Flow and Heat Transfer of Bingham Plastic Fluid over a Rotating Disk with Variable Thickness

Abstract

Abstract This paper studies the steady flow and heat transfer of Bingham plastic fluid over a rotating disk of finite radius with variable thickness radially in boundary layer. The boundary layer flow is caused by the rotating disk when the extra stress is greater than the yield stress of the Bingham fluid. The analyses of the velocity and temperature field related to the variable thickness disk have not been investigated in current literatures. The governing equations are first simplified into ordinary differential equations owing to the generalized von Kármán transformation for seeking solutions easily. Then semi-similarity approximate analytical solutions are obtained by using the homotopy analysis method for different physical parameters. It is found that the Bingham number clearly influences the velocity field distribution, and the skin friction coefficient C fr is nonlinear growth with respect to the shape parameter m. Additionally, the effects of the involved parameters (i.e. shape parameter m, variable thickness parameter β, Reynolds number Re v , and Prandtl number Pr) on velocity and temperature distribution are investigated and analyzed in detail.