Abstract
This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.
Highlights
The cooling and heating effects are required by power manufacturing, transportation, electronics etc
We have investigated the effect of gravity modulation in a horizontal fluid layer saturated by a nanofluid with internal heating effect
External regulations of convection is important in the study of thermal instability, in this paper we have considered gravity modulation for either enhancing or inhibiting the convective heat transport as is required by a real life application
Summary
The cooling and heating effects are required by power manufacturing, transportation, electronics etc. Natural convection in nanofluids have been investigated by many authors in recent past for different physical configurations; Buongiorno [7], Kuznetsov and Nield [8]-[9], Nield and Kuznetsov [10]-[11], Bhadauria and Agarwal [12]-[13] It is a common finding of these studies that the presence of nano-particles in the base fluid can advance or delay the onset of convection, and thereby decrease or increase heat transport, depending on the concentration gradient of the nano-particles. MATEC Web of Conferences effect of temperature modulation on nanofluid convection in porous medium has been reported recently by Umavathi [18] by performing a linear stability analysis It appears that all of the above studies deal with the case of uniform heating from below, and the case of internal heating has been largely neglected. This motivates us to do the present study by performing a weakly nonlinear analysis under gravity modulation and internal heating effects
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