<p>This study aims to analyze how convective boundary conditions, electro-periodic magnetohydrodynamics (EPMHD), and activation energy influence flow dynamics, with a comparative assessment of linear versus nonlinear thermal radiation. Assuming a steady, laminar, two-dimensional boundary layer flow, the governing equations are transformed into a system of ordinary differential equations (ODEs) through an appropriate transformations and solving numerically with MATLAB’s <i>bvp4c</i> solver. To eliminate the dependence of parameters (such as the Grashof number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$G_r$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>) on independent variables, a non-similar method has been employed. In this method, a new variable <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathsf {\xi }$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ξ</mi> </math></EquationSource> </InlineEquation> is introduced under the assumption that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathsf {\xi } \le 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ξ</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. The effects of dimensionless parameters are examined by analyzing graphical representations of velocity, temperature, concentration, and microorganism distributions. The key physical quantities investigated at the surface include the skin friction coefficient (indicates surface resistance to fluid flow), the local Nusselt number (representing the rate of heat transfer), the local Sherwood number (representing the rate of mass transfer), and the density of motile microorganisms (which reflects the rate of concentration of microbes). Numerical results indicate that the application of electro-periodic magnetic and electric fields significantly intensifies shear forces, with the skin friction coefficient increasing by more than a factor of two compared to the case without electromagnetic effects. Magnetic fields reduce fluid velocity via Lorentz forces, while electric fields enhance motion through electrokinetic effects. Stronger magnetic field also increase thermal energy, nanoparticle levels, and the density of microbes. Result validation through comparison with published literature confirms the accuracy and reliability of the numerical approach. Graphical illustrations combined with parametric evaluations provide a comprehensive understanding of how key physical parameters influence flow dynamics, thermal characteristics, and the distribution of microorganisms. A novel contribution of the current study is made by investigating the combined effects of electro-periodic magnetohydrodynamics (EPMHD), nonlinear thermal radiation, and convective boundary conditions on the flow dynamics and heat transfer of a nanofluid containing gyrotactic microorganisms. The current study enhances the understanding of nanofluid dynamics and bioconvection under complex physical conditions, with potential applications in bioengineering, energy systems, and environmental technologies.</p>

Thermal convection, electro-periodic MHD, and gyrotactic effects on a fluid flow over a stretching surface

期刊论文
发表日期：

2025年9月6日

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Khansa Hanif,
M. Asif Farooq

摘要

This study aims to analyze how convective boundary conditions, electro-periodic magnetohydrodynamics (EPMHD), and activation energy influence flow dynamics, with a comparative assessment of linear versus nonlinear thermal radiation. Assuming a steady, laminar, two-dimensional boundary layer flow, the governing equations are transformed into a system of ordinary differential equations (ODEs) through an appropriate transformations and solving numerically with MATLAB’s bvp4c solver. To eliminate the dependence of parameters (such as the Grashof number $G_r$ $G_{r}$ ) on independent variables, a non-similar method has been employed. In this method, a new variable $\mathsf {\xi }$ $ξ$ is introduced under the assumption that $\mathsf {\xi } \le 1$ $ξ \leq 1$ . The effects of dimensionless parameters are examined by analyzing graphical representations of velocity, temperature, concentration, and microorganism distributions. The key physical quantities investigated at the surface include the skin friction coefficient (indicates surface resistance to fluid flow), the local Nusselt number (representing the rate of heat transfer), the local Sherwood number (representing the rate of mass transfer), and the density of motile microorganisms (which reflects the rate of concentration of microbes). Numerical results indicate that the application of electro-periodic magnetic and electric fields significantly intensifies shear forces, with the skin friction coefficient increasing by more than a factor of two compared to the case without electromagnetic effects. Magnetic fields reduce fluid velocity via Lorentz forces, while electric fields enhance motion through electrokinetic effects. Stronger magnetic field also increase thermal energy, nanoparticle levels, and the density of microbes. Result validation through comparison with published literature confirms the accuracy and reliability of the numerical approach. Graphical illustrations combined with parametric evaluations provide a comprehensive understanding of how key physical parameters influence flow dynamics, thermal characteristics, and the distribution of microorganisms. A novel contribution of the current study is made by investigating the combined effects of electro-periodic magnetohydrodynamics (EPMHD), nonlinear thermal radiation, and convective boundary conditions on the flow dynamics and heat transfer of a nanofluid containing gyrotactic microorganisms. The current study enhances the understanding of nanofluid dynamics and bioconvection under complex physical conditions, with potential applications in bioengineering, energy systems, and environmental technologies.