Journal of Advances in Mathematics and Computer Science

This study numerically investigates the effects of variable viscosity and thermal conductivity on natural convection flow along a vertical flat plate with Joule heating and heat generation. Using the implicit finite difference method, specifically the Crank-Nicolson scheme, this work solves the dimensionless governing equations derived from the two-dimensional, laminar, and unsteady boundary layer equations. The study focuses on viscous incompressible fluids where both thermal conductivity and viscosity are temperature-dependent. Key findings from the research include detailed insights into how these variable properties influence fluid dynamics and heat transfer processes. Notably, increased thermal conductivity results in up to a 15% increase in local Nusselt numbers, indicating enhanced heat transfer rates. Conversely, reductions in viscosity lead to lower skin friction coefficients, suggesting less resistance to flow and potentially higher flow rates. The study also demonstrates variable effects on temperature profiles and velocity fields, where higher thermal conductivity correlates with higher overall temperatures and velocities across the studied range. These results, displayed through comprehensive tables and graphs, provide a significant contribution to the understanding of complex interactions in natural convection flows and offer practical insights for optimizing thermal management systems in engineering applications. Comparisons with existing studies affirm the validity of the numerical approaches used and the relevance of the findings to ongoing research in thermal sciences.