Unsteady Convective Heat Transfer of Power-Law Fluid with Variable Fluid Properties in a Concentric Annulus Originating from a Polymer Flooding Process

Abstract

We study the unsteady convective heat transfer of power-law fluid with variable fluid properties in a concentric annulus with isothermal surface. The problem is originated from the polymer flooding process between a sucker rod and oil well. A new power-law rheological model is proposed, which takes the effects of temperature on fluid viscosity and thermal conductivity into account. Numerical solutions are presented for velocity and temperature fields using the Chebyshev spectral method coupled with the strong stability-preserving Runge–Kutta time discretization. The exponential convergence is verified by accuracy testing between a smooth exact solution of the Partial Differential Equations (PDEs) with source terms and the numerical approximation of manufactured solutions. It is found that heat transfer is enhanced in the variable power-law index model, and a decrease in power-law index of pseudoplastic fluids promotes heat transfer due to the increased Nusselt number. Moreover, the influences of other parameters on convective heat transfer behaviors are discussed in detail.