The Effect of Modulation on Heat Transport by a Weakly Nonlinear Thermal Instability in the Presence of Applied Magnetic Field and Internal Heating

Abstract

The present paper deals with a weakly nonlinear stability problem under an imposed time-periodic thermal modulation. The temperature has two parts: a constant part and an externally imposed time-dependent part. We focus on stationary convection using the slow time scale and quantify convective amplitude through the real Ginzburg-Landau equation (GLE). We have used the classical fourth order Runge-Kutta method to solve the real Ginzburg-Landau equation. The effect of various parameters on heat transport is discussed through GLE. It is found that heat transport analysis is controlled by suitably adjusting the frequency and amplitude of modulation. The applied magnetic field (effect of Ha) is to diminish the heat transfer in the system. Three different types of modulations thermal, gravity, and magnetic field have been compared. It is concluded that thermal modulation is more effective than gravity and magnetic modulation. The magnetic modulation stabilizes more and gravity modulation stabilizes partially than thermal modulation.

Thermo-Rheological Effect on Weak Nonlinear Rayleigh-Benard Convection under Rotation Speed Modulation

“…The above boundary conditions are free-free and stress-free isothermal, they are used by [28,29,32,45,54,55].…”

“…These studies present results of gravity modulation on thermal instability in fluid or porous layer. Also, the effect of thermal modulation on convective instability has been investigated in [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. The effect of thermal modulation on chaotic convection [38], throughflow effects in the presence of thermal modulation [39,41,42,49,56], thermal modulation with internal heating [40], thermal modulation on magnetoconvection [43,45,48,54,55] have been investigated.…”

“…Also, the effect of thermal modulation on convective instability has been investigated in [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. The effect of thermal modulation on chaotic convection [38], throughflow effects in the presence of thermal modulation [39,41,42,49,56], thermal modulation with internal heating [40], thermal modulation on magnetoconvection [43,45,48,54,55] have been investigated. The effect of rotation on nonlinear fluid convection under temperature modulation has been reported by Kiran and Bhadauria [57].…”

A numerical technique and effect of magnetic field dependent (MFD) viscosity on thermal instability in a ferrofluid pores with Coriolis force for Darcy model

“…Nadian et al (2020) derived the thermal instability of couple-stress Ferromagnetic Fluid in the presence of variable gravity field, rotation and Magnetic field. Manjula et al (2020) examined the effect of modulation on heat transport by a weakly nonlinear thermal instability in the presence of applied magnetic field and internal heating. Kiran (2020) discussed the Concentration modulation effect on weakly nonlinear thermal instability in a rotating porous Medium.…”

Weakly nonlinear bio-convection in a porous media under temperature modulation and internal heating

“…In order to identify the stable and unstable zones, Kiran and Bhadauria (2015) explored chaotic convection in a Darcy porous layer under thermal modulation. The effect of thermal modulation on heat transport by a weakly nonlinear thermal instability in the presence of applied magnetic field and internal heating was reported by Manjula et al(2020). Kiran and Bhadauria (2016) investigated weakly nonlinear oscillatory convection in a rotating fluid layer under temperature modulation.…”