Heat transfer and fluid flow analysis of an artificially roughened solar air heater: a CFD based investigation

Abstract

In this paper, the effect of rib (circular sectioned) spacing on average Nusselt number and friction factor in an artificially roughened solar air heater (duct aspect ratio, AR= 5:1) is studied by adopting the computational fluid dynamics (CFD) approach. Numerical solutions are obtained using commercial software ANSYS FLUENT v12.1. The computations based on the finite volume method with the semi-implicit method for pressure-linked equations (SIMPLE) algorithm have been conducted. Circular sectioned transverse ribs are applied at the underside of the top of the duct, i.e., on the absorber plate. The rib-height-to-hydraulic diameter ratio (e/D) is 0.042. The rib-pitch-to-rib-height (P/e) ratios studied are 7.14, 10.71, 14.29 and 17.86. For each rib spacing simulations are executed at six different relevant Reynolds numbers from 3800 to 18000. The thermo-hydraulic performance parameter for P/e = 10.71 is found to be the best for the investigated range of parameters at a Reynolds number of 15000.

Keywords

heat transfer / pressure drop / thermo-hydraulic performance parameter

Introduction

Solar air heaters form the major component of solar energy utilization system which absorbs the incoming solar radiation, converts it into thermal energy at the absorbing surface, and transfers the energy to a fluid flowing through the collector. Solar air heaters have been employed to deliver heated air at low to moderate temperatures for space heating, crop drying and industrial applications. The air to be heated is passed through a rectangular cross-section duct below a metal absorber plate with the sun-facing side blackened to facilitate absorption of solar radiation incident on the absorber plate. Transparent covers are placed over the absorber plate to reduce the thermal losses from the heated absorber plate. The thermal performance of conventional solar air heater has been found to be poor because of the low convective heat transfer coefficient from the absorber plate to the air [1,2]. Artificial rib roughness on the underside of the absorber plate has been found to considerably enhance the heat transfer coefficient. Roughness elements have been used to improve the heat transfer coefficient by creating turbulence in the flow. However, it would also result in an increase in friction losses and hence greater power requirements for pumping air through the duct. To keep the friction losses at a low level, the turbulence must be created only in the region very close to the duct surface, i.e. in the laminar sub-layer. The application of artificial roughness in the form of fine wires or ribs of different geometry on the heat transfer surface has been recommended to enhance the heat transfer coefficient by several investigators using experimental and the computational fluid dynamics (CFD) approach. A number of experiments have been performed to optimize the best roughness element, which can enhance heat transfer with the minimum pumping power requirement. More details about different experimental investigations on roughness elements of different shapes, sizes and orientations can be found in Refs [3-5]. But literature search in this area also revealed that very little research on CFD investigation of artificially roughened solar air heater has been conducted to evaluate the optimum rib shape and configurations. Chaube et al. [6] performed a two dimensional CFD analysis of the effect of artificial roughness on heat transfer enhancement of a rectangular duct of a solar air heater on ten different rib shapes, viz. rectangular, square, chamfered, triangular, etc., provided on the absorber plate using commercially CFD software, FLUENT 6.1 and the SST k-ω turbulence model. Kumar and Saini [7] made a CFD based analysis of the effect of arc shaped rib on fluid flow and heat transfer characteristics of a solar air heater, using 3-D models and the FLUENT 6.3.26 commercial CFD code. Karmare and Tikekar [8] performed a CFD simulation of the fluid flow and heat transfer of a solar air heater duct with metal grit ribs as roughness element on circular, triangular and square shape rib grits with the angle of attack of 54, 56, 58, 60 and 62. Sharma and Thakur [9] conducted a CFD study of the heat transfer and fluid friction characteristics of a solar air heater having V-shaped ribs roughness on the underside of the absorber plate, based on the finite volume method with the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. Gandhi and Singh [10] conducted a CFD study of the effect of wedge shaped repeated transverse ribs roughness heat transfer and fluid friction characteristics of a solar air heater. The two dimensional numerical modeling of the duct flow using FLUENT showed reasonably good agreement with the experimental observations except for the friction factor. The numerical results obtained by the commercial CFD code FLUENT were compared with the experimental results. Yadav and Bhagoria [11] conducted a numerical prediction of the only heat transfer behavior of a rectangular duct of a solar air heater having triangular rib roughness on the absorber plate, using a commercial finite volume package ANSYS FLUENT 12.1 as a solver. The maximum value of Nusselt number was found corresponding to relative roughness pitch of 10. Yadav and Bhagoria [12] presented a numerical prediction of fluid flow and heat transfer in a conventional solar air heater by CFD, using a commercial finite volume package ANSYS FLUENT 12.1 to analyze the nature of the flow across the duct of a conventional solar air heater. It was found that the Nusselt number increased and the friction factor decreased with the increase in Reynolds number. Yadav and Bhagoria [13] conducted a numerical analysis of the heat transfer and flow friction characteristics in an artificially roughened solar air heater having square sectioned transverse ribs roughness considered at underside of the top heated wall. The maximum value of thermo-hydraulic performance parameter was found to be 1.82 corresponding to relative roughness pitch of 10.71. Yadav and Bhagoria [14] carried out a numerical investigation of turbulent flows through a solar air heater roughened with semicircular sectioned transverse rib roughness on the absorber plate. The numerical results showed that the flow-field, average Nusselt number, and average friction factor are strongly dependent on the relative roughness height. The thermo-hydraulic performance parameter was found to be the maximum for the relative roughness height of 0.042. Yadav and Bhagoria [15] performed a CFD based investigation of turbulent flows through a solar air heater roughened with square sectioned transverse rib roughness. Three different values of rib-pitch and rib-height were taken such that the relative roughness pitch remains constant. The results showed that the average heat transfer, average flow friction and thermo-hydraulic performance parameter were strongly dependent on the relative roughness height. More details about different CFD investigations on roughness elements of different shapes, sizes and orientations can be found in Yadav and Bhagoria [16], who presented a comprehensive literature survey about different CFD investigations on artificially roughened solar air heater and reported that the results obtained by the renormalization-group (RNG) k-ϵ model were in good agreement with the experimental results.

The relevant dimensionless geometric parameters discussed in previous works are relative roughness height (e/D), relative roughness pitch (P/e) and Reynolds number (Re) [16]. The extensive survey of the literature reveals that very few CFD investigations have been done on artificially roughened solar air heater provided with circular sectioned transverse rib roughness. The objective of this work is to perform such a study by adopting the CFD approach whose application is a rapidly developing discipline due to the continuous development in the capabilities of commercial software and the growth of computer power. Chaube et al. [6] suggested that the calculation with two-dimensional flow model yields the results closer to measurements as compared to that with 3-dimensional flow. In this work, the 2D flow is therefore carried out for saving computer memory and computational time. The purpose of the present work is to investigate the fluid flow and heat transfer characteristics of a two-dimensional rectangular duct of a solar air heater provided with circular sectioned transverse rib roughness by adopting the CFD approach. The CFD code, ANSYS FLUENT v12.1, is used with associated software such as ANSYS DESIGN MODELER v12.1 and ANSYS ICMCFD v12.1 to predict the heat transfer and friction factor of an artificially roughened solar air heater. The main objectives of the present numerical analysis are to investigate the effect of relative roughness pitch (P/e) and Reynolds number (Re) on Nusselt number and friction factor, and to find out the best rib configuration in terms of thermo-hydraulic performance parameter on the basis of equal pumping power.

CFD simulation

Computational domain

In the present analysis, the rectangular duct simulated by Yadav and Bhagoria [13] is adopted as the flow domain for the predictions of the heat transfer and flow friction characteristics. The computational domain of an artificially roughened solar air heater is represented in two dimensional (2D) form by a rectangle and displayed in Fig. 1. The domain consists of an entrance section (L₁), a test section (L₂) and an exit section (L₃). As per ASHRAE Standard [17] a short entrance length is chosen because for a roughened duct, the thermally fully developed flow is established in a short length of 2 to 3 times of the hydraulic diameter. The exit section is used after the test section in order to reduce the end effect in the test section. The internal duct cross section is 100 mm²× 20 mm². The rib height-to-hydraulic diameter ratio, e/D, is selected as 0.042 based on the optimum value reported in Refs [18-20]. The range of rib pitch-to-height ratio, P/e, is selected from 7.14 to 17.86 based on the optimum value reported in Refs [21,22]. The range of Reynolds number, Re, is selected from 3800 to 18000 based on the optimum value reported in Ref [23]. The top wall consists of a 0.5 mm thick absorber plate made of aluminum. Artificial roughness in the form of circular sectioned transverse rib is considered at the underside of the top of the duct on the absorber plate while the other sides are considered as smooth surface. A rib height of 1.4 mm is chosen such that it breaks the viscous sub-layer. The fin and flow passage blockage effects are negligible as recommended by Prasad and Saini [24]. A uniform heat flux of 1000 W/m² is considered on the top of the absorber plate for numerical analysis. The geometrical and operating parameters employed are listed in Table 1. A typically roughened absorber plate with different arrangement of circular sectioned transverse ribs is shown in Fig. 2.

Grid distribution

Automatic (Patch conforming) non-uniform grids are generated for all numerical simulations performed in this work. Meshing of the domain is generated using ANSYS ICEM CFD v12.1 software. A non-uniform grid contains161568 quad cells with a cell size of 0.24 mm to resolve the laminar sub-layer, as demonstrated in Fig. 3. A grid independence test is implemented over grids with different numbers of cells, 103231, 118781, 136910, 161568 and 197977 used in five steps. The average Nusselt number and friction factor values changed less than 1% as further refinements from 161568 cells to 197977 cells are applied. Hence, there is no such advantage in increasing the number of cells beyond this value. Thus, the grid system of 161568 cells is adopted for the current computation. For all cases similar grid density is applied.

Governing equation

The numerical model for fluid flow and heat transfer through an artificially roughened solar air heater is developed under the following assumptions:

1) The fluids maintain single-phase, incompressible turbulent flow across the duct.

2) Steady two-dimensional fluid flow and heat transfer.

3) Both thermally and hydraulically fully developed flow (steady-state conditions).

4) The thermo-physical properties of both the fluid (air) and the solid absorber plate (aluminum) are constant (temperature independent).

5) Negligible radiation heat transfer.

The CFD methods consist of numerical solutions of mass, momentum and energy conservation with other equations like species transport. The solution of these equations accomplishes with numerical algorithm and methods. The governing equations are summarized as follows:

Continuity equation

(1){\displaystyle \frac{\partial }{\partial x_i}}(\rho u_i)=\mathrm{0.}

Momentum equation

(2){\displaystyle \frac{\partial }{\partial x_i}}(\rho u_i{u}_j)=-{\displaystyle \frac{\partial p}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\mu \left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)\right]+{\displaystyle \frac{\partial }{\partial x_j}}\left(-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right).

Energy equation

(3){\displaystyle \frac{\partial }{\partial x_i}}(\rho u_{i}T)={\displaystyle \frac{\partial }{\partial x_j}}\left[(\mathrm{\Gamma }+{\mathrm{\Gamma }}_t){\displaystyle \frac{\partial T}{\partial x_j}}\right],

where Γ and Γ_t are molecular thermal diffusivity and turbulent thermal diffusivity, respectively and are given by

(4)\mathrm{\Gamma }={\displaystyle \frac{\mu }{Pr}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{\Gamma }}_t={\displaystyle \frac{{\mu }_t}{P{r}_t}}.

Boundary conditions

The boundary conditions for the different edges can be created while constructing the geometry of the grid in ANSYS ICEM CFD v12.1. Table 2 tabulates the boundary conditions for the present geometry. The air enters the duct at the ambient temperature (T₀ = 300 K) with a uniform velocity (u₀) at the inlet. The inlet velocities corresponding to different values of Reynolds numbers are calculated from Eq. (17). A pressure outlet condition with a fixed atmospheric pressure of 1.013 × 10⁵ Pa is applied at the exit. Impermeable boundary and no-slip wall conditions are implemented over the duct walls. A constant flux of 1000 W/m² is given at the absorber plate (top wall) while the bottom wall keeps an adiabatic wall condition. The temperature of the air inside the duct is also taken as 300 K at the beginning. The boundary conditions are expressed as follows:

Along the bottom wall of the duct (0≤x≤L, y = H),

(5)u=\mathrm{0},v=\mathrm{0},{\displaystyle \frac{\partial T}{\partial y}}=\mathrm{0.}

Along the upper wall of the duct (y = 0),

(6)\mathrm{0}\le x\le L_{\mathrm{1}},L_{\mathrm{2}}+L_{\mathrm{1}}\le x\le L:u=\mathrm{0},v=\mathrm{0},{\displaystyle \frac{\partial T}{\partial y}}=\mathrm{0},

(7)L_{\mathrm{1}}\le x\le L-L_{\mathrm{3}}(\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\sec \mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}):u=\mathrm{0},v=\mathrm{0},q=\mathrm{1000}\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}.

At the duct inlet (x = 0, 0≤y≤H),

(8)u=u_{\mathrm{0}},v=\mathrm{0},T=T_{\mathrm{0}}.

At the duct exit (x = L, 0≤y≤H),

(9){\displaystyle \frac{\partial u}{\partial x}}=\mathrm{0},{\displaystyle \frac{\partial v}{\partial x}}=\mathrm{0},{\displaystyle \frac{\partial T}{\partial x}}=\mathrm{0.}

The values of the thermo-physical properties of air are assumed to remain constant and evaluated at a temperature of 300 K. The variation in properties of air is very small and negligible within the range of pressure and temperature involved. The thermo-physical properties of the working fluid and absorber plate are listed in Table 3.

Selection and validation of turbulence model

In the present numerical simulation the RNG k-ϵ model is selected to simulate the heat transfer and fluid flow characteristic based on its closer results to the Dittus-Boelter empirical correlation and Blasius empirical correlation results. More details for the selection of best turbulence model for an artificially roughened solar air heater can be found in Yadav and Bhagoria [16]. More details of other turbulence models can be found in <FootNote>

ANSYS FLUENT 12.1. Documentation. ANSYS, Inc., 2003-2004

</FootNote>.

The modeled turbulence kinetic energy, k, and its rate of dissipation, ϵ, are obtained from

(10){\displaystyle \frac{\partial }{\partial x_i}}(\rho k{u}_i)={\displaystyle \frac{\partial }{\partial x_j}}\left({\alpha }_k{\mu }_{eff}{\displaystyle \frac{\partial k}{\partial x_j}}\right)+G_k-\rho ϵ,

and

(11){\displaystyle \frac{\partial }{\partial x_i}}(\rho ϵu_i)={\displaystyle \frac{\partial }{\partial x_j}}\left({\alpha }_{ϵ}{\mu }_{eff}{\displaystyle \frac{\partial ϵ}{\partial x_j}}\right)+C_{\mathrm{1}ϵ}{\displaystyle \frac{ϵ}{k}}{G}_k-C_{\mathrm{2}ϵ}\rho {\displaystyle \frac{{ϵ}^{\mathrm{2}}}{k}}-R_{ϵ},

where G_k represents the generation of turbulence kinetic energy due to the mean velocity gradients, which may be defined as

(12)G_k=-\rho \overline{u_i^{\prime }{u}_j^{\prime }}{\displaystyle \frac{\partial u_j}{\partial x_i}},

where μ_eff represents the effective turbulent viscosity and is given by

(13){\mu }_{eff}=\mu +{\mu }_t.

The turbulent (or eddy) viscosity, μ_t, is computed by combining k and ϵ as

(14){\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^{\mathrm{2}}}{ϵ}},

where C_μ is a constant.

The quantities α_k and α_ϵ are the inverse effective turbulent Prandtl numbers for k and ϵ, respectively. The model constants C_1ϵ, C_2ϵ, C_3ϵ, α_k and α_ϵ have the following default values [25]:

C_{\mathrm{1}ϵ}=\mathrm{1.42},C_{\mathrm{2}ϵ}=\mathrm{1.68},C_{\mu }=\mathrm{0.0845},{\alpha }_k=\mathrm{1.39} and {\alpha }_{ϵ}=\mathrm{1.39.}

Solution method

All governing equations are discretized by a second order upwind-biased scheme using a finite volume approach and then solved in a segregated manner. Commercial CFD software, ANSYS FLUENT 12.1, is used to solve the equations. The SIMPLE algorithm to couple pressure and velocity is selected for the incompressible flow computation [26]. The RNG k-ϵ model is employed to simulate the flow and heat transfer. The convergence criteria for all the dependent variables are specified as 0.001. Whenever convergence problems are noticed, the solution is started using the first order upwind discretization scheme and continued with the second order upwind scheme. A uniform air velocity is introduced at the inlet while a pressure (fixed) outlet condition is applied at the outlet. The adiabatic boundary condition is implemented over the bottom duct wall while the constant heat flux condition is applied to the upper duct wall of the test section.

Data reduction

The aim of the present CFD work is to investigate the average Nusselt number and average friction factor in artificially roughened solar air heater having circular sectioned transverse rib roughness on the underside of the absorber plate.

The average Nusselt number for artificially roughened solar air heater is computed by

(15)N{u}_r={\displaystyle \frac{hD}{k}},

where h is convective heat transfer co-efficient.

The average friction factor for artificially roughened solar air heater is computed by

(16)f_r={\displaystyle \frac{(\mathrm{\Delta }P/l)D}{\mathrm{2}\rho v^{\mathrm{2}}}},

where ∆P is the pressure drop across the duct of an artificially roughened solar air heater.

The Reynolds number is defined as

(17)\mathit{R}\mathit{e}=\rho vD/\mu .

It is important to note that the enhancement of heat transfer as a result of using artificial roughness is accompanied by a considerable enhancement of friction losses. This results in considerably large additional pumping costs. Consequently any enhancement scheme must be evaluated on the basis of consideration of pumping costs. The solar air heater duct roughened with circular sectioned transverse rib results in a higher Nusselt number as well as friction factor as compared to smooth solar air heater. Therefore, a thermo-hydraulic performance parameter needs to be determined that takes into account both thermal i.e., Nusselt number and hydraulic i.e., friction factor to evaluate its effectiveness. Webb and Eckert [27] proposed a thermo-hydraulic parameter which evaluates the enhancement in heat transfer of a roughened duct compared to that of the smooth duct for the same pumping power requirement and is defined as

(18)Thermo-hydraulicperformance parameter={\displaystyle \frac{N{u}_r/N{u}_s}{{(f_r/f_s)}^{\mathrm{1}/\mathrm{3}}}}.

For an enhancement scheme to be viable, the value of this index must be greater than unity.Nu_s represents the Nusselt number for smooth duct of a solar air heater and can be obtained by the Dittus-Boelter equation [28]:

(19)N{u}_s=\mathrm{0.023}\mathit{R}{\mathit{e}}^{\mathrm{0.8}}\cdot \mathit{P}{\mathit{r}}^{\mathrm{0.4}},

where f_s represents the friction factor for smooth duct of a solar air heater and can be obtained by the Blasius equation [29]:

(20)f_s=\mathrm{0.0791}\mathit{R}{\mathit{e}}^{-\mathrm{0.25}}.

Results and discussion

Grid independence test

A grid independence test is implemented over grids with different numbers of cells, 103231, 118781, 136910, 161568 and 197977 in five steps. Five different grid distributions are tested on artificially roughened solar air heater with a relative roughness height (e/D) of 0.042, a relative roughness pitch (P/e) of 7.14 at a Reynolds number of 12000 to ensure that the calculated results are grid independent. The average Nusselt numbers, friction factors and percentage difference for five different sets of grids using the RNG k-ϵ model are listed in Table 4. The average Nusselt number and friction factor values changes less than 1% as further refinements from 161568 cells to 197977 cells are applied. Hence, there is no such advantage in increasing the number of cells beyond this value. Thus, the grid system of 161568 cells is adopted for the current computation. For all cases similar grid density is applied.

Heat transfer characteristics

Figure 4 depicts the variation of average Nusselt number as a function of Reynolds number for different relative roughness pitch (P/e) and for fixed values of the relative roughness height (e/D) of 0.042. It can be seen that the average Nusselt number increases with the Reynolds number in all cases as expected. It is well known that the increase in Reynolds number increases the turbulence kinetic energy and turbulence dissipation rate, which leads to the increase in the turbulence intensity and thus increases the Nusselt number. As the Reynolds number increases the roughness elements begin to project beyond the laminar sub-layer. Laminar sub-layer thickness decreases with the increase in Reynolds number. In addition, there is local contribution to the heat removal by the vortices originating from the roughness. This increases the heat transfer rate as compared to the smooth surface. The heat transfer phenomenon can be observed and described by the contour map of turbulence intensity. The contour map of turbulence intensity for relative roughness pitch, P/e = 7.14 and Reynolds number, Re = 15000 is displayed in Fig. 5. The highest value of turbulence intensity is seen near the absorber plate and between the first and second rib region, and then it decreases with the increase in distance from the absorber plate. From Fig. 4, it is also seen that the average Nusselt number values decrease with the increase in relative roughness pitch (P/e) for fixed value of relative roughness height (e/D). This is due to the fact that with the increase in relative roughness pitch, the number of reattachment points over the absorber plate decreases. Similar patterns of average Nusselt number are observed by Verma and Prasad [30] and Prasad and Saini [31] in their experiments for circular transverse wire rib roughness on the absorber plate.

To compare the enhancement of the heat transfer achieved as a result of providing artificial roughness in the form of circular sectioned transverse rib on the absorber plate with that of the smooth duct of a solar air heater, the values of the Nusselt number ratio (Nu_r/Nu_s) for fixed values of the relative roughness height (e/D) of 0.042, and different values of relative roughness pitch (P/e) are presented in Fig. 6. It can be seen that the average Nusselt number ratio increases with the decrease in relative roughness pitch (P/e) for all the cases. It is also observed that the average Nusselt number ratio increases with the increase of Reynolds number, attains a maximum value and decreases with the further increase in Reynolds number for the investigated range of parameters. The maximum enhancement in the average Nusselt number is found to be 2.31 times that of smooth duct corresponding to a relative roughness pitch of 7.14 and a relative roughness height of 0.042 at a Reynolds number of 15000 for the investigated range of parameters.

Fluid friction characteristics

Figure 7 shows the variation of average friction factor as a function of Reynolds number for different relative roughness pitch (P/e) and for fixed values of relative roughness height (e/D) of 0.042. It can be seen that the average friction factor decreases with the increase in Reynolds number. The shedding of vortices originating from the circular sectioned rib top causes an additional loss of energy resulting in increased friction factor. It is also observed that the friction factor decreases with the increase in Reynolds number because of the suppression of viscous sub-layer. The flow friction phenomena in artificially roughened solar air heater are demonstrated by the contour map of pressure. The contour map of pressure for the relative roughness pitch, P/e = 7.14 and Reynolds number, Re = 15000 is displayed in Fig. 8. As the air enters the roughened region of duct of a solar air heater, the air starts to accelerate, resulting in an increase in pressure drop. The pressure drop is more profound for the higher value of Reynolds number. From Fig. 7, it is also seen that average friction factor values decrease with the increase in relative roughness pitch (P/e) for fixed value of relative roughness height (e/D). It happens because the duct of solar air heater contains less circular sectioned rib at higher relative roughness pitch which results in low flow resistance in the duct. Similar patterns of average friction factor were observed by Verma and Prasad [30] and Prasad and Saini [31] in their experiments for circular transverse wire rib roughness on the absorber plate.

Figure 9 shows the variation of average friction factor ratio (f_r/f_s) as a function of Reynolds number for different relative roughness pitch (P/e) and for a fixed value of relative roughness height of 0.042. It can be seen that the average friction factor ratio increases with the decrease in relative roughness pitch (P/e) for all the cases. It is also seen that the average friction factor ratio decreases with the increase of Reynolds number for the investigated range of parameters. The maximum enhancement in average friction factor is found to be 3.14 times that of smooth duct corresponding to a relative roughness pitch of 7.14 and a relative roughness height of 0.042 at a Reynolds number of 3800 for the investigated range of parameters.

Thermo-hydraulic performance

As pointed out above, any heat transfer enhancement techniques having a value of thermo-hydraulic parameter i.e. thermo-hydraulic performance parameter greater than unity ensures the effectiveness of using enhancement technique and therefore, this parameter is generally used to compare the thermal as well as hydraulic performance of different roughness arrangements to select the best roughness arrangement among all the possible combinations. Figure 10 shows the variation of the thermo-hydraulic performance parameter with Reynolds number for different values of relative roughness pitch (P/e) and for a fixed value of relative roughness height (e/D). It is found that the thermo-hydraulic performance parameter values vary from 1.54 to 1.64 for the range of parameters investigated. It is seen that the thermo-hydraulic performance parameter of a relative roughness pitch, P/e = 10.71 is found to be the best for the investigated range of parameters at a Reynolds number of 15000. Hence artificially roughened solar air heater with circular sectioned transverse rib roughness on the absorber plate with P/e = 10.71 and e/D = 0.042 can be employed for heat transfer augmentation.

Validation of model

To validate the present model, the numerical results are compared with the previous experimental results of Verma and Prasad [30]. Figure 11 shows the comparison of the average Nusselt number predicted by the present CFD investigation with the correlation developed by Verma and Prasad [30]. It can be seen that the results predicted by the present CFD investigation are much closer to the experimental results of Verma and Prasad [30]. The discrepancy between the experimental data and the present computational results is less than ± 5.5%. Figure 12 shows the comparison of the average friction factor predicted by the present CFD investigation with the correlation developed by Verma and Prasad [30]. It can also be seen that the results predicted by the present CFD investigation are much closer to the experimental results of Verma and Prasad [30]. The discrepancy between the experimental data and the present computational results is less than ± 7.5%. Similar results are obtained by Prasad and Saini [31] who investigated the effect on the heat transfer and flow friction characteristics for flow of air in an artificially roughened solar air heater provided with circular sectioned transverse rib roughness.

Conclusions

In view of the present CFD predictions, the following relevant conclusions can be obtained by investigating the heat transfer and flow friction in two-dimensional duct of a solar air heater roughened with circular sectioned transverse rib roughness on the absorber plate:

1) The maximum average Nusselt number ratio is found to be 2.31 corresponding to a relative roughness pitch of 7.14 at a Reynolds number of 15000 for the investigated range of parameters.

2) The maximum average friction factor ratio is found to be 3.14 corresponding to a relative roughness pitch of 7.14 at a Reynolds number of 3800 for the investigated range of parameters.

3) It is found that the solar air heater roughened with circular sectioned transverse rib roughness on the absorber plate with P/e = 10.71 provides a better thermo-hydraulic performance parameter at a Reynolds number of 15000 and hence can be employed for heat transfer augmentation.

4) The results predicted by the present CFD investigation are much closer to previous experimental results. It can, therefore, be concluded that the present numerical results have validated the proposed system.

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