This study investigates boundary layer natural convection over a vertical plate subject to low-pressure gradients and viscous dissipation using the Variational Iteration Method (VIM). The governing nonlinear partial differential equations are transformed into a coupled system of ordinary differential equations via similarity transformations. Key physical parameters such as the Prandtl number Eckert number  and pressure gradient  are considered in detail. The results obtained using VIM are validated against numerical solutions, showing excellent agreement with relative errors as low as 0.18% for temperature profiles at higher Prandtl numbers. Comparative analysis with other semi-analytical methods including the Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and Semi-Analytical Decomposition Method (SADM) demonstrates that VIM offers superior convergence, computational efficiency, and accuracy in capturing velocity and temperature gradients. Notably, increasing Pr reduces thermal boundary layer thickness, while higher Ec values elevate temperature profiles due to viscous dissipation. The study confirms that VIM is a robust and efficient method for solving nonlinear convective heat transfer problems relevant to thermal system design and optimization in engineering applications.

convective heat transfer, Variational Iteration Method (VIM), nonlinear equations, Numerical Method (NM), pressure gradient, viscous dissipation