Heat transfer analysis of unsteady nanofluid flow between moving parallel plates with magnetic field: Analytical approach

In this study, we use the differential transform method and Akbari-Ganji method to examine the influence of uniform magnetic field on the natural convection heat transfer of nanofluids flowing between two infinite parallel plates. The effects of the primary parameters of Prandtl number, squeeze number, Schmidt number, Hartmann number, Eckert number, Brownian motion parameter, and thermophoresis parameter have been investigated after obtaining the governing equations and solving the problem with specified boundary conditions. The similarity transformation is used to find the system of ordinary differential equations, and the Rung-Kutta fourth-order numerical technique is contrasted. The findings suggest that increasing the squeeze number leads to a decrease in velocity, while increasing the Hartman number has a similar effect. Moreover, the temperature rises with an increase in Hartman number, Eckert number, and thermophoretic parameters and is directly proportional to Prandtl number. Our study compares Akbari-Ganji and differential transform methods for solving nonlinear differential equations. It demonstrates that the former requires fewer computational steps and less computational time, making it a more efficient approach. The answers acquired using the suggested methods are consistent with those found in the literature. These results can help researchers to analyze quicker and easier and provide important insights into the complex behavior of nanofluid flow in the presence of electromagnetic fields.

Automated summary

In this study, the influence of a uniform magnetic field on natural convection heat transfer in nanofluids flowing between two infinite parallel plates is examined using the differential transform and Akbari-Ganji methods. The effects of various primary parameters are investigated, and the governing equations are solved with specific boundary conditions. The findings reveal that increasing the squeeze number leads to a decrease in velocity, while increasing the Hartmann number has a similar effect. Moreover, temperature rises with increasing Hartmann number, Eckert number, and thermophoretic parameters, and is directly proportional to Prandtl number. The study compares the efficiency of Akbari-Ganji and differential transform methods for solving nonlinear differential equations, and demonstrates that the former requires fewer computational steps and less time.