Abstract
The present numerical study deals with the analysis of thermal characteristics during the flow of an incompressible Herschel-Bulkley fluid of constant physical and rheological properties. The flow takes place within a pipe, of circular cross section, maintained at uniform wall temperature. Because of the viscous character of this kind of fluid, viscous dissipation is taken into account. The effect of this parameter is analyzed for various values of the fluid index flow and the Herschel-Bulkley number. The governing equations are resolved by means of the finite volume method and using the SIMPLER algorithm and the line by line method. The results reveal that heat transfer is significantly underestimated when viscous dissipation is neglected, particularly for shear-thinning fluids and for high values of the Herschel-Bulkley number. In addition, heat transfer is more important in the case of heating and the curves display a discontinuity, and negative values of Nusselt number are obtained.
Highlights
The general model of Herschel-Bulkley describes a large variety of natural and industrial fluids such as lavas, avalanche, ketchup [1], yoghurt [2], Carbopol 940 [3], waxy crude oil [4] and cement grouts [5]
Our contribution focuses on the effect of neglecting viscous dissipation when dealing with a Herschel-Bulkley fluid flow within a circular pipe maintained at uniform wall temperature
We consider in the present paper the laminar steady flow of an incompressible Herschel-Bulkley fluid through a circular pipe of length L and diameter D maintained at constant wall temperature Tw (Fig. 1)
Summary
The general model of Herschel-Bulkley describes a large variety of natural and industrial fluids such as lavas, avalanche, ketchup [1], yoghurt [2], Carbopol 940 [3], waxy crude oil [4] and cement grouts [5]. The author considered the laminar heat transfer of a Herschel-Bulkley fluid in the entrance region of a square duct assuming fully developed velocity profile. He found that the Nusselt number decreases with the increase of the flow index and increases with the increase of both yield stress and Brinkman number. Our contribution focuses on the effect of neglecting viscous dissipation when dealing with a Herschel-Bulkley fluid flow within a circular pipe maintained at uniform wall temperature. This investigation was motivated by the fact that only few papers deal with. We consider, for this purpose, a wide range of flow index ranging from 0.4 to 2.0 in order to draw abacuses illustrating heat transfer performances within the pipe
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