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This study explores forced convection in a viscous, electrically conducting fluid over a stretching sheet with variable thickness. It examines the effects of a varying free stream, magnetic field, and viscous dissipation on flow and heat transfer. The governing equations for mass, momentum, and energy are converted into ordinary differential equations using similarity transformations and solved numerically with the finite difference method. The results reveal dual solutions within specific parameter ranges: one stable and aligned with natural phenomena, the other unstable with higher skin friction and velocity. Viscous dissipation significantly alters velocity and temperature profiles. These insights are valuable for optimizing flow conditions in applications such as metal sheet cooling and polymer processing.
Rai et al. (Tue,) studied this question.