Study of heat transport in a temperature-dependent viscous liquid under temperature modulation

B.S Bhadauriaa,M Belhaq

doi:10.1051/matecconf/20141609002

B.S Bhadauriaa, M Belhaq

Open Access

https://doi.org/10.1051/matecconf/20141609002

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Abstract

The effect of time-periodic temperature modulation on thermal instability in a temperature dependent viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis. The amplitude of temperature modulation is considered to be very small, and the disturbances are expanded in terms of power series of amplitude of convection. The Ginzburg–Landau equation for the stationary mode of convection is obtained and consequently the effect of temperature modulation on heat transport has been investigated. Effect of various parameters has been explained graphically. It has been found that, an increment in the values of thermo-rheological parameter and Prandtl number is to enhance the heat transport in the system. Further, temperature modulation can be used to control the heat transport effectively as external mechanism to the system.

Highlights

The effect of time-periodic temperature modulation on thermal instability in a temperaturedependent viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis
These are due to Siddheshwar et al [18], who studied stationary magneto-convection in a Newtonian liquid under temperature or gravity modulation using Ginzburg-Landau model, Bhadauria et al [19], investigated a non-linear thermal instability in a rotating viscous fluid layer under temperature/gravity modulation, and calculated heat transfer across the fluid layer, Bhadauria et al, [20] studied weak nonlinear of time-periodic thermal boundary conditions and internal heating on heat transport in a porous medium
The effect of temperature modulation on thermal instability in a temperature dependent viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis

Summary

Introduction

At present there are very few studies available in the literature in which nonlinear analysis has been done under temperature modulation These are due to Siddheshwar et al [18], who studied stationary magneto-convection in a Newtonian liquid under temperature or gravity modulation using Ginzburg-Landau model, Bhadauria et al [19], investigated a non-linear thermal instability in a rotating viscous fluid layer under temperature/gravity modulation, and calculated heat transfer across the fluid layer, Bhadauria et al, [20] studied weak nonlinear of time-periodic thermal boundary conditions and internal heating on heat transport in a porous medium. Ching and Cheng [26], studied the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. It was shown that, considering linear stability analysis under Oberbeck-Boussinesq approximation for the case of impermeable, perfectly conducting upper and lower boundaries, the values of the critical value of critical Rayleigh number is 4π2 Most of these studies are done with steady temperature gradient across the fluid layer. The basic state is Landau equation for stationary mode of convection

Governing Equations

Ginzburg-Landau equation and heat transport

Results and discussion

Analytical solution for Unmodulated case

Conclusions