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The present study focuses on the effects of viscous dissipation and axial heat conduction on the asymptotic behavior of the laminar forced convection in a circular duct for a Herschel-Bulkley fluid with variable wall heat flux. Analytical asymptotic solutions are presented for the case of axial variations of the wall heat flux, with finite non-vanishing values at infinity along the flow direction. The asymptotic bulk and mixing Nusselt numbers and the asymptotic bulk and mixing temperature distributions are evaluated analytically in the case of axially variable wall heat flux for which polynomial and logarithmic functions are considered as examples. It is shown that the asymptotic bulk Nusselt number depends on the dimensionless radius of the plug flow region a, on the power-law exponent n, on the Peclet number Pe and the asymptotic Brinkman number BBBB∞. The effects of yield stress, Peclet number, and Brinkman number on the asymptotic bulk Nusselt number are discussed.

frontiers in heat and mass transfer

EFFECTS OF VISCOUS DISSIPATION AND AXIAL HEAT CONDUCTION ON FORCED CONVECTION FLOW OF HERSCHEL-BULKLEY FLUID IN CIRCULAR DUCT WITH AXIALLY VARIABLE WALL HEAT FLUX