Journal of Advances in Mathematics and Computer Science

The present study investigates the combined effects of thermal relaxation and magnetic field on the transport characteristics of an electrically conducting fluid using the modified Fourier law, namely the Cattaneo–Christov heat-flux model. Unlike the classical Fourier formulation, the proposed model accounts for finite thermal propagation speed and eliminates the paradox of instantaneous heat transfer. The governing nonlinear partial differential equations describing the momentum and energy transport are transformed into a coupled system of nonlinear ordinary differential equations through appropriate similarity transformations. The resulting boundary value problem is solved numerically using the bvp5c scheme. A detailed parametric analysis is performed to examine the influence of the magnetic parameter, Prandtl number, Eckert number, thermal stratification parameter, material parameter, and thermal relaxation parameter on the velocity, temperature, and microrotation profiles. The results reveal that an increase in the thermal relaxation parameter significantly suppresses the temperature distribution and reduces the local Nusselt number, indicating delayed thermal response within the fluid. Furthermore, the magnetic field is found to decelerate the fluid motion due to the Lorentz force, while enhancing thermal energy accumulation. A comparative analysis between the classical Fourier and Cattaneo–Christov heat-flux models highlights notable deviations in thermal behavior, particularly at higher relaxation times. The numerical results are validated through comparison with existing literature for limiting cases, demonstrating excellent agreement. The present findings provide deeper physical insight into non-Fourier heat transport mechanisms and are relevant to advanced thermal systems involving high-frequency heating, micro–nano scale transport, and energy conversion devices.