Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet

Abstract

Convective heat transfer of non-Newtonian fluids within a thin liquid film on an unsteady stretching sheet is investigated, taking into consideration the viscous dissipation effect. Results for the temperature distribution, the free-surface temperature, and the wall temperature gradient are illustrated at selected values of the unsteadiness parameter, the power-law index, and Eckert number for a wide range of the generalized Prandtl number, ranging from 0.001 to 1000. Also, new results for the velocity profiles, the free-surface velocity, and the wall shear stress are presented. The deviation from Newtonian behavior on the variation of the horizontal velocity component across the liquid film is observed more significant than that reported in the previous investigation. As compared to the case where viscous dissipation is neglected, the dimensionless fluid temperature is found to increase when the fluid is being heated but to decrease when the fluid is being cooled. For the fluid heating case, the dimensionless fluid temperature decreases monotonically in the vertical direction; while for the fluid cooling case it decreases rapidly at first, reaches a minimum value, and then increases more gradually to its free-surface value. The wall temperature gradient takes a higher value for a negative Eckert number but a lower value for a positive Eckert number, as compared to the case without viscous dissipation. The effects of positive or negative Eckert numbers on heat transfer are found to be more pronounced for higher generalized Prandtl numbers.