Role of Heat Generation/Absorption on Mixed Convection Flow in a Vertical Tube Filled with Porous Material Having Time-Periodic Boundary Condition: Steady-Periodic Regime

This paper discusses the hydrodynamic and thermal behaviours of a fully developed mixed convective flow of a viscous incompressible heat generating/absorbing fluid in a vertical tube filled with isotropic porous material having time-periodic boundary condition. The dimensionless governing equations of motion and energy subjected to the Boussinesq approximation and asymmetric heat conditions are solved analytically. Closed-form solutions are expressed in terms of modified Bessel function of first kind. The solutions obtained are graphically represented, and the effects of the dimensionless heat generation/absorption H, the dimensionless frequency Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document} and the Darcy number Da on the fluid flow are investigated. It is discovered that velocity is maximum at two different locations in the flow domain, one near the surface of the tube and another at the axis of the tube. The presence of the heat generation parameter is seen to enhance the temperature distribution and this is reflected as increase in the magnitude of the oscillation dimensionless velocity, whereas in the presence of heat absorption a reversed trend occurs.