Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy

I K Khalid,S S A Gani,N F M Mokhtar,I Hashim,Z B Ibrahim

doi:10.1155/2017/2789024

I K Khalid, S S A Gani + Show 3 more

Open Access

https://doi.org/10.1155/2017/2789024

Copy DOI

Abstract

A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system.

Highlights

The importance of understanding convective heat transfer in nanofluids has been a topic of interest for the last few years
Buongiorno [6] discussed the seven slip mechanisms that can produce a relative velocity between the nanoparticles and the base fluid. These are inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage, and gravity settling. He concluded that the effects of Brownian diffusion and thermophoresis are important for convective transport in nanofluids and his model is the basis for the present study
Haddad et al [12] reported that the thermophoresis and Brownian motion are significant in the thermal enhancement of the natural convection in a nanofluid layer

Summary

Introduction

The importance of understanding convective heat transfer in nanofluids has been a topic of interest for the last few years. Yadav et al [39, 40] and Nield and Kuznetsov [41] included the effect of an internal heat source on the thermal instability in a nanofluid layer and found that the heat source advances the onset of convection. We intend to scrutinize the effect of internal heat source on the thermal instability of double-diffusive convection in a rotating nanofluid layer with feedback control. It is reported that between 20% and 50% of industrial energy input is lost as waste heat [76], which has attracted numerous studies on energy efficiency, recovering waste heat, and so on This motivated us to contribute mathematically by providing a mathematical model that can simulate the influence of an internal heat source and feedback control in a nanofluid layer with other crucial parameters. Numerical computations of the various relevant parameters are presented graphically

Mathematical Formulation

Results and Discussion

Conclusion