Analytical solution to boundary layer flow and convective heat transfer for low Prandtl number fluids under the magnetic field effect over a flat plate

Abstract

The present study aims to quantify the flow field, flow velocity, and heat transfer features over a horizontal flat plate under the influence of an applied magnetic field, with a particular emphasis on low Prandtl number fluids. Nonlinear partial differential expressions can be incorporated into the ordinary differential framework with the use of appropriate transformations. This research utilizes the variational iteration method (VIM) to approximate solutions for the system of nonlinear differential equations that define the problem. The objective is to demonstrate superior flexibility and broader application of the VIM in addressing heat transfer issues, compared to alternative approaches. The results obtained from the VIM are compared with numerical solutions, revealing a significant level of accuracy in the approximation. The numerical findings strongly suggest that the VIM is effective in providing precise numerical solutions for nonlinear differential equations. The analysis includes an examination of the flow field, velocity, and temperature distribution across various parameters. The study found that improving temperature patterns, velocity distribution, and flow dynamics were all positively impacted by increasing the Prandtl numbers. As a result, this leads to the thickness of the boundary layer to decrease and improves heat transfer at the moving surface. Thus, the convection process becomes more efficient. When the strength of the magnetic field is increased, the velocity of the fluid decreases. This observation aligns with expectations since the magnetic field hampers the natural flow of convection. Notably, the convection process can be precisely controlled by carefully applying magnetic force.