Numerical Analysis of Compressible Boundary Layer Flow with Heat Transfer and Pressure Gradient

In this paper, numerical solution of similarity equations for compressible laminar boundary layer flow considering heat transfer and arbitrary pressure gradienthas been undertaken. These equations have been solved upon the assumption of small difference in viscosity, and having a Prantle number of 1 for Falkner-Skan typecompressible flow. Since similarity equations of momentum and energy of the flow are coupled anddependent on each other, they have to be solvedsimultaneously. The numerical technique applied in this work is fourth order Runge-Kutta method for ordinarydifferential equations using shooting method for governing boundary conditions which have to be solved iteratively to reach convergence. Obtained results showthat for favorable pressure gradient (negative pressure gradient), there is no separation in the flow neither for hot wall nor for the cold one. It also supports the factthat unfavorable pressure gradient (positive pressure gradient) is a necessity for separation but there is a difference between two obtained face angles that causeseparation in these two face conditions. As heat transfer in boundary layer from wall to the fluid causediscontinuity in the velocity profile and increase the tendency of backflow, this angle is less for hot wall compared to the cold one. Also, the problem has beensimulated using the FluentTM code and the numerical results are compared by the results of Fluent, to validate the each other.

Keywords:

Compressible Laminar Boundary Layer , Similarity Equations , Pressure Gradient , Heat Wall and Cold Wall , Separation