Power-law nanosuspension natural convection in a cavity having a heat-producing element depending on the heat-conducting substrate material

Constantly reducing the size and improving the performance of electronics lead to the heat generation enhancement and unstable operation of such devices. Therefore, the modeling and production of the efficient cooling systems is one of the most important modern challenges. Based on this, in the present research a numerical study on the heat-conducting base material influence on the power-law nanofluid thermal convection within a cavity having a local source of constant volumetric heat generation is performed. The problem is described by transient differential equations written using the Oberbeck–Boussinesq approximation, the Ostwald-de Waele power law and the single-phase nanoliquid approaches. The nanosuspension characteristics are calculated employing the experimental relations reflecting the impact of the nanoparticles concentration and liquid temperature. The equations are solved using the developed in-house numerical algorithms based on the finite difference technique. The locally one-dimensional difference scheme has been used to reduce 2D problem to a set of 1D problems. Convective terms have been approximated by the second upstream scheme, the diffusion terms are approximated by the central differences, while the transient terms are discretized by the Euler scheme. The obtained sets of algebraic equations have been solved using effective direct and iterative methods. The work analyzes the impact of the power-law index, the material of the thermally conductive substrate, the material of nanoparticles and their concentration on heat transfer performance and the cooling technique efficiency. Numerical simulations show that the simultaneous usage of a thermally conductive copper substrate and copper nanoparticles makes it possible to diminish the mean temperature of the heated element. Moreover, a growth of the nanoparticles volume fraction allows to decrease the heater average temperature. The obtained results can be used for improvement of the electronics cooling systems, modern heat exchangers and thermal energy storage systems where the combination of non-Newtonian nanofluid as a working fluid and heat-conducting substrates can be considered as an effective approach for the optimization of the heat transfer.