The role of dual-phase-lag (DPL) heat conduction model on transient free convection flow in a vertical channel

Abstract

This work investigates the role of dual-phase-lag (DPL) heat conduction model on transient free convection flow of an incompressible viscous fluid in a vertical channel. The semi-analytical solutions for temperature, velocity, and skin-friction in a dimensionless form are presented in Laplace domain using the Laplace transform technique, while the Laplace expression are inverted back to the time domain, using Riemann sum approximation (RSA). The effects of dimensionless time, Prandtl number, thermal relaxation time, and thermal retardation time on dimensionless temperature and velocity profiles are graphically demonstrated. The numerical values for variation of dimensionless temperature, velocity, and skin-friction for pertinent flow parameters are computed and presented in tabular form. It is found that the increase in dimensionless time leads to an increase in both temperature and velocity, while decrease in thermal relaxation time and retardation time account for the increase in temperature and velocity. Also, the temperature is higher when thermal relaxation time precedes the thermal retardation time for air (Pr=0.71). However, the temperature is highly recorded when thermal retardation time precedes the thermal relaxation time for water (Pr=7.0).