Semi‐Analytical Verification of MHD Jeffrey Fluid Flow With Heat Source and Chemical Reaction via Shehu‐HPM and Elzaki‐HPM

ABSTRACT

This study investigates steady magnetohydrodynamic (MHD) free‐convective Jeffrey fluid flow with heat source and chemical reaction effects over an exponentially stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using suitable similarity transformations. Two semi‐analytical approaches, namely, the Shehu transform homotopy perturbation method (Shehu‐HPM) and the Elzaki transform homotopy perturbation method (Elzaki‐HPM), are employed to obtain approximate analytical solutions for the velocity, temperature, and concentration fields. The primary objective is to develop a dual solution framework and to assess the consistency and reliability of both transform‐based methods for nonlinear transport problems. The effects of the Hartmann number, Deborah parameter, thermal and solutal buoyancy parameters, Prandtl number, heat source parameter, Schmidt number, and chemical reaction parameter are examined in detail. The results indicate that increasing the Hartmann number suppresses the fluid velocity, whereas thermal and solutal buoyancy parameters enhance the flow field. The temperature distribution increases with the heat source parameter and decreases with the Prandtl number, while stronger chemical reactions reduce the concentration profile. A comparison with published results demonstrates excellent agreement and validates the proposed methodology. The close agreement between the Shehu‐HPM and Elzaki‐HPM solutions confirms the effectiveness of the proposed semi‐analytical framework for solving nonlinear MHD non‐Newtonian fluid flow problems involving coupled heat and mass transfer.