<p>The present study elucidates the influence of transpiration in a uniform shear flow over a stretching/shrinking surface of a Powell–Eyring fluid in the presence of thermal radiation. Owing to the strong nonlinearity of the governing partial differential equations, exact analytical solutions are not feasible. Consequently, Lie group analysis is employed to derive appropriate similarity transformations, reducing the system to a set of ordinary differential equations. These transformed equations are solved numerically using MATLAB’s ‘bvp4c’ solver. The results reveal the existence of dual solution branches for both stretching and shrinking surfaces over a wide range of material and transpiration parameters. Although both solutions satisfy the mathematical requirements, they exhibit distinct velocity and temperature characteristics. A linear temporal stability analysis is conducted to identify the physically realizable solution, demonstrating that the first solution branch is stable and hence physically meaningful. Furthermore, multiple linear regression analysis is performed to establish predictive relationships between key physical quantities and the governing parameters. The regression models exhibit excellent predictive performance, with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$R^2 > 0.999$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>></mo> <mn>0.999</mn> </mrow> </math></EquationSource> </InlineEquation> in all cases, indicating strong statistical correlations. It is observed that the fluid velocity and temperature decrease in the first solution branch with increasing suction parameter (<i>S</i>). In contrast, increasing the Powell–Eyring parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(\epsilon )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>ϵ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> enhances the fluid velocity while reducing the fluid temperature in the first solution branch. The effects of the controlling parameters on the physical quantities, velocity and thermal fields are discussed in detail through graphical and tabular presentations.</p>

Similarity solutions, stability, and regression analysis of radiative Powell–Eyring fluid under uniform shear flow

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2026年6月29日

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Sradharam Swain,
Golam Mortuja Sarkar

摘要

The present study elucidates the influence of transpiration in a uniform shear flow over a stretching/shrinking surface of a Powell–Eyring fluid in the presence of thermal radiation. Owing to the strong nonlinearity of the governing partial differential equations, exact analytical solutions are not feasible. Consequently, Lie group analysis is employed to derive appropriate similarity transformations, reducing the system to a set of ordinary differential equations. These transformed equations are solved numerically using MATLAB’s ‘bvp4c’ solver. The results reveal the existence of dual solution branches for both stretching and shrinking surfaces over a wide range of material and transpiration parameters. Although both solutions satisfy the mathematical requirements, they exhibit distinct velocity and temperature characteristics. A linear temporal stability analysis is conducted to identify the physically realizable solution, demonstrating that the first solution branch is stable and hence physically meaningful. Furthermore, multiple linear regression analysis is performed to establish predictive relationships between key physical quantities and the governing parameters. The regression models exhibit excellent predictive performance, with $R^2 > 0.999$ $R^{2} > 0.999$ in all cases, indicating strong statistical correlations. It is observed that the fluid velocity and temperature decrease in the first solution branch with increasing suction parameter (S). In contrast, increasing the Powell–Eyring parameter $(\epsilon )$ $(ϵ)$ enhances the fluid velocity while reducing the fluid temperature in the first solution branch. The effects of the controlling parameters on the physical quantities, velocity and thermal fields are discussed in detail through graphical and tabular presentations.