Design plots are useful for determining the ideal roughness parameter values in solar air heaters to maximize their thermal efficiency. The design plots were plotted for the estimated values of the effective efficiency of the solar air heaters, which contain absorber plates roughened artificially by diagonally chamfered cuboids and arranged in diverse configurations. These design plots are highly beneficial for forecasting the impact of the designed roughness parameter on the performance of a solar air heater under different solar radiation intensities and for identifying the optimal configuration. The effective efficiency can be used as a basis for assessing the actual performance of the system. The study examines a relative roughness pitch ranging from 5 to 10, an arm length of diagonally chamfered cuboids between 6 and 14 mm, and a relative roughness height from 0.44 to 0.088. In addition, the Reynolds numbers investigated span from 4250 to 25,000, while a constant heat flux of 1000 W/m2 is applied to the absorber plate. The maximum effective efficiency achieved at a Reynolds number of 14,500 is 0.75 (75%), representing a 19% improvement over smooth ducts, which yielded an efficiency of 0.63 (63%). This enhancement was observed at a relative roughness height of 0.077, a relative roughness pitch (P/e) of 6, and a cuboid arm length (A) of 6. Effective efficiencies are evaluated using correlations for the Nusselt number and friction factor as defined by Azad (Int J Thermofluid Sci Technol 9:090401, 2022. <a href="https://doi.org/10.1016/0196-8904(95)00164-9">https://doi.org/10.1016/0196-8904(95)00164-9</a>).Correlation for Nusselt number developed is as follows<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41403_2025_538_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="652" /> </InlineMediaObject> <EquationSource Format="TEX">\({\text{Nu}} = { }0.108{\text{ Re}}^{0.67} \left( {\frac{{\text{P}}}{{\text{e}}}} \right)^{1.17} \left( {\frac{{\text{e}}}{{\text{D}}}} \right)^{0.19} \left( {\frac{{\text{A}}}{6}} \right)^{0.33} \left[ {{\text{exp}}\left\{ { - 0.386\left( {{\text{Ln}}\left( {\frac{{\text{P}}}{{\text{e}}}} \right)} \right)^{2} } \right\}} \right]\left[ {{\text{exp}}\left\{ {0.506\left( {{\text{Ln}}\left( {\frac{{\text{A}}}{6}} \right)} \right)^{2} } \right\}} \right]\)</EquationSource> </InlineEquation>.Correlation for friction factor developed is as follows<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41403_2025_538_Article_IEq2.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="637" /> </InlineMediaObject> <EquationSource Format="TEX">\( {\text{f}} = { }0.087{\text{ Re}}^{ - 0.12} \left( {\frac{{\text{P}}}{{\text{e}}}} \right)^{1.16} \left( {\frac{{\text{e}}}{{\text{D}}}} \right)^{0.26} \left( {\frac{{\text{A}}}{6}} \right)^{0.48} \left[ {{\text{exp}}\left\{ { - 0.49\left( {{\text{Ln}}\left( {\frac{{\text{P}}}{{\text{e}}}} \right)} \right)^{2} } \right\}} \right]\left[ {{\text{exp}}\left\{ {0.706\left( {{\text{Ln}}\left( {\frac{{\text{A}}}{6}} \right)} \right)^{2} } \right\}} \right] \)</EquationSource> </InlineEquation>.The evaluation based on effective efficiency (ηEx) indicates more favorable outcomes at lower Reynolds numbers. Whereas, for higher Reynolds number ranges, a smooth duct design is deemed appropriate.

Design Plots for Effective Efficiency Estimation of Solar Air Heater Roughened Artificially by Diagonally Chamfered Cuboids

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发表日期：

2025年6月24日

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Man Singh Azad

摘要

Design plots are useful for determining the ideal roughness parameter values in solar air heaters to maximize their thermal efficiency. The design plots were plotted for the estimated values of the effective efficiency of the solar air heaters, which contain absorber plates roughened artificially by diagonally chamfered cuboids and arranged in diverse configurations. These design plots are highly beneficial for forecasting the impact of the designed roughness parameter on the performance of a solar air heater under different solar radiation intensities and for identifying the optimal configuration. The effective efficiency can be used as a basis for assessing the actual performance of the system. The study examines a relative roughness pitch ranging from 5 to 10, an arm length of diagonally chamfered cuboids between 6 and 14 mm, and a relative roughness height from 0.44 to 0.088. In addition, the Reynolds numbers investigated span from 4250 to 25,000, while a constant heat flux of 1000 W/m² is applied to the absorber plate. The maximum effective efficiency achieved at a Reynolds number of 14,500 is 0.75 (75%), representing a 19% improvement over smooth ducts, which yielded an efficiency of 0.63 (63%). This enhancement was observed at a relative roughness height of 0.077, a relative roughness pitch (P/e) of 6, and a cuboid arm length (A) of 6. Effective efficiencies are evaluated using correlations for the Nusselt number and friction factor as defined by Azad (Int J Thermofluid Sci Technol 9:090401, 2022. https://doi.org/10.1016/0196-8904(95)00164-9).

Correlation for Nusselt number developed is as follows

\({\text{Nu}} = { }0.108{\text{ Re}}^{0.67} \left( {\frac{{\text{P}}}{{\text{e}}}} \right)^{1.17} \left( {\frac{{\text{e}}}{{\text{D}}}} \right)^{0.19} \left( {\frac{{\text{A}}}{6}} \right)^{0.33} \left[ {{\text{exp}}\left\{ { - 0.386\left( {{\text{Ln}}\left( {\frac{{\text{P}}}{{\text{e}}}} \right)} \right)^{2} } \right\}} \right]\left[ {{\text{exp}}\left\{ {0.506\left( {{\text{Ln}}\left( {\frac{{\text{A}}}{6}} \right)} \right)^{2} } \right\}} \right]\) .

Correlation for friction factor developed is as follows

\( {\text{f}} = { }0.087{\text{ Re}}^{ - 0.12} \left( {\frac{{\text{P}}}{{\text{e}}}} \right)^{1.16} \left( {\frac{{\text{e}}}{{\text{D}}}} \right)^{0.26} \left( {\frac{{\text{A}}}{6}} \right)^{0.48} \left[ {{\text{exp}}\left\{ { - 0.49\left( {{\text{Ln}}\left( {\frac{{\text{P}}}{{\text{e}}}} \right)} \right)^{2} } \right\}} \right]\left[ {{\text{exp}}\left\{ {0.706\left( {{\text{Ln}}\left( {\frac{{\text{A}}}{6}} \right)} \right)^{2} } \right\}} \right] \) .

The evaluation based on effective efficiency (η_Ex) indicates more favorable outcomes at lower Reynolds numbers. Whereas, for higher Reynolds number ranges, a smooth duct design is deemed appropriate.