Linear and weakly nonlinear analysis of a ferrofluid layer for an LTNE model with variable gravity and internal heat sou
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Linear and weakly nonlinear analysis of a ferrofluid layer for an LTNE model with variable gravity and internal heat source Amit Mahajan · Hemant Parashar
Received: 14 February 2020 / Accepted: 26 July 2020 © Springer Nature B.V. 2020
Abstract A ferrofluid saturated porous layer convection problem is studied in the variable gravitational field for a local thermal nonequilibrium (LTNE) model. Internal heating and variation (increasing or decreasing) in gravity with distance through the layer affected the stability of the convective system. The Darcy model is employed for the momentum equation and the LTNE model for the energy equation. The boundaries are considered to be rigid-isothermal and paramagnetic. For the linear stability analysis of the three-dimensional problem, the normal mode has been applied and the eigenvalue problem is solved numerically using Chebyshev pseudospectral method, while weakly nonlinear analysis is carried out with a truncated Fourier series. The effect of different dimensionless parameters on the Rayleigh number has also been studied. We found that the system becomes unstable on the increasing value of nonlinearity index of magnetization (M3 ), porosity-modified conductivity ratio (β), and internal heat parameter (ξ ). It is observed that the system is stabilized by increasing the value of the Langevin parameter (αL ), variable gravity coefficient (δ), and effective heat transfer parameter (H1 ). Runge–Kutta–Gill method has been used for solving the finite-amplitude equations to study the transient behavior of the Nusselt number. Streamlines and isotherms patterns are determined for the steady case and are presented graphically. Keywords Ferrofluid · Gravity variation · Internal heat generation · Local thermal nonequilibrium · Nusselt number Mathematics Subject Classification 76E06 · 76E25
1 Introduction Papell [1] prepared a liquid with the objective to provide a positive feed of liquid rocket fuel to the intake of pumps in the reduced gravity conditions of outer space. Later, Rosensweig together with Kaiser [2] broadened the range of ferrofluid compositions to include other ferrites, other surfactants, and other carrier liquids including water. The A. Mahajan · H. Parashar (B) Department of Applied Sciences, National Institute of Technology Delhi, Narela, Delhi 110040, India e-mail: [email protected] A. Mahajan e-mail: [email protected]
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A. Mahajan, H. Parashar
world interest in ferrofluids was further stimulated by the first commercial application of ferrofluids, the leakagefree seals, an excellent component today of many high-tech devices [3]. Since then, a number of theoretical and experimental works are taken by various authors to find the possible applications in a variety of fields including the medical field, optics, heat transfer, and energy harvesting to name a few. The experiments in microgravity are expensive and access to associated facilities is limited, still, a number of experiments in the microgravity environment are also conducted (see Oden
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