Blottner finite difference analysis for non-Darcy flow of variable viscosity power-law nanofluids over a truncated cone with Arrhenius activation energy

Examining the behaviors of power-law nanofluid flow and the rate of heat transfer over different surfaces has received great attention due to its numerous industrial applications, such as polymer solutions, molten plastics, pulps, and foods. Also, the investigators focused on the case of constant viscosity, while in several practical situations, the dynamic viscosity of the power-law suspension is variable. So this study aims to examine non-similar solutions for the coupled flow of power-law non-Newtonian nanofluids over a truncated cone. The dynamic viscosity is varied according to the Reynolds viscosity model, and an exponential decaying form is considered for the internal heat generation. The non-Darcy model, where the quadratic drag is significant, is applied to formulate this situation, and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both the Arrhenius activation energy and non-linear thermal radiation impacts are considered. The solution methodology is based on the effective finite differences method with the Blottner scheme. The significant outcomes revealed that the rise in the power-law index n accelerates the flow and boosts the heat transfer rate. The values of the local Nusselt number in the case of the Darcy flow are higher than those of the non-Darcy case. Additionally, considering the case of variable dynamic viscosity, it is recommended to enhance the heat transfer rate. Furthermore, the rate of the heat transfer is enhanced by 29.1% viscosity parameter delta is varied from 0 to 0.5.