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Abstract In practical engineering, heating and cooling are among the most common applications. Typically, during these processes, the heat flux to the heat transfer surface is not uniform. This study analyzes convection heat transfer between parallel plates subjected to non-uniform heat flux. The flow between the parallel plates is laminar, hydrodynamically developed, and thermally developing. A two-dimensional unsteady model is developed, and the momentum and energy equations are derived and solved numerically to obtain the velocity and temperature fields. An indigenous solver is created to solve the two-dimensional unsteady partial differential energy equation using the finite difference method. The algorithm for this solver is written in MATLAB and verified against analytical solutions. Temperature profiles are plotted and analyzed under various heat flux conditions to describe the rate of heat transfer. Local and average Nusselt numbers are calculated from the obtained temperature and velocity fields and presented graphically. This study is valuable for practical engineering applications, heating and cooling systems, and radiation calorimeters. Additionally, the development of this solver contributes to the research field of CFD simulations.
Ram Niwas Verma (Thu,) studied this question.