<p>Researchers are motivated to understand the behavior and properties of hybrid nanofluids due to their wide range of applications. For example, unsteady hybrid nanofluid flow can occur in marine propellers, hydrofoil flutters, rotor blades, and turbomachines. This study examines the unsteady mixed convection flow of a hybrid nanofluid over a radially shrinking disk. The time-dependent governing partial differential equations and associated boundary conditions are formulated and transformed into a system of non-linear ordinary differential equations using similarity transformations. These equations are solved numerically using MATLAB’s bvp4c function. Two solutions are obtained, and a stability analysis confirms that only the first solution is stable. In this flow problem, increasing both the Biot number and the mixed convection parameter increases the local Nusselt number and local skin friction coefficient. Increasing the mixed convection parameter from its lowest to highest considered values leads to increases of 113% and 353% in the physical quantities of interest, indicating its significant influence. However, increasing the magnitude of the unsteadiness parameter reduces the local skin friction coefficient while enhancing the local Nusselt number. Response surface methodology (RSM) reveals that the mixed convection parameter has a more significant effect on heat transfer enhancement than the Biot number. With a desirability of 100%, the local Nusselt number is maximized when the mixed convection parameter and Biot number are at their highest levels, while the unsteadiness parameter is at its lowest level (i.e., <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha =-0.7, Bi=0.7,\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda =1.5\)</EquationSource> </InlineEquation>). Meanwhile, the local skin friction coefficient is minimized when these parameters are at their lowest levels (i.e., <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha =-0.7, Bi=0.3,\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\lambda =0.5\)</EquationSource> </InlineEquation>). At these optimal conditions, the local sensitivity analysis suggests that the local Nusselt number is most sensitive to the Biot number, whereas the local skin friction coefficient is most sensitive to the mixed convection parameter.</p>

Optimization of unsteady mixed convection axisymmetric hybrid nanofluid flow over a radially shrinking disk with convective boundary condition

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发表日期：

2026年5月23日

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Rusya Iryanti Yahaya,
Norihan Md Arifin,
Ioan Pop,
Fadzilah Md Ali,
Siti Suzilliana Putri Mohamed Isa

摘要

Researchers are motivated to understand the behavior and properties of hybrid nanofluids due to their wide range of applications. For example, unsteady hybrid nanofluid flow can occur in marine propellers, hydrofoil flutters, rotor blades, and turbomachines. This study examines the unsteady mixed convection flow of a hybrid nanofluid over a radially shrinking disk. The time-dependent governing partial differential equations and associated boundary conditions are formulated and transformed into a system of non-linear ordinary differential equations using similarity transformations. These equations are solved numerically using MATLAB’s bvp4c function. Two solutions are obtained, and a stability analysis confirms that only the first solution is stable. In this flow problem, increasing both the Biot number and the mixed convection parameter increases the local Nusselt number and local skin friction coefficient. Increasing the mixed convection parameter from its lowest to highest considered values leads to increases of 113% and 353% in the physical quantities of interest, indicating its significant influence. However, increasing the magnitude of the unsteadiness parameter reduces the local skin friction coefficient while enhancing the local Nusselt number. Response surface methodology (RSM) reveals that the mixed convection parameter has a more significant effect on heat transfer enhancement than the Biot number. With a desirability of 100%, the local Nusselt number is maximized when the mixed convection parameter and Biot number are at their highest levels, while the unsteadiness parameter is at its lowest level (i.e., \(\alpha =-0.7, Bi=0.7,\) and \(\lambda =1.5\) ). Meanwhile, the local skin friction coefficient is minimized when these parameters are at their lowest levels (i.e., \(\alpha =-0.7, Bi=0.3,\) and \(\lambda =0.5\) ). At these optimal conditions, the local sensitivity analysis suggests that the local Nusselt number is most sensitive to the Biot number, whereas the local skin friction coefficient is most sensitive to the mixed convection parameter.