Joule heating effect on radiating MHD slip flow and heat transfer over an exponentially stretching permeable sheet embedded in porous medium with heat source

Department of Mathematics, Vivekananda Global University, Jaipur (Raj.), India

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Published online: 10 March 2026

Abstract

This article inquiries into the steady Joule Heating Effect on Radiating Thermal transfer and MHD slip movement across an exponentially extending permeable sheet embedded within a medium that is porous with a source of heat. Using similarity transformations, the border layer problem is formulated and transformed into a nonlinear ordinary differential equation. The Runge-Kutta fourth order approach is then used to find the numerical result using the shooting methodology. Joule heating is widely applied in domestic and industrial devices to convert electrical energy into heat, primarily using high-resistance materials like Nichrome. Major applications include heating appliances (iron, toaster, kettle, oven), safety devices (fuses), and lighting (incandescent bulbs). The impact of different physical characteristics on temperature and velocity distributions is conferred quantitatively and illustrated graphically. Heat and the flow rate rise as the Prandtl number rises Pr, mixed convection restriction λ, Suction restriction S, and exponential restriction N, while reverse effect is seen in magnetic restriction M, radiation restriction Ra, thermal slip restriction S_t, and heat Source restriction δ. Skin friction coefficient and Nusselt number both are increasing function of radiation restriction Ra, while reverse effect is seen in magnetic restriction M, and exponential restriction N. Skin friction coefficient is increasing function and Nusselt number is decresing function of restriction velocity slip restriction S_v while reverse effect is seen in radiation restriction Ra, and heat Source restriction δ.