Viscous dissipation effects on thermal entrance heat transfer to power-law fluids in arbitrary cross-sectional ducts

Abstract

The effect of viscous dissipation on forced convection heat transfer to power-law fluids in arbitrary cross-sectional ducts is examined. Both the flow and heat transfer develop simultaneously from the entrance of the duct, the walls of which are maintained at a constant temperature which is different from the entering fluid temperature. The governing conservation equations, written in curvilinear coordinates, are solved using the line successive overrelaxation (LSOR) method. Numerical results of dimensionless heat transfer coefficients are presented for the triangular, circular, trapezoidal and square ducts for several values of the Brinkman number Br and the power-law index n. For cooling (Br > 0.0), viscous dissipation generally augments heat transfer. At low values of the 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 (which is geometry dependent) is reached for which the effect of viscous dissipation is always predominant irrespective of the axial location. For heating (Br < 0.0), 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. Before the singularity, Nu x* decreases with increasing magnitude of Br, while the opposite behaviour is observed beyond the singular point. At any X*, an increase in the power-law index results in a decrease in Nu x*. Far downstream of the duct, for a fixed n, Nu x* attains an asymptotic value which is independent of Br and is at least three times that for forced convection without viscous dissipation.