of FYshrub-FPAR in the Shapotou shrub area was noticeable (Figure 5c), and the annual FPAR was generally low. In this area, the high value period of FPAR ran from June to September, the vegetation coverage was high, and the FPAR values were lower at other times, most of which were lower than 0.2 (and lower than 0.1 in January and February). The seasonal variation of the shrub FPAR was consistent with the law of vegetation growth, but this shrub had the characteristics of shrub vegetation itself, and there was a difference in the distribution of FPAR.  
The seasonal variation of FYbroadleaf-FPAR in the Dinghushan broadleaf forest study area was unclear (Figure 5d). Its overall FPAR was higher than 0.6 in 2014. In this area, the FPAR was higher from September to December, with most FPAR values greater than 0.8. This was because the Dinghushan broadleaf forest study area belonged to a deciduous broadleaf forest; moreover, defoliation occurred in autumn and winter after September, thereby covering the exposed land and increasing the FPAR value.  
The seasonal variation of FYneedleleaf-FPAR in the Changbai Mountain needleleaf forest study area was relatively obvious (Figure 5e). The FPAR values for 2014 showed a trend of first increasing and then declining. The FPARs of June-August were higher; most of them were greater than 0.7. However, the FPAR of October-December and January-March were relatively low (similar to the grassland), in line with the seasonal growth of vegetation.  
Figure 5: The spatial distribution of the result of FPAR inversion and FPAR products; (**a–e**) are grassland, cropland, shrub, broadleaf forest, and needleleaf forest, respectively.
# Effects of Invasive Watermilfoil on Primary Production in Littoral Zones of North-Temperate Lakes
## 3 Results
### Primary Production Rates
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Coefficient of Predictors**} & \multicolumn{1}{c}{**Intercept**} & \multicolumn{1}{c}{**Adjusted**} & \multicolumn{1}{c}{**P**} \\
**Response** & **Light** & **Water** & **TON** & **Macrophyte** & **Epibibibib** & **Phytopalkon** & **Intercept** & **R2** & **Adjusted** & **R2** & **Of** & **\(p\)** \\  & **Eticination** & **Temperature** & **TON** & **Standing Crop** & **Chla1** & **AFOM** & & & & & \\ \hline benthic Periphyton CPP & – & 23.066 & – & –0.64 & **\(\bullet\)** & **\(\bullet\)** & \(\bullet\)** & \(-\)342.15 & 0.50 & 6.54 & 2.9 & 0.02 \\ Epiphyte CPP & – & – & \(-\)181.86 & 0.21 & **\(\bullet\)** & \(\bullet\)** & \(\bullet\)** & \(-\)111.17 & 0.21 & 2.48 & 2.9 & 0.14 \\ Phytoplankton CPP & – & 13.86 & – & – & **\(\bullet\)** & \(\bullet\)** & \(-\)251.35 & 0.46 & 10.34 & 1.10 & 0.099 \\ benthic Periphyton Chla 1 & – & 0.11 & – & \(-\)003 & **\(\bullet\)** & \(\bullet\)** & \(-\)012.0 & 0.49 & 6.25 & 2.9 & 0.02 \\ Epiphyte Chla 1 & – & – & \(-\)14.8 & 0.002 & **\(\bullet\)** & \(\bullet\)** & \(-\)120.0 & 0.20 & 2.41 & 2.9 & 0.15 \\ Phytoplankton Chla 1 & – & – & 1.40 & 0.001 & **\(\bullet\)** & \(\bullet\)** & \(-\)024.0 & 0.65 & 11.06 & 2.9 & 0.004 \\ Bentlie Periphyton APMM 1 & –0.21 & – & 0.001 & **\(\bullet\)** & \(\bullet\)** & \(\bullet\) & 2.39 & 0.47 & 5.89 & 2.9 & 0.02 \\ Epiphyte APMM & – & – & \(-\)16.89 & 0.02 & **\(\bullet\)** & \(\bullet\) & 10.044 & 0.20 & 2.39 & 2.9 & 0.15 \\ Phytoplankton APMM & – & 0.95 & – & – & **\(\bullet\)** & \(\bullet\)** & \(-\)153.3 & 0.30 & 5.70 & 1.10 & 0.04 \\ Plat GP 1 & – & – & – & – & – & **\(\bullet\)** & NA & NA & NA & NA \\ Plat ER 1.2 & – & \(-\)0.08 & – & – & **\(\bullet\)** & \(-\) & 2.51 & 0.25 & 4.66 & 1.10 & 0.06 \\ \hline \hline \end{tabular}  
* \({}^{1}\) Log transformed.  
\({}^{2}\) Converted to positive values from negative values. – Predictor not included in lowest AIC scored model.
* \({}^{*}\) Not included as a predictor for multiple linear regression analysis. NA = not applicable no model produced.  
\end{table} 
Table 4: Stepwise multiple linear regression models selected for responses of primary producers across all plots. Best models were selected for fit and parsimony by examining Akaike information criterion (AIC) scores.
# Deterministic and Robust Optimization Approach for Single Artillery Unit Fire Scheduling Problem
## 4 Robust Counterpart Formulation
### Robust Counterpart Formulation with Box Uncertainty  
To transform the RFS model proposed in Section 3.2 into a robust counterpart formulation with box uncertainty, we assume that the uncertain enemy target threat level \(\widetilde{f_{j}}\) belongs to the box set \(\left[f_{j},\ f_{j}+\hat{f_{j}}\right]\). With respect to the uncertain data \(\widetilde{f_{j}}\), the random variable, \(\eta_{j}=\left(\widetilde{f_{j}}-f_{j}\right)/\hat{f_{j}}\) can be defined. This variable is unknown but lies within the interval [0,1].  
**Proposition 1**.: _Equation (6) can be transformed into the following equation when the uncertain enemy target threat level \(\widetilde{f_{j}}\) lies within the predefined interval\(\left[f_{j},\ f_{j}+\hat{f_{j}}\right]\):_  
\[\sum_{j=1}^{n}\overline{f_{j}}x_{j}\leq y\ \ \ \ \ \ j=1,2,\ \ldots,\ n \tag{7}\]  
_where \(\overline{f_{j}}\) is the maximum threat level of target j._  
**Proof.** On the left-hand side of Equation (6), both the uncertain enemy target threat level \(\widetilde{f_{j}}\) and the starting time \(x_{j}\) for firing at target \(j\) are nonnegative. Therefore, we have the following relationship:  
\[\sum_{j=1}^{n}\widetilde{f_{j}}x_{j} =\ \sum_{j=1}^{n}f_{j}x_{j}+\sum_{j=1}^{n}\hat{f_{j}}\eta_{j}x_{j }\leq\sum_{j=1}^{n}f_{j}x_{j}+\sum_{j=1}^{n}\hat{f_{j}}x_{j}=\sum_{j=1}^{n} \overline{f_{j}}x_{j}\ \leq\ y \tag{8}\]RFS can be transformed into robust counterpart formulation with box uncertainty (RCFB) by Equation (8). Thus, RCFB becomes a tractable problem:  
\[\text{minimize }y\qquad(\text{RCFB})\]  
subject to  
\[\sum_{j=1}^{n}\overline{f}_{j}x_{j}\leq y\qquad j=1,2,\ \ldots,\ n\]  
(2), (3), and (4).  
The solution of the discrete optimization model RCFB is feasible for all uncertain target threat levels, but it is too conservative [9]. To overcome the drawback of the excessively conservative solution of the robust counterpart formulation with box uncertainty, [PERSON] [10] proposed an efficient algorithm for solving convex optimization problems with data uncertainty by considering the uncertainty set of the data to be an ellipsoid. However, because the formulations proposed by [PERSON] involve conic quadratic problems, his method cannot be applied directly to discrete optimization. [PERSON] and [PERSON] proposed a method to control the level of conservatism in the solution [11,16]. The advantage of their method is that it can be transformed into a linear discrete optimization problem and applied directly. In the next section, we propose a single artillery unit fire scheduling model by applying the methodology of [PERSON] and [PERSON] [11,16].
# Numerical Study of Heat Transfer Enhancement for Laminar Nanofluids Flow
## 2 Mathematical Formulation
### Governing Equations  
The present study was conducted for both the constant heat flux (\(q_{w}^{n}=10\),000 W/m\({}^{2}\)) and constant wall temperature (T\({}_{w}\) = 313.15 K) boundary conditions. At the inlet, the uniform axial velocity u\({}_{0}\) and initial temperature (T\({}_{\rm o}\) = 293 K) were assumed. The fully developed conditions are assumed at the tube exit section, which means all axial derivatives are zero. A no-slip condition and uniform heat flux are imposed on the tube wall. The continuity, momentum and energy equations subject to above boundary conditions were solved using control volume finite difference scheme. The governing equations are expressed as follows:  
\[\
abla\cdot\left(\rho_{nf}\overset{\rightarrow}{V}\right)\ =\ 0 \tag{1}\]  
\[\rho_{nf}\left(\overset{\rightarrow}{V}\cdot\
abla\overset{\rightarrow}{V} \right)\ =\ -\
abla P+\
abla\cdot\left(\mu_{eff}\
abla\overset{ \rightarrow}{V}\right) \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Author** & **Nanofluids** & **Re Range** & **Pr Range** & \(\mathbf{\phi_{b}}\) \\ \hline [PERSON] and [PERSON] [20] & Al\({}_{2}\)O\({}_{3}\)-water & 500–2100 & 6–12 & 0.6–1.6 \\ [PERSON] et al. [21] & Al\({}_{2}\)O\({}_{3}\)-water, Al\({}_{2}\)O\({}_{3}\)-EG & 250–1000 & 6–753 & 0–10.0 \\ [PERSON] et al. [22] & CuO-water, Al\({}_{2}\)O\({}_{3}\)-water & 650–2050 & 6–12 & 0.2–3.0 \\ [PERSON] et al. [23] & Al\({}_{2}\)O\({}_{3}\)-water & 650–2050 & 350–500 & 0–1 \\ [PERSON] et al. [24] & Al\({}_{2}\)O\({}_{3}\)-water & 500–2000 & 6–12 & 1.0–6.0 \\ [PERSON] et al. [25] & Al\({}_{2}\)O\({}_{3}\)-water & 420–990 & 6–12 & 0.5–2.5 \\ [PERSON] et al. [26] & Al\({}_{2}\)O\({}_{3}\)-water & 800–2400 & 6–12 & 0–3 \\ [PERSON] et al. [27] & Al\({}_{2}\)O\({}_{3}\)-water, ZrO\({}_{2}\)-water & 10–2000 & 6–12 & 0–6.0 \\ [PERSON] et al. [28] & Al\({}_{2}\)O\({}_{3}\)-water, ZrO2-water, TiO\({}_{2}\)-water & 1150–1900 & 6–12 & 0.5–2 \\ [PERSON] et al. [29] & Al\({}_{2}\)O\({}_{3}\)-water, ZrO2-water, TiO\({}_{2}\)-water & 10–2300 & 6–12 & 2.3 \\ [PERSON] et al. [30] & Al\({}_{2}\)O\({}_{3}\)-EG, CuO\({}_{2}\)-EG, SiO\({}_{2}\)-EG, ZnO-EG & 10–1500 & 6–500 & 1–4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The different nanofluids and their process parameters.  
\[\
abla\cdot\left(\rho_{nf}C_{p,nf}\vec{V}T\right)\ =\ \
abla\cdot\left(k_{eff} \
abla T\right) \tag{3}\]  
where \(\rho_{nf}\), \(\mu_{eff}\), \(C_{p,nf}\), \(k_{eff}\) are the density, effective viscosity, specific heat and effective thermal conductivity of the nanofluid, respectively.