Nonlinear Analysis of Mixed Convection Flow With Temperature‐Dependent Suction Over a Vertical Surface

ABSTRACT Numerical study on the isothermal vertical plate, with temperature‐dependent suction as a control to the flow along the plate, studied coupled two‐dimensional, laminar mixed convection flows. Grounded on a stream function transformation, a coupled, nonlinear system of partial differential equations was first formulated and then reduced to a system of nonlinear ordinary differential equations. The boundary value problem is solved as an initial value problem using the shooting method, available in MATLAB, with iterative refinement applied to ensure accurate satisfaction of boundary conditions. The influence of Prandtl number, temperature‐dependent suction parameter, and mixed convection parameter, which are the key dimensionless parameters, are examined closely concerning the velocity and temperature profiles. Increasing the mixed convection parameter results in a significant rise of the dimensionless velocity gradient close to the surface, which reveals stronger buoyancy effects and a thicker velocity boundary layer. Despite this, the temperature profile demonstrates the contrary effect; it has a more pronounced descending slope, which is a sign of improved convective heat transfer, a sign of more active mixing of hot and cold water. Temperature‐sensitive suction parameter squeezes both the velocity and thermal boundary layers, resulting in penetrating flow and enhanced cooling efficiency. Graphical and tabular representations are thorough and provide strong support of such effects, displaying changes in skin friction and heat transfer rate in the nonlinear case. Furthermore, in association with the Prandtl number's presence, it has been illustrated that higher values associated with lower thermal diffusivity slow down momentum transport and thereby lead to the development of thinner and more stable boundary layers. The significant drop in temperature profiles at high Prandtl numbers is in favor of the argument that the heat transfer efficiency is raised because of smaller thermal diffusion.