Importance of convective boundary layer flows with inhomogeneous material properties under linear and quadratic Boussinesq approximations around a horizontal cylinder

This study investigates boundary layer flows with inhomogeneous material properties driven by natural convection using linear and quadratic Boussinesq approximations around a horizontal cylinder. The cylinder's surface was kept at a uniform temperature. The governing equations for the setup were formulated from the principles of mass continuity, momentum and energy under realistic assumptions. Four coupled partial differential equations were obtained and reduced using stream function to two. Using perturbation techniques with one spatial coordinate as the perturbation parameter, the partial differential equations were further reduced to a set of nonlinear coupled ordinary differential equations. The fluid's velocity, as well as the temperature distributions, were computed and analyzed using the Maple 17 platform. The results obtained were consistent with existing results from reference literature. Further analysis of the embedded flow parameters was also carried out and analyzed with relevant tables and graphical illustrations for the linear and quadratic Boussinesq approximations. The results of the study show a fundamental difference between the linear and quadratic Boussinesq approximation alongside an interconnection between constant and variable thermophysical properties.