Numerical solutions for unsteady laminar boundary layer flow and heat transfer over a horizontal sheet with radiation and nonuniform heat Source/Sink

This paper investigates the unsteady laminar boundary layer flow and heat transfer over a horizontal sheet subjected to radiation and a nonuniform heat source/sink. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and solved via the bvp4c numerical method. The key findings indicate that increasing the unsteadiness parameter leads to a reduction in both velocity profiles and heat flux, while higher values of the Prandtl number reduce thermal boundary layer thickness. In contrast, the radiation and magnetic parameters enhance the temperature profile within the boundary layer. The study offers new insights into the effects of flow parameters on boundary layer behaviour, validated through table and graphical comparisons with existing literature. These findings provide practical approaches for optimizing heat transfer systems in engineering applications. • Investigates unsteady laminar boundary layer flow and heat transfer over a horizontal sheet. • Incorporates nonuniform heat source/sink effects and radiation in the mathematical model. • Utilizes the bvp4c numerical method to solve transformed ordinary differential equations. • Examines the impact of key parameters: unsteadiness, Prandtl number, radiation, and magnetic field. • Provides practical insights for optimizing thermal management in engineering systems.