Effects of Viscous Dissipation on Heat Transfer between an Array of Long Circular Cylinders and Power Law Fluids

Abstract

The free surface model has been combined with the equations of motion and of thermal energy to investigate the role of viscous dissipation on heat transfer between banks of long cylinders and power law (shear‐thinning and shear‐thickening) fluids. The equations of motion cast in the stream function/vorticity formulation have been solved numerically using a second‐order accurate finite difference method to obtain extensive information on the behaviour of local and surface‐averaged Nusselt numbers over a range of Reynolds numbers 1 – 500, for a wide range of power law indices (0.4 ≤ n ≤ 2.0), Brinkman numbers (0 ≤ Br ≤ 5) and Prandtl numbers (Pr = 1, 1000) at two representative solid volume fractions corresponding to the porosities of e = 0.4 and 0.9. Two different thermal boundary conditions are considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results presented herein provide a fundamental knowledge about the influence of viscous dissipation on the heat transfer characteristics. The results reported herein further show that the effect of Brinkman number on heat transfer is strongly conditioned by the thermal boundary condition, Prandtl number and the power law index.

Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime

“…The surface of the square cylinder is assumed to be subjected to either a constant wall temperature T w or an uniform heat flux q w . The thermo-physical properties are assumed to be independent of temperature and further there is no viscous dissipation [21]. Under these conditions, the integral forms of the equations of continuity, momentum and thermal energy in their non-dimensional forms are written as follows:…”

Effect of temperature-dependent viscosity on forced convection heat transfer from a cylinder in crossflow of power-law fluids

“…The numerical solution procedure used here is an iterative Gauss-Seidel relaxation method, identical to that employed in our earlier studies [4,44,45], and to avoid redundancy, only the main features are included here. The set of non-linear differential equations, namely the vorticity, stream function and energy Eqs.…”

Aiding-Buoyancy Mixed Convection from a Pair of Side-by-Side Heated Circular Cylinders in Power-Law Fluids

“…35 Also, over the ranges of conditions spanned here, the gradients are not expected to be steep and, therefore, it is justified to neglect the viscous dissipation contribution in the energy equation; i.e., the Eckert number is assumed to be small (≪1), and this is considered to be a reasonable approximation in most situations. 34−37 For incompressible fluids, the components of the stress tensor (τ ij ) are related to the components of the rate of deformation tensor (ε ij ) as follows:…”