Development and Validation of a 3-D Analytical Fluidic Model in Cartesian Coordinates for a Magnetic Refrigeration Application

Abstract

This paper focuses on the development and validation of a three-dimensional (3-D) analytical model based on the formal resolution of the incompressible Navier-Stokes equations in Cartesian coordinates. This analytical fluidic model calculates the evolution of the fluid flow velocity for various pressure gradient shapes (i.e., square, trapezoidal, ramp, triangle, sinusoidal signals, etc.), with or without mean value, using Fourier series. The model can consider square and rectangular channels of any dimensions in terms of height, width, and depth. It allows for the study of different types of fluid flow and geometries. The introduction highlights the significance of analytical modeling, particularly in the context of Magnetic Refrigeration (MR) technologies. The model assumptions and governing equations are presented. The results obtained from the analytical model are validated and show good convergence with those obtained using the COMSOL Multiphysics® software. The comparison demonstrates a high level of agreement between the two models. The analytical model performs well in terms of computation time and accuracy. It will be coupled with an analytical thermic model and used to optimize Active Magnetic Regenerative Refrigeration (AMRR) cycles. The ultimate objective is to determine an optimal pressure gradient evolution in order to maximize heat exchange in a regenerator channel.