Heat Transfer in Non-Newtonian Flows by a Hybrid Immersed Boundary–Lattice Boltzmann and Finite Difference Method

A hybrid immersed boundary–lattice Boltzmann and finite difference method for fluid–structure interaction and heat transfer in non-Newtonian flow is presented. The present numerical method includes four parts: fluid solver, heat transfer solver, structural solver, and immersed boundary method for fluid–structure interaction and heat transfer. Specifically, the multi-relaxation time lattice Boltzmann method is adopted for the dynamics of non-Newtonian flow, with a geometry-adaptive technique to enhance the computational efficiency and immersed boundary method to achieve no-slip boundary conditions. The heat transfer equation is spatially discretized by a second-order up-wind scheme for the convection term, a central difference scheme for the diffusion term, and a second-order difference scheme for the temporal term. The structural dynamics is numerically solved using a finite difference method. The major contribution of this work is the integration of spatial adaptivity, thermal finite difference method, and fluid flow immersed boundary-lattice Boltzmann method. Several benchmark problems including the developing flow of non-Newtonian fluid in a channel, non-Newtonian fluid flow and heat transfer around a stationary cylinder and flow around a stationary cylinder with a detached filament are used to validate the present method and developed solver. The good agreements achieved by the present method with the published data show that the present extension is an efficient way for fluid–structure interaction and heat transfer involving non-Newtonian fluid. The heat transfer around an oscillating cylinder in non-Newtonian fluid flow at Reynolds number of 100 is also numerically studied using the present solver, considering the effects of the oscillating frequency and amplitude. The results may be used to expand the currently limited database of fluid–structure interaction and heat transfer benchmark studies