Abstract
The temperature difference of the various applications such as microchannel heat exchangers, microelectronics, solar collectors, automotive systems, micro fuel cells, and microelectromechanical systems (MEMS) is relatively large. The buoyancy force (mixed convection) modeled by the conventional Boussinesq approximation is inadequate since the density of the operating fluids fluctuates non-linearly with the temperature difference. Therefore, the mixed non-linear convective transport of the flow of Cross fluid through three different geometric aspects (horizontal, vertical, and inclined) of the microchannel under the non-linear Boussinesq (NBA) approximation is investigated. Mechanisms of internal heat source, Rosseland radiative heat flux, and frictional heating are incorporated into the thermal analysis. The mathematical construction is proposed using the Cross fluid model for a steady-state, and subsequent non-linear differential equations are deciphered by the spectral quasi-linearization method (SQLM). Graphical sketches were constructed and displayed that explore the stimulus of various key parameters on Bejan number, velocity, temperature, and entropy generation. It is found that the Bejan number and entropy production improved due to the non-linear density temperature variation. The convective heating boundary conditions augment the entropy production. The pressure gradient accelerates the transport of fluid in a microchannel. Furthermore, among three different geometries, the velocity, entropy production, and temperature are the highest for the vertical microchannel.