article · International Journal of Thermofluids
This study investigates the heat transfer capabilities of an ethylene glycol-based Williamson hybrid nanofluid flowing over stretching and shrinking flat surfaces, accounting for heat sources and viscous dissipation. Using conservation laws, a mathematical model of non-linear coupled partial differential equations was formulated and solved using the bivariate spectral weighted residual method. The results indicate that the fluid temperature rises under the influence of viscous dissipation and heat sources. Increasing the fluid parameter decreases velocity while raising temperature. Additionally, the presence of nanoparticles thickens both the velocity and thermal boundary layers, which slows the fluid down. Quantitatively, specific increases in viscous dissipation reduce skin drag and Nusselt numbers across both sheet types, while a doubled porosity parameter increases skin friction coefficients and Nusselt numbers. These insights aim to inform the thermal design and efficiency enhancement of solar panel plates.
Improving heat transfer is critical for optimising renewable energy technologies, particularly solar panels. By detailing how specialised hybrid nanofluids move and distribute heat over variable surfaces, this mathematical modelling helps researchers understand how to manage thermal loads more effectively, which is essential for improving overall energy capture and device efficiency.
This research provides theoretical and mathematical insights that could assist engineers and solar panel designers in developing more efficient cooling or heat transfer mechanisms. Given that the work relies on theoretical modelling and non-similarity transformations, it represents early-stage research that requires physical experimentation and prototype testing before direct industrial adoption.
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The global requirement for sustainable energy supply to enhance industrial productivity and reduce production costs has focused researchers’ attention to renewable energy in recent years. Solar energy mitigates the dangers connected with the use of fossil fuels in electricity generation. This work is set to evaluate the heat transmission capacities of Williamson hybrid nanofluid flow across a flat plate with viscous dissipation and a heat source. The mathematical model explaining the flow interaction of Williamson hybrid nanofluid, combining viscous dissipation, heat source, and temperature-variation thermal conductivity and viscosity, is created using conservation laws. The specified system of non-linear coupled partial differential equations undergoes non-similarity transformation. The resulting non-dimensional model is solved using the bivariate spectral weighted residual method. The accuracy of the method is proven by comparing obtained results with those in the literature, and a good agreement is observed. Graphs are utilized to explain the thermophysical properties that are being considered. The results show that the fluid temperature rises when there is a source of heating and viscous dissipation. The velocity and the fluid parameter ( W e ) have an inverse connection, whereas the temperature of the fluid has the opposite impact. Moreover, when nanoparticles are present, the thermal boundary layer rises along with the nanoparticles, thickening the velocity boundary layer and decreasing fluid velocity. Findings also show that for the V d ∈ [ 0 . 1 , 0 . 5 ] , the skin drag force and Nusselt number retard by 0 . 64 % , 14 . 06 % for the shrinking sheet and 0 . 21 % , 6 . 57 % for the stretching sheet respectively. In the same vein, an 100% surge in the porosity parameter escalate the skin friction coefficient by 19.13% and 26.91% and the Nusselt number by 4.92% and 2.06% repsectively for both the contracting and elastic sheet. The findings in the research will provide more insight in the design and improvement of solar panel plate efficiency.
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DOI: 10.1016/j.ijft.2024.100892
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