Prediction of heat transfer of two different types of roughened solar air heater using Artificial Neural Network technique

Accepted Manuscript Prediction of heat transfer of two different types of roughened solar air heater using Artificial Neural Network technique Harish Kumar Ghritlahre, Radha Krishna Prasad PII: DOI: Reference:

S2451-9049(17)30422-5 https://doi.org/10.1016/j.tsep.2018.08.014 TSEP 224

To appear in:

Thermal Science and Engineering Progress

Received Date: Revised Date: Accepted Date:

4 November 2017 18 August 2018 18 August 2018

Please cite this article as: H.K. Ghritlahre, R.K. Prasad, Prediction of heat transfer of two different types of roughened solar air heater using Artificial Neural Network technique, Thermal Science and Engineering Progress (2018), doi: https://doi.org/10.1016/j.tsep.2018.08.014

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Prediction of heat transfer of two different types of roughened solar air heater using Artificial Neural Network technique Harish Kumar Ghritlahre1, Radha Krishna Prasad2,* 1Department

of Mechanical Engineering, National Institute of Technology, Jamshedpur, Jharkhand, 831014, India. E-mail address: [email protected]

2Department

of Mechanical Engineering, National Institute of Technology, Jamshedpur, Jharkhand, 831014, India. Email address: [email protected] 2Corresponding

Author: Tel.:+919431340910

Abstract In the present article, the Feed forward Neural Network (FFNN) model has been used to predict the heat transfer from roughened absorber plate to air passing through the ducts of solar air heater and compare with actual experimental data. One side and three sided roughened absorber plates have been taken up for experimental study of solar air heater (SAH) heat transfer analysis. Total 50 data sample have been used in the present neural model. Artificial Neural Network (ANN) model developed with feed forward back-propagation (FFBP) multi -layer perceptron using five parameters (number of rough surfaces side, relative roughness height, relative roughness pitch, roughness size and Reynolds Number) and one parameter (Nusselt number) have been used in input layer and output layer respectively. Levenberg-Marquardt (LM) algorithm with 6-12 neurons has been used to find out the optimal model. The 10 numbers of neurons in hidden layer model has been found as optimal on the basis of statistical error analysis. The 5-10-1 neural model predict the heat transfer characteristics as Nusselt number with higher value of R2 gives satisfactory results. The values of root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) were found 0.89202, 0.66261 and 0.99532 respectively during training stage. Similarly for testing stage these values were 0.55094, 0.3168 and 0.99791 respectively. The traditional statistical multiple linear regression (MLR) model has also been used in prediction of heat transfer. The MLR model has been compared with ANN model. The Performance criteria show that the ANN model performs better as compared the MLR model. The average value of coefficient of determination for the ANN model was higher by 1.79 % than for the MLR model. The results indicated that the proposed ANN model successfully predicts the heat transfer analysis of roughened solar air heater. Keywords: Solar air heater, Artificial Neural Network, Levenberg-Marquardt Learning algorithm, Nusselt Number, Heat transfer

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Nomenclature A ANN ai bj BFG CGP Cd Cp Dh e e/D h k LM mf MAE MAPE MLP Nu ∆P P/e Qu R RBF R2 Re RMSE SAH SCG T wij YA YP 𝑌 Y Greek letters ρa β

Collector surface area (m2) Artificial Neural Network Input Variables Bias Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi-Newton Polak - Ribiére Conjugate Gradient Coefficient of discharge Specific heat of air (kJ/kg K) Hydraulic Diameter Roughness height (mm) Relative roughness height Heat transfer coefficient (W/m2 K) thermal conductivity of air (W/m K) Levenberg–Marquardt Mass flow rate of air (kg/s) Mean Absolute Error Mean Absolute Percentage Error Multi-Layered Perceptron Nusselt number Pressure drop (N/m2) Relative roughness pitch Energy gained by air (W) Correlation coefficient Radial basis function Coefficient of determination Reynolds number Root mean square error Solar Air Heater Scaled Conjugate Gradient Temperature (oC) Weights Actual value Predicted value Average value Experimental value Density of air ((kg/m3). Ratio of orifice diameter to pipe diameter

3

μ

dynamic viscosity of air (Pa.s)

Subscripts fo fi

Outlet air Inlet air

1. Introduction Energy is the basic requirement of quality life and economic growth of a nation. It is utilized in various forms. The energy consumption rate is the measure of growth and development of a nation. The available resources of energy can be broadly classified as conventional and nonconventional. Conventional energy resources are exhaustible source in nature e.g. coal, oils and natural gas etc.. As it is known that these resources shall last for a few decades, it needs a limited and confined use of these resources. The researchers are, therefore, in search of alternative sources of energy so as to fill shortage of energy. Of the several types of renewable energy available on the earth, the solar energy is one of the most abundant and clean source. There are two ways of solar energy utilization: active and passive. In passive solar energy utilization sun rays are directly used without the aid of any equipment, but in active way sun rays are not directly used but some kind of mechanical equipment are needed to convert the solar energy into other forms of energy. Solar air heater comes in the category of active solar energy utilization systems. In the solar air heating collector, absorber plate is main component which collects the solar energy in the form of heat and transfers this energy to flowing air. Due to low heat capacity and low thermal conductivity of flowing air, the convective heat transfer coefficient between absorber plate and the air is low, and hence the major issue to increase the value of heat transfer coefficient and thereby the heat transfer rate. This objective can be achieved by using extended surfaces on the absorber plate on air flow side [1, 2], artificial roughness on air flow side [3-9], and porous heat absorbing materials in the air flow duct. Bhushan and Singh [3] studied that the performance of roughened solar air heaters. They represent the research works on the basis of roughness geometry for creating artificial roughness. They also reported the correlations of heat transfer and friction factor developed by various researchers. Chamoli et al. [4] reported a review on various turbulence promoters used in solar air heaters. Prasad [5] conducted experiments using artificial wire rib roughened SAH and found that the ratio of the respective values of the parameters collector heat removal factor (FR), collector efficiency factor (F′) and thermal efficiency (ηth) for the roughened collectors to the smooth collectors were 1.786, 1.806 and 1.842 respectively. Gawande et al. [6] studied the effect of roughness geometries on heat transfer enhancement in solar air heaters. Behura et al. [7, 8] carried out experiments with 3-sided transverse rib roughness and found 40-48 % enhancement in thermal performance over the 1-side artificially roughened solar air heater. Kumar et al. [9] reported on comparative study of effect of various blockage arrangements on thermal hydraulic performance in a roughened air passage.

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The experimental study as well as the analytical study followed by the computational techniques, requires a lot of time to arrive at an accurate result due to extensive computer codes that lead to huge programming algorithms especially when the solution of complex differential equations are involved. The use of Artificial Neural Network (ANN) technique, on the other hand, saves time and also provides key information patterns in a multi-dimensional information domain and, therefore, this technique has been becoming increasingly popular in Science and Engineering, especially in Thermal Engineering applications in recent years. Many researchers have used ANN in the past: Kalogirou [10] used neural network in renewable energy systems to predict solar radiation, wind speed and also used for load forecasting of photovoltaic (PV) and building service systems. Facao et al. [11] constructed two different types of neural network (NN) model by using multilayer perceptron (MLP) and radial basis function (RBF), and predicted the collector efficiency and useful heat gain of plate and tube type heat pipe hybrid solar collector. They also found that MLP model performed slightly better than RBFs model. Islamoglu et al. [12] applied neural technique to predict the heat transfer analysis of corrugated channel. They conducted experiments and collected data for ANN modeling. They found the accuracy between experimental and ANNs approach results was achieved with a mean absolute relative error less than 4 %. Kalogirou [13] predicted the performance parameters of flat plate collector using neural network. For predicting the parameters six different types of ANN model were constructed on the basis of measuring experimental data and predicted with satisfactory results. Sozen et al. [14] conducted experiments on flat plate solar air heater and calculated the thermal efficiency. By the use of experimental and calculated data optimal ANN was constructed using seven parameters in input layer, twenty neurons with two hidden layers and one neuron used in output layer and predicted the thermal efficiency with satisfactory results. Akdag et al. [15] structured ANN model to predict the heat transfer in oscillating annular flow. They found the predicted results with less than 5% error. Caner et al. [17] used neural network tool for estimating the thermal efficiency of solar air collector. For evaluating the thermal efficiency, experiments were performed with two types of zigzagged absorber plate are used in solar air heater and collect the data for five days for constructing ANN model designed on the LM learning algorithm in nftool tool module in MATLAB. They found on the basis of stastiscal error analysis the predicted thermal efficiency ANN model was proved reliable and accurate. Benli [18] initiated ANN technique for determining the thermal efficiency of two different types solar air heater with trapeze and corrugated shaped absorber plate. For estimating this collector efficiency experiments are performed and collected data for modeling of ANN model with LM learning algorithms. Finally predicted results are found with LM-3 neurons in hidden layer for successfully and accurate thermal performance of solar air collector. Akdag et al.[19] applied ANN method to predict heat transfer from a flat plate subjected to a transversely pulsating jet using optimal neural model. They are also found that the ANN predictions errors are less than 1%. Azizi et al. [20] developed ANN

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model for estimating the heat transfer coefficient during condensation of R134a in inclined tubes. They predicted results with values of mean absolute percentage error (MAPE) and correlation coefficient (R) was 1.61% and 0.9963. Ghritlahre and Prasad [21-28] used ANN technique to predict the performances of different types of solar air heaters. From the above literature, few ANN method is used to predict the heat transfer of SAH. Therefore, heat transfer prediction of roughened SAH has been developed with MLP model in the present work. 5-input parameters and 1-output parameter have been used in neural model. Total 50 data samples were used with LM learning algorithm. The optimal model has been obtained by statistical error analysis. The MLP model performance has been compared with statistical model i.e. MLR model. 2. Experimentation and Data Collection The experimental setup consists of two ducts A and B, the cross-sections of which are shown in Fig. 1. In duct A, there is a single roughened absorber plate with a glass cover at the top (Fig. 1a). Whereas in duct B, the roughened absorber plates have been used in three sides, each enclosed with transparent glass covers (Fig.1b). The photographic view of setup is shown in Fig. 2, and that of the absorber plate is shown in Fig. 3. Experiments have been performed in clear sky days at Jamshedpur (India). The rectangular duct dimension is 2000 mm x 200 mm x 25 mm, in which the test section is of 1500 mm length. The duct is connected with flow pipe with an orifice meter fitted to it. Two U-tube manometers have been used. For measuring the temperature of air 6 digital thermometers were used in each duct. For measurement of plate temperature copper- constantan 28 Standard Wire Gauge (SWG) thermocouples have been used. The experiments were conducted for a range of Reynolds number, Re 5000-13000, relative roughness pitch range, P/e 10-20 and relative roughness height, e/D 0.0315-0.0247 [8]. 50 sets of experimental data have been taken for heat transfer analysis using ANN in the present investigation. The method of uncertainty analysis, as proposed by Kline and McClintock [30], was used to calculate the uncertainty associated with measured experimental data and the results. The uncertainties in measurements are: length and width ±1 mm, vernier caliper 0.02 mm, temperature of inlet and outlet air flowing through duct ± 0.16 oC, ambient air temperature ± 0.432 oC, pressure drop ±0.001 m, and solar radiation intensity ± 1 W/m2. Considering to the relative uncertainties in the individual factors denoted by un, uncertainties estimation was made using the following equation [31]: (1) U  [(u ) 2  (u ) 2 ................(u ) 2 ]0.5 1

2

n

The uncertainty occurred in the thermal efficiency is ±1.34 %.

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(a) Duct A

(b) Duct B Figure 1. Detail schematic diagram of duct. (a) One side roughened absorber plate duct. (b) Three sides roughened absorber plate duct

Figure 2. Photographic view of experimental setup [8].

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(a)

(b) Figure 3. Absorber plates photographic view. (a) Single side rough (b) Three sided rough 3. Heat transfer calculation of solar air heater At Steady state condition, the values of flowing air and absorber plate temperatures at various sections in the duct were used to determine the values of different parameters. Mass flow rate of air mf is calculated with pressure drop, using following formula [16]:

8 0.5

 2 (P)  m f  Cd Ao  a 4 a  (2)  1   Where Ao and ∆P are area of the orifice meter and pressure drop across the orifice plate respectively. The experimental value of useful heat gain of air is calculated by the following expression: (3) Qu  m f C p (T fo  T fi )

Where, Tfo and Tfi are outlet and inlet air temperatures respectively. The Reynolds number, which depends strongly on the velocity of air, has been written as VDh Re 

(4)



Where 𝐷ℎ is hydraulic diameter and V is velocity of air which are calculated by following equations: (5) 4A Dh  D P (6) m V f  a AD Where AD and P are cross section area and perimeter of the duct respectively, and ρa is the density of the air. The heat transfer coefficient h, between plate and air is determined as: Qu h (7) A(Tp  T f ) Where, A is collector area, 𝑇𝑝 is average plate temperature and 𝑇𝑓 is average air temperature. The Nusselt number is calculated by following formula: hD Nu  h (8) k Where, 𝐷ℎ is hydraulic diameter and k is thermal conductivity of air. 4. Basics of Artificial Neural Networks Artificial Neural Networks (ANNs) follows the ideology of human brain functionality. It can learn, estimate, optimize and decision making in fields of Engineering and management [23]. Basically ANN is a complex information processing system, which structure is interconnected with processing elements called as neurons. These neurons collect the data or information from other sources and then perform generally a non-linear operation on the result and then give final data as output. The most commonly neural network is multi-layer perceptron or feed –forward back propagation model. The basic structure of MLP model is shown in Fig. 4. The MLP structure

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consists with an input layer, an output layer and hidden layer. The first layer, which collects data or information from other sources, is called as input layer. The last layer, which gives the final output data, is called as output layer. In between first and last layer, the middle layer is called hidden layer. In feed forward networks (Figure 4), each product of input elements (ai) and weights (wij) are fed to summing junctions and is summed with bias (bj) of neurons as follows [29]:  n  X    wi j ai   b j  i 1 

(5)

Figure 4. Basic structure of artificial neurons Then this sum X passes through transfer function F which generates an output.  n   F ( X )  u j  F   wi j ai   b j    i 1 

(6)

tansig and logsig are most commonly used transfer functions in hidden layer. The nonlinear activation function which is widely used is called as sigmoid function whose output lies in the mid of 0 and 1, and the sigmoid transfer function is written as: F(X ) 

1 1  e X

(7)

If the values of input and output layers are negative, then tansig transfer function is used. F(X ) 

e X  e X e X  e X

(8)

During training process, the learning algorithms adjust the weights and biases iteratively to minimize the error between actual and predicted values of ANN model. These training process is repeated until the error reduces to an acceptable value.

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The mostly used learning algorithms are SCG, CGP, BFG and LM, in which LM learning algorithms are faster than other learning algorithms [23]. 4.1 Performance criteria The optimal ANN model, applied to predict the heat transfer, is based on the criteria of minimum errors of RMSE and best fit of ANN predicted data with experimental data on the basis of correlation coefficient R. Root mean square error: 1 n (YA,i  YP ,i ) 2  n i 1

RMSE 

(9)

Correlation coefficient: n

R

 (Y i 1

P ,i

 Y P )(YA,i  Y A )

n

n

i 1

i 1

 (YP,i  Y P )2  (YA,i  Y A )2

(10)

5. Experimental study of heat transfer of roughened solar air heaters Investigation for one side and for three sided roughened solar air heater ducts gives the values of Nusselt number for the range of flow parameters. Fig. 5 and Fig. 6 show the effect of the roughness and flow parameter on the value of the average Nusselt number of one side and three sides roughened ducts based on the roughness parameters P/e and e/D respectively. i. Variation of Nusselt number with Reynolds number The effect of Reynolds number on average Nusselt number for constant value of P/e and e/D have been shown in Fig.5 and Fig. 6 respectively for one side and three sides roughened ducts. From these Figs. it is observed that the average Nusselt number increases with decrease in P/e or increase in e/D with increase in Reynolds number. ii. Effect of relative roughness pitch on Nusselt number From Fig. 5, it has been found that the average Nusselt number decreases with increase in P/e. The maximum average Nu corresponding to P/e =10 for both cases of one side and three sides roughened ducts has been found. iii. Effect of relative roughness height on Nusselt number From Fig. 6, it has been found that the average Nusselt number increases with increase in e/D and it is maximum at e/D= 0.0247 for one side and three sides roughened ducts.

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The values of Nusselt number for three sides roughened collector enhance by an amount of 2178% over those of for one side roughened collector.

Fig. 5. Variation of heat transfer based on p/e.

Fig. 6. Variation of heat transfer based on e/d.

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6. Results and Discussion 6.1. ANN structure development In the present work, a total 50 sets of data were taken from experiments. MLP model has been used to estimate the heat transfer of roughened solar air heaters. This neural model is structured with three layers such as input layer, output layer and hidden layer (Fig. 7). At the input layer, five parameters such as number of rough surface side, relative roughness height, roughness height, relative roughness pitch and Reynolds number, and average Nusselt number has been selected as output parameter in output layer. The ranges of parameters are given in Table 1.

Table 1 Range of parameters used for prediction of heat transfer characteristics. Input parameters Number of sides of rough surface , Ri Relative roughness pitch, P/e Relative roughness height, e/D Roughness size, e(mm) Reynolds number, Re Output parameters Average Nusselt number, Nu

Range 1- 3 10 - 20 0.0135 - 0.0247 0.6 - 1.1 5250 - 12100 23.80 - 79.00

Fig. 7. Present study ANN model

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In the present MLP model, 34 data sets were used for training process and 16 data sets for testing process. Feed forward back propagation LM learning algorithm has been used for training process. In this model, adaption learning function as LEARNGDM has been selected after the selection of training functions. The Tansig transfer function has been selected in hidden layer and the purelin transfer function has employed in output layer. Before developing of neural structure, the input and output sample data must be normalized for accuracy of prediction. The following equation has been used to normalize data between -1 and 1 [23, 29]. Y  ( Highvalue  Lowvalue )

Yi  Ymin  Lowvalue Ymax  Ymin

(11)

Where Y is experimental data, min and max stands for minimum and maximum respectively. The high and low values are 1 and -1 respectively. The trial and error method is adopted to select number of neurons in hidden layer. However, some thumb rules are available in the literature for selection of number of neurons in hidden layer. One of them reported by Kalogirou and Bojic [17] to calculate the optimal number of neurons is, as given below:

H 

I O  T 2

(12)

where I and O are input and output parameters respectively, and T is number of training data sets. Using above formula, the number of neurons is obtained as 9, so on the basis of trial and error, 612 number of neurons have been selected in hidden layer to predict the output data accurately. Each neural model with different neurons has been trained for 50 times with LM learning algorithm. This training algorithm adjusts the weights and biases iteratively to minimize the error between actual and predicted values of ANN model. The performance of training processes has been shown in Fig. 8, from this Fig., it has been found that 10 neurons is optimum because of lowest value of RMSE error and highest value of R. The performance of different models was based on RMSE and R, which is calculated by using Eq. (9) and (10) respectively. The weights and biases of optimal ANN model with LM-10 are shown in Table 2.

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Fig 8 The training performances of different neural model

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Table 2 Weights and biases of LM-10 model. Weights between input layer and hidden layer (W10x5): 0.65618 -0.70401 0.65981 0.32211 -1.13000 -0.29873 -0.29012 -2.68220 0.95320 0.49385 Bias in hidden layer(B10x1): -0.20412 0.11291

-0.46234

1.16544 -0.01821 -0.61911 -0.37462 -0.12721 0.25691 -0.49944

Weights in output layer (W10x1): -2.74723 2.23273

-2.21651

-2.84232

Bias in output layer (B1x1): 0.21892

-0.89021 -1.44050 -0.60021 -0.56324 0.84884 -0.92699 0.61285 -0.30841 0.80315 0.92291

0.84696 0.69134 1.01081 -0.18347 1.31691 0.76975 -1.30270 -0.41506 -1.12630 0.79524

0.32161

-1.68120 0.58176 0.36469 1.93831 -0.17833 -1.29881 0.49732 -0.69711 -1.63920 -0.23192

0.59973

-1.40961 0.30708 0.41573 0.36529 1.33062 -2.17381 -0.90957 -0.83050 2.33020 3.06144

0.22509 -0.72621 0.87458 -1.21691

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The regression plot of the LM-10 based MLP model of training data sets, is shown in Fig. 9. The value of correlation coefficient was 0.99773, which confirms the acceptable performance of the neural network. The experimental data and ANN predicted data are compared and presented in Fig. 10. The individual error of all samples are also given in Fig.11. From the bar chart error graph, it has been found that the highest error is 1.6607 at sample-21 and lowest error is -2.53048 at sample-14. The performance of MLP predicted data are given in Table 3. From this Table 3, at training stage, the value of RMSE, MAE and R2 are 0.89202, 0.66261 and 0.99532 respectively. At testing stage, similarly these values are 0.55094, 0.31683 and 0.99791 respectively, which is calculated by Eq. (9), (13) and (14). The formula of mean absolute error and coefficient of determination are as below: Mean absolute error: 1 n MAE   (YA  YP ) n i 1

(13)

Coefficient of determination: n

R2  1 

 (Y i 1

A

n

 YP ) 2

(14)

Y i 1

2 P

Fig. 9 The regression plot of LM-10 based after training

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(a)

(b)

18

(c)

(d) Fig.10. Comparison of ANN predicted values and experimental data. (a-b) based on P/e, and (c-d) based on e/d.

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Fig. 11 Individual errors graph all data samples. Table 3 Statistical performance of proposed MLPNN predicted data.

Training

Statistical errors MAE RMSE 0.66261 0.89202

R2 0.99532

Testing

0.31683

0.55094

0.99791

All

0.48972

0.72148

0.99661

Process

6.2. Comparison of performance of MLP model with MLR model For determining the effectiveness of MLP model, multiple linear regression (MLR) analysis has been performed using the same parameters. The performance of multiple regression analysis is shown in Table 4. From Table.4, it has been found that the degree of meaningfulness of input variables used in present work. This degree of meaningfulness is decided by the value of p-val., which should be less than 0.05 for meaningful factors. It is found that all five input factors are meaningful variable. The performance of MLR model is shown in Table 5, which is based on the values of RMSE and R2. From this Table, it has been found that the values of RMSE and R2 were 1.97951 and 0.97712 respectively for MLR model. Similarly 0.72148 and 0.99661 respectively for ANN model. Fig. 12 illustrates a comparison between the observed versus predicted values for

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MLP and MLR models. On the comparative study of both model, it has been found that prediction of ANN model is better than MLR model with 1.79 % more value of coefficient of determination. In view of the above, it is confirmed that the proposed MLP model of ANN technique has been successfully predicted the heat transfer of single and three sided roughened absorber plate solar air heater. Table. 4 Results of Multiple Linear Regression (MLR) analysis. Coefficients Standard t Stat P-value Error Intercept (C0) -4.66551 2.43955 -1.91244 0.062496 C1 5.51825 0.29203 18.89596 1.91E-22 C2 -0.64487 0.09391 -6.86695 2.01E-08 C3 -148777 20569.54 -7.23287 5.93E-09 C4 3356.976 461.2983 7.27723 5.12E-09 C5 0.00432 0.00011 37.33321 2.11E-34

Model MLR ANN

Table.5 Comparison of MLR and ANN model R2 RMSE 0.97712 1.97951 0.99661 0.72148

Fig. 12 Comparison of experimental and predicted values for both the MLP and MLR models.

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7. Conclusion Predicting the heat transfer characteristic as Nusselt number is very helpful to study the heat transfer analysis of roughened solar air heater. In the present work, MLP model has been developed for prediction. Two different types of roughened solar air heater: one with single sidedabsorber plate and other with three - sided absorber plate are used in the experiments. Total 50 data sets have been in neural model collected from experiments. Five parameters in input layer and one parameter in output layer have been used. Seven different numbers of neurons from 6 to 12 were used in hidden layer and trained with LM learning algorithm. 10 numbers of neurons in hidden layer found as optimal on the basis on the statistical error analysis. Finally the 5-10-1 neural model successfully predicts the heat transfer of SAH. The predicted results were compared with actual data and found that the values of MAE were 0.66261 and 0.31683, and RMSE were 0.89202 and 0.55094 for testing and training data sets respectively. Similarly the values of R2 were 0.99532 and 0.99791 respectively. In addition, MLP model has been compared with MLR statistical model to see the effectiveness of ANN model. It has been found that the MLP model performs better than MLR model with 1.79 % more value of coefficient of determination. The present study reveals that the heat transfer characteristic predicting model of one side and three sided roughened solar air heater computes with high degree of accuracy using ANN technique. As this new technique requires lesser time and number of test as compared to other experimental approaches and other conventional techniques which requires very complex governing equations, it is easier as well as economical for the manufactures to adopt the ANN technique for analyzing the heat transfer study of roughened solar air heater. It is advantageous for both engineering effort and financial concerns.

Acknowledgement The Authors are very thankful to NIT Jamshedpur for providing all the facilities to carry out the research work. References [1]. Duffie, J.A., Beckman, W.A., 1991,Solar Engineering of Thermal Processes, second ed.,Wiley Publication, New York. https://www.wiley.com. [2]. Tiwari, G.N., 2004, Solar Energy: Fundamentals, Design, Modelling and Applications, Narosa Publishing House, New Delhi, India. https://www.crcpress.com. [3]. Bhushan, B., Singh, R., 2010. A review on methodology of artificial roughness used in duct of solar air heaters. Energy35,pp-202–212. https://doi.org/10.1016/j.energy.2009.09.010

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