Mathematical models for free and mixed convection boundary layer flows of micropolar fluids

Abstract

The phenomena of free and mixed convection are encountered in many industrial and engineering applications, for example, in the cooling of electronic equipment, materials processing and drilling operations. Free convection has also been used to explain the connection between skin disease and respiratory disease such as eczema and asthma. In this study, the mathematical models for steady laminar free and mixed convection boundary layer flows over a horizontal circular cylinder and a sphere immersed in an incompressible micropolar fluid are developed. The theory of micropolar fluid was proposed, as the classical Navier-Stokes theory is inadequate to describe most industrial fluids. Examples of micropolar fluids include polymeric fluids and colloidal suspensions that take into account the microscopic effects arising from the local structures and micromotions of the fluid elements. Both isothermal and nonisothermal boundary conditions are considered. The governing nonlinear partial differential equations are first transformed using an appropriate nonsimilar transformation before they are solved numerically using the Keller-box method, an unconditionally stable implicit finite-difference scheme. Numerical results presented include the velocity, temperature and angular velocity profiles as well as the fluid flow and heat transfer characteristics, for a range of the material parameter or the vortex viscosity K, the Prandtl number Pr, and the mixed convection parameter A. The numerical codes in the form of software packages have been developed using Matlab@. The packages and numerical results presented constitute an invaluable reference against which other exact or approximate solutions can be compared in the future.