GENERALIZED NUMERICAL SOLUTION OF BOUNDARY LAYER FLOW OF THIN GRAY FLUIDS

Abstract

Since the physical description of the boundary layer by Ludwig Prandtl in 1905, there have been many developments in this field. There have been many seminal works on boundary layer flows of thin Gray fluids with linear thermal radiations. Radiation effects in the boundary layer flow where temperature difference between the surface temperature and ambient temperature is very small have been studied and their linearized solution have been found out. The goal of this research is to find out a generalized numerical solution which will give results for all temperature differences i.e. for both the cases when 𝜃𝑤=1 ( Linear Radiations ) and for 𝜃𝑤>1 ( Non-Linear Radiations). Firstly, the two dimensional boundary layer equations for fluid flow and heat transfer of thin Gray fluid over a moving flat plate are presented. The job is then extended for three dimensional rotating flow of thin Gray fluid over a stretching surface. The systems of governing partial differential equation are converted into highly non-linear ordinary differential equations by introducing appropriate similarity transformations. By using bvp4c process, the governing ordinary differential equations are solved numerically, and the effects of the related parameters of practical importance are studied. The results of the research conclude that the non-dimensional parameter temperature ratio parameter 𝜃𝑤 shows thinness in boundary layer in both 2D and 3D flows. The Radiational effects are strengthen as 𝜃𝑤 becomes greater than 1.The rotating and stretching rates ratio parameter 𝜆 showed decrease in boundary layer by 2.46 % and velocity ratio 𝛾 showed decrease by 10.27 % . Prandtl number 𝑃𝑟 and Radiation Parameter 𝑅𝑑 show same effects when there is an increment in their values, thermal boundary layer thickness increases by 103.3 % and 336.6% in the case of 𝑅𝑑 .