Heat transfer and flow analysis in a spiral channel filled with steel balls

Abstract

Flow through a porous medium, still fascinates the curious minds of researchers with many unknown properties, and characteristics ready to be discovered. Hydrodynamical effects within the flow, and corresponding heat transfer outcomes, all create impacts that assist the enhancement in the thermal properties of the porous system. In this study, a flow in a spiral channel filled with AISI 1010 steel balls is studied based on the experimental results of Gokaslan et al. (2022), under different flow rates, considering a constant wall heat flux boundary condition through side walls of the channel. The study aimed to create analytical solutions and a simulation using COMSOL Multiphysics software to study thermal dispersion values using results obtained from experimental data and analytical solutions. While processing the analytical solutions, due to the complex geometry of the experimental system (Arithmetic spiral), some assumptions have been made to simplify and obtain analytical solutions for the system. Therefore, both momentum and energy equations for the system are solved using cylindrical coordinates due to the low curvature ratio, considering an incompressible, steady-state fully developed flow. Finally, as a contribution to literature, to make analytical solutions independent of values derived from experimental results and overcome this constraint, these values were used as boundary conditions to obtain a valid solution, a correlation-based equation for temperature distribution along the channel, according to fluid properties such as viscosity, thermal conductivity, and inlet flow rate, besides channel and system properties of applied heat flux, utilized steel balls diameter and channel width, was obtained. Both analytical solutions and the correlation-based equations show good agreement with experimental results, and their error for temperature distribution values has been at a maximum value of %6.1 which can be considered accurate. Furthermore, the coefficients used in the correlation-based equation have only an error value of %5.35 considering the same coefficients derived from experimental results.