Heat transfer enhancement produced by an oscillatory flow of a viscoelastic fluid in a tube partially filled of porous medium

This work is devoted to the detailed investigation of heat transfer enhancement caused by an oscillatory flow of a viscoelastic fluid within a tube that is partially filled with a porous medium, which results in two distinct concentric regions: a central core of free fluid and an annular layer of porous material saturated with the same fluid. Heat transfer along the tube is driven by the oscillating flow of a Maxwell fluid induced by an oscillatory pressure gradient. For the analysis, the Darcy–Brinkman and Cauchy–Euler momentum equations are employed to describe the behavior of the viscoelastic fluid flow in the porous and non-porous regions, respectively. The governing equations are presented in its dimensionless version as they are solved analytically, enabling a more precise and comprehensive analysis of key parameters, such as the Darcy, Deborah, and Womersley numbers on heat transfer, and the effective thermal diffusivity is calculated and the conditions that increase its value are analyzed, revealing that it occurs at a specific porous layer thickness. The results show that heat transfer can be enhanced compared to viscoelastic flow in a tube without a porous medium, provided that the porous insert does not reduce the permeability. For a purely viscous fluid, an increase in effective thermal diffusivity also occurs for the same dimensionless thickness of the porous medium. Overall, the combination of an oscillatory viscoelastic fluid flow through a tube that is partially filled with a porous medium improves heat transfer within the tube for a given porous layer thickness.