ANALYTICAL SOLUTIONS OF FULLY DEVELOPED FLOW AND HEAT TRANSFER OF A FOURTH GRADE FLUID IN A CHANNEL

. In this paper, heat transfer of a fully developed steady flow of a fourth grade non-Newtonian fluid with constant properties between two stationary parallel plates has been taken into consideration taking into account the viscous dissipation term. The momentum equation was analytically solved and the average velocity (um) and thus an implicit correlation for pressure gradient (A) were obtained. By applying the velocity profile, the energy equation was also analytically solved for uniform wall heat flux. To illustrate the viscous dissipation effects, the temperature distribution and Nusselt numbers are analytically determined. It was observed that they are strongly under the influence of non-Newtonian parameter (B*) and the modified Brinkman number (Brq).

Keywords:

Fourth grade fluid , Viscous dissipation , Fully developed , Channel