Laminar Forced Convection Heat Transfer from a Rotating Cylinder to Power-Law Fluids

Abstract

Forced convection heat transfer from a heated cylinder rotating in streaming power-law fluids has been investigated in this work. The governing differential equations have been solved numerically to elucidate the influence of power law index (n = 0.2, 0.6, and 1), Prandtl number (1 ≤ Pr ≤ 100), Reynolds number (1 ≤ Re ≤ 40), and nondimensional rotational velocity (0 ≤ α ≤ 6) on the detailed temperature field, distribution of Nusselt number on the surface of the cylinder and on the mean Nusselt number. As expected, the mean Nusselt number shows positive dependence on both Reynolds and Prandtl numbers, which is obviously due to the gradual thinning of the boundary layer. Furthermore, the mean Nusselt number also conforms to the conventional scaling of Pr^1/3 . For a non-rotating cylinder, all else being equal, shear-thinning facilitates heat transfer. This is also true for a rotating cylinder up to Re ∼ 1 and rotational velocity α ≤ 4 for all values of Prandtl number used in this work. As the Reynolds number is increased, though the main flow strengthens but anticlockwise rotation of the cylinder somewhat counters it. Thus, depending upon the values of the Re, α, and n, there is an envelope of conditions in which the rotation has a negative influence on heat transfer. Indeed, depending upon the values of the power-law index, α, Re, and Pr the rate of heat transfer from a rotating cylinder can reduce by up to 60–70% below the corresponding value for a non-rotating cylinder. Therefore, a judicious choice of parameters may be useful to regulate the rate of heat transfer in power-law fluids.