Abstract
Heat transfer of a power-law non-Newtonian incompressible fluid in channels with porous walls has not been carefully studied using a proper numerical method despite a few constructions of approximate analytic solutions through the similarity transformation and perturbation method for Newtonian fluids (i.e. power-law index being one). In this paper, we propose a finite element method for the thermal incompressible flow equations. The incompressible condition is treated by a penalty formulation. Numerical solutions are validated by comparing them with an approximate analytic solution of the Navier-Stokes equation in the Newtonian fluid case. Then, the method is used to simulate the heat transfer of various power-law fluids. Additionally, unlike previous studies, we allow the thermal diffusivity to be a function of temperature gradient. The effect of different values of the parameters on the temperature and velocity is also discussed in this paper.
| Original language | English |
|---|---|
| Pages (from-to) | 1121-1129 |
| Number of pages | 9 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 37 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 30 May 2014 |
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