The effects of viscous dissipation on heat transfer to power law fluids in arbitrary cross-sectional ducts

In this paper, the analytical study of forced convection heat transfer to power-law fluids in arbitrary cross-sectional ducts with finite viscous dissipation is undertaken. Both the flow and heat transfer develop simultaneously from the entrance of the duct the walls of which are maintained at a constant temperature different from the entering fluid temperature. The governing conservation equations written in curvilinear coordinates are solved using the Line-Successive-Over relaxation (LSOR) method. Numerical results of dimensionless heat transfer coefficients and temperature profiles are presented for the trapezoidal, triangular, circular and square ducts. For cooling, viscous dissipation generally augments heat transfer. At low values of Brinkman number (Br∼0.1), the cooling effect dominates over viscous heating in the entrance region. As Br is increased, the location where viscous dissipation becomes important shifts closer to the entrance until a value is reached for which the effect of viscous dissipation is always predominant irrespective of the axial location. When the walls are heated, for a non-zero Brinkman number, the Nu_X* distribution exhibits a singularity from the negative side of the Nu_X* axis. As the power-law index increases, the position of this singularity shifts closer to the entrance of the duct. Far downstream of the duct, for a fixed n, Nu_X* attains an asymptotic value which is independent of Br and is at least thrice that for forced convection without viscous dissipation.