The Thermoconvective Instability in Hydrodynamics of Relaxational Liquids

Akhatov, Iskander; Chembarisova, R. G.

doi:10.1007/978-1-4899-1594-8_23

Cited by 6 publications

(4 citation statements)

References 7 publications

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“…This led the authors to use the modified Darcy's law to study the nonequilibrium effects that arise in these systems. Motivated by the above physical consideration, the modified Darcy's law is used in the present investigations as proposed by Akhatov and Chembarisova, 50 Alishaev and Mirzadjanzade, 51 Kiran, 23 and Kim et al, 34 utilizing the modified Boussinesq approximation. 38 In view of the above discussion, the basic hydrodynamical equations that govern the double-diffusive (thermohaline) convection in a viscoelastic fluid saturating porous medium, which respectively represents, the equation of continuity, equations of motion, equation of heat transfer, equation of mass transfer, and equation of state, are given by…”

Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

“…where ε is porosity) in the last bracket on the right hand of equations of momentum (2) as considered by Kumar and Bhadauria 52 and Malashetty et al 53 in their respective analyses is not included here, as we have followed the analyses of Akhatov and Chembarisova, 50 Alishaev and Mirzadjanzade, 51 Kim et al, 34 and Kiran 23 for convective flow in a porous medium using modified Darcy law for Oldroydian viscoelastic fluid model.…”

Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

“…Using Equations ( 24)-( 25), ( 49)- (50), and ( 54)-(55), the horizontally averaged Nusselt and Sherwood numbers, represented by Equations ( 56) and (57), respectively, now can be written as…”

Section: Third-order Problemmentioning

confidence: 99%

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Modified stability analysis of double‐diffusive convection in viscoelastic fluid layer saturating porous media

2022

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The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double‐diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.

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Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

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Modified stability analysis of double‐diffusive convection in viscoelastic fluid layer saturating porous media

2022

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“…The thermal instability caused by buoyancy forces in a horizontal porous layer saturated with a viscoelastic fluid has been addressed by Kim et al, [19]. Following Akhatov and Chembarisova's [20] approach, Yoon et al, [21] investigated the beginning of thermal convection in an isothermally heated porous layer saturated with viscoelastic fluid analytically. The impact of local thermal non-equilibrium on the initiation of convection within a porous medium saturated with an Oldroyd-B viscoelastic fluid has been examined by Shivakumara et al, [22] and Malashetty et al, [23,24].…”

Section: Introductionmentioning

confidence: 99%

Effect of Temperature Gradients and DC Electric Field on Electrothermal Convection in a Rotating Layer of Walter's-B Fluid Saturated Porous Media

Pavithra Heelalige Mariyappa,

Deepa Kumaran Nair

2023

ARFMTS

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Thermal convection in fluid-saturated porous media has diverse applications across geothermal energy utilisation, thermal insulation engineering, grain storage and understanding geodynamic processes. The thermal convection's physics is crucial for optimising the thermofluid system, improving energy efficiency, and enhancing our understanding of natural phenomena. The study examines how the initiation of electrothermal convection in a rotating viscoelastic fluid layer (Walter's B) is influenced by basic temperature gradients and a uniform vertical DC electric field, considering three different types of velocity boundary conditions: free-free, rigid-rigid, and lower rigid and upper free. By applying an electric field to a fluid, studying electrothermal convection helps engineers design effective cooling systems for electronics. The eigenvalue problem is solved by using the Galerkin technique. The Galerkin method is a widely used numerical technique for solving eigenvalue problems. The DC electric field effect exhibits a more stabilising effect for free-free boundaries than rigid and rigid-rigid boundaries. Moreover, the linear temperature profile exhibits a more stabilising effect than the parabolic temperature profile. The control of electrothermal convection on the system with the impact of other physical parameters is also discussed.

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Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed.

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The Thermoconvective Instability in Hydrodynamics of Relaxational Liquids

Cited by 6 publications

References 7 publications

Modified stability analysis of double‐diffusive convection in viscoelastic fluid layer saturating porous media

Modified stability analysis of double‐diffusive convection in viscoelastic fluid layer saturating porous media

Effect of Temperature Gradients and DC Electric Field on Electrothermal Convection in a Rotating Layer of Walter's-B Fluid Saturated Porous Media

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

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