Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer

Abstract

Penetrative convection due to purely internal heating in a horizontal ferrofluid-saturated porous layer is examined by performing linear stability analysis. Four different types of heat supply functions are considered. The Darcy model is used to incorporate the effect of the porous medium. Numerical solutions are obtained by using the Chebyshev pseudospectral method, and the results are discussed for all three boundary conditions: when both boundaries are impermeable and conducting; when both boundaries are conducting with lower boundary impermeable and free upper boundary; and when both boundaries are impermeable with lower boundary conducting and upper with constant heat flux. The effect of the Langevin parameter, width of ferrofluid layer, permeability parameter, and nonlinearity of the fluid magnetization has been observed at the onset of penetrative convection for water-and ester-based ferrofluids. It is seen that the Langevin parameter, width of ferrofluid layer, and permeability parameter have stabilizing effects on the onset of convection, while the nonlinearity of the fluid magnetization advances the onset of convection.

Effect of Internal Heat Generation on the Onset of Brinkman-Benard Thermomagnetic Convection in a Saturated Porous Layer

“…The effect of internal heating is to alter the basic temperature distribution from linear to parabolic with respect to porous layer height and found that it has a profound effect on the stability characteristics of the system. The following conclusions can be drawn from the present study: 20 and references therein [21][22][23][24] ).…”

“…Jitender Singh and Renu Bajaj 17 have studied thermal convection of ferrofluids in the presence of uniform vertical magnetic field with boundary temperatures modulated sinusoidally about some reference value. Recently, Idris and Hashim 18 and Ferdows et al [21][22][23][24] have investigated the instability of Benard-Marangoni ferroconvection in a horizontal layer of ferrofluid under the influence of a linear feedback control and cubic temperature gradient.…”

Cattaneo–LTNE porous ferroconvection

“…Later, a series of investigations on thermal convection in magnetized ferrofluids for different situations has been discussed (Odenbach, 2004; Kaloni and Lou, 2004; Afifah et al , 2016; Pérez et al , 2017). Many studies on convective instability in a ferrofluid-saturated porous layer are available in the literature (Rosensweig et al , 1978; Borglin et al , 2000; Mahajan et al , 2017; Nadeem, Raishad, Muhammad and Mustafa, 2017; Muhammad et al , 2017a; Shafii and Mohsen, 2018 and references therein). Works on MHD nanofluids heat transfer in a porous medium have also been undertaken in the past (Sheikholeslami, 2018a, b, 2019; Sheikholeslami and Rokni, 2018a, b; Sheikholeslami and Seyednezhad, 2018).…”