Non-Newtonian fluids have recently attracted research attention owing to their vast application across numerous engineering fields. These fluids are associated with convective heat transfer problems which have been so far studied theoretically, experimentally and numerically. Research findings have shown that non-Newtonian fluids can be used to improve the heat transfer performance of thermal devices when used as working fluids. To this end, various design approaches have been proposed to improve the thermal efficiency of these systems. However, most of these approaches are based on size optimization depending on initial geometrical setting that limits their abilities to obtain optimum improvements. Recently, topology optimization comprising of mathematical algorithms and physical laws has been identified as a promising solution. Unfortunately, topology optimization of non-Newtonian convective heat transfer problems has not been fully explored.
Dr. Bin Zhang and Professor Limin Gao from Northwestern Polytechnic University investigated the topology optimization of convective heat transfer problems for non-Newtonian fluids. The power-law constitutive model as used to determine the shear-dependent viscosity. Their main objective was to maximize the heat exchange in the non-Newtonian thermal devices by utilizing a material distribution-based optimization method, which was assumed to be equivalent to maximizing heat transfer between the cooling fluid and solid domain. Also, the effects of non-Newtonian behaviors on optimal designs and configurations of thermal devices were assessed. The work is currently published in the Structural and Multidisciplinary Optimization journal.
A topology optimization problem with non-Newtonian convective heat transfer equations was successfully established. The density material was updated based on the gradient information gathered from the adjoint-based sensitivity optimization process. The optimization was eventually implemented through the classical optimization algorithm. Results showed a variation in the design variable and convergence history of the objective function in the optimization process. The occurrence of branched flow channels at the optimal designs was attributed to the growth in pressure difference and heat generation. This also resulted in a high amount of heat exchange for optimal configurations.
The effects of non-Newtonian power low index on optimal designs was evident. From the optimization cases discussed: shear thickening fluids, shear-thinning fluids, and Newtonian fluids, it was observed that the optimal layout was dependent on the power-law index (see Figure 1 and Figure 2). For instance, a higher power-law index resulted in a lower flow rate and even more complex configurations. Nonetheless, different effective ways for enhancing heat transfer performance of different types of non-Newtonian fluids based thermal devices were identified. They included increasing flow rate for lower power-law index problems and enlarging the heat exchange area for larger power-law index problems. Furthermore, the authors confirmed that the optimal design of the high-power law index problem exhibited better heat transfer performance than the low power-law index problem under the same conditions.
Overall, the Bin Zhang and Limin Gao study presented a topology optimization of two-dimensional non-Newtonian heat sinks using a density-based optimization method and provided good insights on the effects of non-Newtonian behavior on optimal designs of thermal devices. With an effective approach regarding the choice of the types of non-Newtonian working fluids and design principles of various non-Newtonian problems, Dr. Bin Zhang observed that their study will significantly enhance the performance of heat transfer devices.
Zhang, B., & Gao, L. (2019). Topology optimization of convective heat transfer problems for non-Newtonian fluids. Structural and Multidisciplinary Optimization, 60(5), 1821-1840.