Heat Transfer in Laminar Flow of a Herschel-Bulkley Fluid between Parallel Plates

Abstract

In this work, the heat transfer, subject to the effect of viscous dissipation, in a laminar fully-developed flow of a Herschel-Bulkley fluid between parallel plates was analyzed analytically. Both constant and asymmetric wall heat fluxes are considered. For a power-law index, n, higher than 0.5 the average calorific power generated by viscous effects only depends on the ratio between the fluid yield and wall stresses, c. In dimensional form, the temperature difference between the two walls and the temperature gradient at the duct symmetry plane, are independent of the rheological characteristics of the fluid, only depending on the fluid thermal conductivity, the distance between the walls and the difference between the wall heat fluxes. When the Brinkman number, Br*, is equal to 0.25 a singular point arises where the Nusselt numbers, Nu, remains constant and equal to 4 regardless of the values of n, c and wall heat fluxes. This behavior can be explained by the competing effects of n or c on the heat transfer. While decreasing n or increasing c increases the value of Nu for Br*<0.25 and decreases it for Br*>0.25, an increase in the Brinkman number always decreases the Nusselt number.