Fractional Stochastic Magnetohydrodynamic Natural Convection Flow in a Porous Vertical Annulus with Variable Thermal Conductivity: An Analytical Study Using the Polynomial Approximation Method

Fractional Stochastic Magnetohydrodynamic Natural Convection Flow in a Porous Vertical Annulus with Variable Thermal Conductivity: An Analytical Study Using the Polynomial Approximation Method

Fractional Stochastic Magnetohydrodynamic Natural Convection Flow in a Porous Vertical Annulus with Variable Thermal Conductivity: An Analytical Study Using the Polynomial Approximation Method

^1*MKPEDEM K. A; ²OLAYIWOLA R.O; ³FADEPO J. T
1. *Department of Mathematics, University of Abuja, Nigeria.
2. Department of Industrial Mathematics, Federal University of Science and Technology, Minna, Niger State, Nigeria.
3. Department of Industrial Mathematics, Federal University of Science and Technology, Minna, Niger State, Nigeria.
Corresponding author: *kufremkpedem@gmail.com, olayiwola.rasaq@Futminna.edu.ng, fadepoj@gmail.com

 Abstract
This study investigates the fractional stochastic magnetohydrodynamic (MHD) natural convection flow of an electrically conducting viscous fluid in a porous vertical annulus with variable thermal conductivity. The model incorporates the effects of buoyancy, magnetic field, porous medium permeability, thermal conductivity variation, and stochastic disturbances. To account for memory effects, the governing momentum and energy equations are formulated using the Caputo-Fabrizio fractional derivative operator. The resulting system of fractional partial differential equations is transformed into a dimensionless form and solved analytically using the Polynomial Approximation Method (PAM). Approximate analytical expressions for the velocity and temperature distributions are obtained. The influence of key physical parameters, including the Hartmann number, Grashof number, Darcy number, Prandtl number, and fractional parameter, is examined graphically. The results reveal that the magnetic field suppresses fluid motion, whereas buoyancy and permeability enhance both velocity and heat transfer. Furthermore, fractional memory effects significantly influence the transport characteristics. The developed model provides valuable insight into thermal transport processes in porous engineering and energy systems.

Keywords: Fractional magnetohydrodynamics (MHD), Natural convection, Porous vertical annulus, Variable thermal conductivity, Caputo–Fabrizio fractional derivative

DOI: https://doi.org/10.46654/sjstrd.v1n6.16062