Power-law fluid flow and heat transfer in a channel with a built-in porous square cylinder: Lattice Boltzmann simulation

• A porous block is considered in the channel for analysis of non-Newtonian fluids.
• Both regular and random arrangements of fibers are employed in the channel.
• The Nusselt number for both arrangements are presented using ‘confidence interval’.
• Several blockage ratios with different arrangements are checked to obtain a correlation.
• The method is verified through comparison with existing results.

The lattice Boltzmann method (LBM) has been established as an efficient technique for solving a fluid dynamics problem in a complex porous medium. In this paper, the power-law fluid flow and heat transfer are studied numerically in a channel partially filled with an anisotropic porous block for three power-law indices, n = 0.8, 1 and 1.2. Combined pore level simulations of flow and heat transfer are performed for a 2D channel that is partially filled with square obstacles in both ordered and random arrangements. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The effects of the different arrangements of obstacles, Reynolds number, power index n, blockage ratio and porosity on the velocity and temperature profiles are studied. The local and averaged Nusselt numbers are also calculated on the channel walls. It is found that pseudo plastic fluids generate the highest heat transfer rate for all configurations of obstacles. For constant porosity and block size, the increase is noticeable when the arrangement of square obstacles is random. Also by decreasing the porosity, the value of averaged Nusselt number is increased. Two correlations for regular and random obstacle arrangements between the Nusselt number, Reynolds number, power index n, blockage ratio and porosity are presented. The values of averaged Nusselt number with the respective confidence interval are also reported in the case of random arrangement of obstacles.