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ORIGINAL PAPER
The Effect of Modulation on Heat Transport by a Weakly Nonlinear Thermal Instability in the Presence of Applied Magnetic Field and Internal Heating
1
Division of Mathematics, Vignan’s Foundation for Science, Technology and Research, Guntur, Andhra Pradesh, -522213, India
2
Department of Mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, Telangana-, 500075, India
3
Faculty of Applied Sciences and Technology, University Tun Hussein Onn, Malaysia 84600, Pagoh, Muar, Johor, Malaysia
Online publication date: 2020-11-26
Publication date: 2020-12-01
International Journal of Applied Mechanics and Engineering 2020;25(4):96-115
KEYWORDS
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.
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