Forced convection heat transfer of power law non-Newtonian fluids between two semi-infinite plates with variable thermal conductivity

Abstract

This paper presents an investigation of forced convection heat transfer in power-law non-Newtonian fluids between two semi-infinite plates with variable thermal conductivity. Three cases of different thermal conductivity models are considered: (i) thermal conductivity is a constant, (ii) thermal conductivity is a linear function of temperature, (iii) thermal conductivity is a power-law function of temperature gradient (Zheng's model). Governing equations are solved using the finite element method with the 'ghost' time introduced to the control equations, which does not affect the results because the velocity and temperature will remain unchanged when the steady state is reached. Results for the solutions of different variable models are presented as well as the analysis of the associated heat transfer characteristics. It is shown that the heat transfer behaviours are strongly dependent on the power-law index (n) in all models. For example, when n < 1, the temperature in model (iii) is higher than that in model (i) and (ii), while the situation is reversed when n > 1.