Integral Transform Solution for the Forced Convection of Herschel-Bulkley Fluids in Circular Tubes and Parallel-Plates Ducts

Abstract

The thermal entry region in laminar forced convection of Herschel-Bulkley fluids is solved analytically through the integral transform technique, for both circular and parallel-plates ducts, which are maintained at a prescribed wall temperature or at a prescribed wall heat flux. The local Nusselt numbers are obtained with high accuracy in both developing and fully-developed thermal regions, and critical comparisons with previously reported numerical results are performed

Thermal development of the laminar flow of a Bingham fluid between two plane plates with viscous dissipation

“…However, the comparison between our results and those resulting from the analytical study carried out by Quaresma and Macêdo [29] (seen Table 5), has shown a deviation in our friction factor values not exceeding 0.4%. This deviation can be argued by the difference existing in the limit of weak shearing between the continuous viscoplastic equation (Eq.…”

“…We thus note that the increase in Re causes Table 5 Friction factor (f Re) for various values of the Bingham number. (,) present work, (*) Quaresma and Macêdo [29]. a lengthening of the development length, an effect which is substantially reduced by the existence of a yield shear stress.…”

“…This deviation can be argued by the difference existing in the limit of weak shearing between the continuous viscoplastic equation (Eq. (5)) used in the present work and the ideal Bingham model (IBM) considered by [29]. Fig.…”

Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

“…It is the Generalized Integral Transform Technique -GITT [3], a method which has been used successfully to solve several diffusive problems such as those dealing with the flow in ducts with irregular geometries [4,5], with time varying coefficients and problems involving space dependence for the boundary conditions [6,7], problems with thermally and hydrodynamically developing flows [8,9], diffusive problems involving moving boundaries [10,11], problems of non-Newtonian fluid flows [12,13], among others.…”

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

“…However, the Graetz problem has been extended over problems that focus on turbulent flows [33,[41][42][43][44][45][46], slip flows [7,16,20,37], non-Newtonian flows [9][10][11][12]23,24,27,31,34,38], and forced convection in a porous medium [18,25,[27][28][29] and that include streamwise heat conduction [5,16,18,19,[23][24][25]28,29,39,[41][42][43][44][45][46], and viscous dissipation [1][2][3][4]9,10,16,18,[...…”