Effects of time and diffusion phase-lags in a thin circular disc with axisymmetric heat supply

S.K. Garg,Lajvinder Singh Reen,Timothy Marchant,Rajneesh Kumar

doi:10.1080/23311835.2017.1369848

Abstract

The present investigation is concerned with an axisymmetric problem of thin circular disc in a thermoelastic diffusive body within the context of dual-phase-lag heat transfer and dual-phase-lag dif...

Highlights

Catteno (1958) and Vernotte (1958) proposed a thermal wave with a single phase lag in which the temperature gradient after a certain elapsed time was given by q +
An investigation has been conducted to compare the effect of time on dual phase lag model in heat conduction and diffusion and the graphs have been plotted for the range 0 ≤ r ≤ 10, phase lags are taken as p = 0.01, = 0.03, t = 0.05 and q = 0.07
The problem is discussed within the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models

Summary

Introduction

Classical Fourier heat conduction law implies an infinitely fast propagation of a thermal signal which is violated in ultra-fast heat conduction system due to its very small dimensions and short timescales. Catteno (1958) and Vernotte (1958) proposed a thermal wave with a single phase lag in which the temperature gradient after a certain elapsed time was given by q +. Abbas, 2015a, 2015b, 2015c; Abbas, Kumar, & Reen, 2014; Abbas & Zenkour, 2013, 2014, 2015; Abdallah, 2009; Atwa & Jahangir, 2014; Ezzat & Awad, 2010; Kaushal, Kumar, & Miglani, 2011; Kumar & Gupta, 2014; Kumar & Mukhopadhaya, 2010a, 2010b; Kumar, Sharma, & Garg, 2014; Kaushal, Sharma, & Kumar, 2010; Sharma & Marin, 2013; Youssef, 2006, 2011) In this investigation, a generalized form of mass diffusion equation is introduced instead of classical Fick’s diffusion theory using two diffusion phase-lags in axisymmetric form. The initial temperature in the thin disc is given by a constant temperature T0, the heat flux g0 F(r, z) is prescribed along with vanishing of stress components on the upper and lower boundary surfaces along with traction free boundary z = ±b Under these conditions, the thermoelastic quantities in a thin circular disc are required to be determined.

Particular cases

Coupled thermoelasticity with mass diffusion

Numerical results and discussion

Findings

Conclusion