Heat transfer to power-law dilatant fluids in a channel with a built-in square cylinder

Abstract

In this study, heat transfer to power-law dilatant fluids from a long square cylinder (heated) confined in a channel in the steady flow regime is investigated. The effects of Reynolds number, Prandtl number and flow behavior index on the heat transfer characteristics of a cylinder is examined for the range of conditions 1 ⩽ Re ⩽ 45 , 1 ⩽ n ⩽ 2.0 and 1 ⩽ Pr ⩽ 100 (the maximum Peclet number being 4000) for a fixed blockage ratio, β = 1 / 8 . The variation of the local Nusselt number on the individual surfaces of the square obstacle for the constant wall temperature (CWT) and uniform heat flux (UHF) boundary conditions prescribed on the surface of the square obstacle are presented. Likewise, the representative isotherm plots for the two classical thermal boundary conditions are shown. The average Nusselt number and the heat transfer factor ( j h ) have also been calculated. Irrespective of the value of the flow behavior index, the value of the local Nusselt number at each corner of the square cylinder increases with an increase in the Reynolds and/or Prandtl number. The average Nusselt number increases monotonically with an increase in the Reynolds and/or the Prandtl number. Finally, simple heat transfer correlations have been provided for the range of conditions covered here.