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Research Paper | Mathematics | Volume 15 Issue 7, July 2026 | Pages: 1451 - 1457 | India
A Generalized Finite-Difference Framework for MHD Mixed Convection in Two Immiscible Conducting Fluids
Abstract: This paper presents a numerical investigation of steady magnetohydrodynamic (MHD) mixed convection heat transfer in a vertical parallel plate channel containing two immiscible electrically conducting fluids with variable transport properties. Such flows are encountered in thermal management systems, metallurgical processing, electronic cooling, chemical engineering, and energy conversion applications, where accurate prediction of coupled momentum and heat transfer is essential for efficient system design. A unified finite-difference numerical framework is developed by simultaneously incorporating temperature-dependent viscosity, variable thermal conductivity, thermal radiation, internal heat generation, viscous dissipation, velocity-slip, thermal-slip, and interface continuity conditions within a single mathematical formulation. The coupled nonlinear momentum and energy equations are transformed into dimensionless form and discretized using a second-order central finite-difference scheme. The resulting nonlinear algebraic equations are solved iteratively using the Gauss-Seidel method with a convergence tolerance of 10-6. A comprehensive parametric investigation is performed by varying the Grashof number, magnetic parameter, radiation parameter, heat source parameter, Eckert number, viscosity parameter, thermal conductivity parameter, velocity-slip parameter, and thermal-slip parameter to evaluate their effects on the velocity distribution, temperature distribution, wall shear stress (St-I and St-II), and local Nusselt numbers (Nu-I and Nu-II). The proposed computational framework provides a stable, accurate, and computationally efficient numerical methodology for analyzing coupled transport phenomena in immiscible MHD channel flows and offers a practical tool for the analysis and design of advanced thermal-fluid systems.
Keywords: Magnetohydrodynamic flow, Mixed convection, Immiscible fluids, Finite-difference method, Variable viscosity, Variable thermal conductivity, Thermal radiation, Internal heat generation, Velocity slip, Thermal slip, Gauss-Seidel iteration
How to Cite?: Dr. G. Kiran Kumar, "A Generalized Finite-Difference Framework for MHD Mixed Convection in Two Immiscible Conducting Fluids", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 1451-1457, https://www.ijsr.net/getabstract.php?paperid=SR26719170021, DOI: https://dx.doi.org/10.21275/SR26719170021