Non-similar approach for enhanced heat and mass transfer in nanofluid using Keller box algorithm

The nanofluids provide various benefits over pure fluids in heat and mass transport applications; hence, their research is crucial. For instance, they can increase heat transfer rate by enhancing the fluid's thermal conductivity and may enhance mass transfer rate by changing the surface characteristics. Furthermore, nanofluids are being demonstrated to effectively diminish pressure drops in exchangers for heat, which can lower energy consumption and operating expenses. In the existing literature, the majority of the theoretical studies considered self-similar flows. However, there are certain actual flow situations that do not allow for a self-similar solution. The current study considers such of those situations where the non-similarity of the transport phenomena is unavoidable. The non-similarity of the present problem is caused by the consideration of thermophoretic diffusion or the contribution of viscous dissipation when the wall temperature follows a power-law form. For a pure fluid, the same problem admits a self-similar solution in the absence of viscous dissipation effects. In this problem, the non-similarity is caused by the nature of the thermal transport process and not because of the momentum transport. Therefore, the consideration of viscous dissipation in the boundary layer of nanofluid is an interesting aspect to explore the behavior of thermal and mass transport phenomena. Moreover, the current analysis intends to investigate the transport enhancement in a non-similar flow of a nanofluid by utilizing the Buongiorno model. In the current nonsimilar modeling, possibilities for the existence of a self-similar solution are also highlighted. An implicit finite-difference numerical scheme, the Keller-Box method, is utilized. The problem involves several physical parameters of interest, such as the Eckert number, Lewis number, Brownian motion parameter, and thermophoresis parameter, whose potential impact on the non-similar nature of the problem and on thermal enhancement is analyzed and quantified.