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Journal of Engineering Mathematics
Published in: Journal of Engineering Mathematics 1/2020

29-10-2020

Effects of spatially varying gravity, temperature and concentration fields on the stability of a chemically reacting fluid layer

Authors: Amit Mahajan, Vinit Kumar Tripathi

Published in: Journal of Engineering Mathematics | Issue 1/2020

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Abstract

In the present study, the effects of different types of basic temperature and concentration gradients on a layer of reactive fluid under variable gravity field are analyzed using linear and non-linear analysis. Energy method is applied to obtain the non-linear energy threshold below which the solution is globally stable. It is found that the linear and non-linear analysis are not in agreement for the considered models of temperature and concentration gradients. The obtained results of non-linear analysis for different values of reaction terms and variable gravity coefficients in each given model of temperature and concentration gradients are compared with the linear instability results. The Chebyshev pseudospectral method is used to obtain the numerical and graphical results of subsequent analysis.
previous article The limits of Riemann solutions to Euler equations of compressible fluid flow with a source term

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Literature
1.
Turner JS (1974) Double-diffusive phenomema. Annu Rev Fluid Mech 6(14):37–54
2.
3.
Kaufman J (1994) Numerical models of fluid flow in carbonate platforms: implications for dolomitization. J Sediment Res 64A(1):128–139
4.
Oldenburg CM, Pruess K (1998) Layered thermohaline convection in hypersaline geothermal systems. Transp Porous Media 33(1):29–63
5.
Bear J, Gilman A (1995) Migration of salts in the unsaturated zone caused by heating. Transp Porous Media 19(2):139–156
6.
Ariman T, Turk MA, Sylvester ND (1973) Microcontinuum fluid mechanics—a review. Int J Eng Sci 11(8):905–930MATH
7.
Hayat T, Nawaz M (2011) Unsteady stagnation point flow of viscous fluid caused by an impulsively rotating disk. J Taiwan Inst Chem Eng 42(1):41–49
8.
Harfash AJ (2013) Magnetic effect on instability and nonlinear stability of double-diffusive convection in a reacting fluid. Contin Mech Thermodyn 25(1):89–106MathSciNetMATH
9.
Harfash AJ (2015) Magnetic effect on convection in a porous medium with chemical reaction effect. Transp Porous Media 106(1):163–179MathSciNet
10.
Wollkind DJ, Frisch HL (1971) Chemical instabilities: I. A heated horizontal layer of dissociating fluid. Phys Fluids 14(1):13–17
11.
Wollkind DJ, Frisch HL (1971) Chemical instabilities. III. Nonlinear stability analysis of a heated horizontal layer of dissociating fluid. Phys Fluids 14(3):482–487
12.
Bdzil JB, Frisch HL (1971) Chemical instabilities. II. Chemical surface reactions and hydrodynamic instability. Phys Fluids 14(3):475–481MATH
13.
Bdzil JB, Frisch HL (1980) Chemically driven convection. J Chem Phys 72(3):1875–1886
14.
Gutkowicz-Krusin D, Ross J (1980) Rayleigh–Bénard instability in reactive binary fluids. J Chem Phys 72(6):3577–3587MathSciNet
15.
Gitterman M, Steinberg V (1983) Onset of convective instabilities in binary liquid mixtures with fast chemical reactions. Phys Fluids 26(2):393–396MATH
16.
Steinberg V, Brand HR (1983) Convective instabilities of binary mixtures with fast chemical reaction in a porous medium. J Chem Phys 78(5):2655–2660
17.
Steinberg V, Brand HR (1984) Amplitude equations for the onset of convection in a reactive mixture in a porous medium. J Chem Phys 80(1):431–435
18.
Pritchard D, Richardson CN (2007) The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer. J Fluid Mech 571:59–95MathSciNetMATH
19.
Wang S, Tan W (2009) The onset of Darcy–Brinkman thermosolutal convection in a horizontal porous media. Phys Lett A 373(7):776–780MATH
20.
Al-Sulaimi B (2015) The energy stability of Darcy thermosolutal convection with reaction. Int J Heat Mass Transf 86:369–376
21.
Graham A (1933) Shear patterns in an unstable layer of air. Philos Trans R Soc Lond 232(12):285–296
22.
Chandra K (1936) Instability of fluids heated from below. Proc R Soc A Math Phys Eng Sci 236(917):352–383
23.
Sutton OG (1950) On the stability of a fluid heated from below. Proc R Soc A Math Phys Eng Sci 204(1078):297–309
24.
Graaf JGAD, Held EFMV (1931) The relation between the heat transfer and the convection phenomena in enclosed plane air layers. Appl Sci Res 3(1):393–409
25.
Currie IG (1967) The effect of heating rate on the stability of stationary fluids. J Fluid Mech 29(2):337–347
26.
Lick W (1965) The instability of a fluid layer with time-dependent heating. J Fluid Mech 21(3):565–576MathSciNetMATH
27.
Nield DA (1975) The onset of transient convective instability. J Fluid Mech 71(3):441–454MATH
28.
Dombrovsky LA, Sazhin SS (2003) A parabolic temperature profile model for heating of droplets. J Heat Transfer 125(6):2002–2004
29.
Ficker T, Myslín J, Podešvová Z (2001) Non-linear temperature profiles. Acta Polytech 41(6):66–68
30.
Sparrow EM, Goldstein RJ, Jonsson VK (1964) Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile. J Fluid Mech 18(4):513–528MathSciNetMATH
31.
Homsy GM (1973) Global stability of time-dependent flows: impulsively heated or cooled fluid layers. J Fluid Mech 60(1):129–139MATH
32.
Shivakumara IS, Rudraiah N, Nanjundappa CE (2002) Effect of non-uniform basic temperature gradient on Rayleigh–Benard–Marangoni convection in ferrofluids. J Magn Magn Mater 248(3):379–395
33.
Rudraiah N, Veerappa B, Balachandra Rao S (1980) Effects of nonuniform thermal gradient and adiabatic boundaries on confection in porous media. J Heat Transfer 102(2):254–260
34.
Rudraiah N, Veerappa B (1982) Convection in fluid-saturated porous layer with non-uniform temperature gradient. Int J Heat Mass Transf 25(8):1147–1156MATH
35.
Shivakumara IS (2010) Onset of convection in a couple-stress fluid-saturated porous medium: effects of non-uniform temperature gradients. J Appl Fluid Mech 80(1):949–957MATH
36.
Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins MM (2004) GRACE measurements of mass variability in the earth system. Science 305(5683):503–505
37.
Hirt C, Claessens S, Fecher T, Kuhn M, Pail R, Rexer M (2013) New ultrahigh-resolution picture of Earth’s gravity field. Geophys Res Lett 40(16):4279–4283
38.
Pradhan GK, Samal PC (1987) Thermal stability of a fluid layer under variable body forces. J Math Anal Appl 122(2):487–495MathSciNetMATH
39.
Alex SM, Patil PR, Venkatakrishnan KS (2001) Variable gravity effects on thermal instability in a porous medium with internal heat source and inclined temperature gradient. Fluid Dyn Res 29(2):1–6
40.
Alex SM, Patil PR (2002) Effect of a variable gravity field on convection in an anisotropic porous medium with internal heat source and inclined temperature gradient. J Heat Transfer 124(1):144–150
41.
42.
Straughan B (2004) The energy method, stability, and nonlinear convection. Springer, New YorkMATH
43.
Rionero S, Straughan B (1990) Convection in a porous medium with variable internal heat source and variable gravity. Int J Eng Sci 28(6):497–503MATH
44.
Harfash AJ, Alshara AK (2015) Chemical reaction effect on double diffusive convection in porous media with magnetic and variable gravity effects. Korean J Chem Eng 32(6):1046–1059
45.
Mahajan A, Sharma MK (2018) The onset of convection in a magnetic nanofluid layer with variable gravity effects. Appl Math Comput 339:622–635MathSciNetMATH
46.
Yadav D (2019) Numerical investigation of the combined impact of variable gravity field and throughflow on the onset of convective motion in a porous medium layer. Int Commun Heat Mass Transf 108:104274
47.
Kaloni PN, Qiao Z (2001) Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects. Int J Heat Mass Transf 44(8):1585–1591MATH
48.
Herron IH (2001) Onset of convection in a porous medium with internal heat source and variable gravity. Int J Eng Sci 39(2):201–208MathSciNetMATH
49.
Harfash AJ (2014) Convection in a porous medium with variable gravity field and magnetic field effects. Transp Porous Media 103(3):361–379MathSciNet
50.
Chandrasekhar S (1981) Hydrodynamic and hydromagnetic stability. Dover, New yorkMATH
51.
52.
Joseph DD (1966) Nonlinear stability of the Boussinesq equations by the method of energy. Arch Ration Mech Anal 22(3):163–184MathSciNet
53.
Joseph DD (1976) Stability of fluid motions. Springer, Berlin, HeidelbergMATH
54.
Straughan B (2004) Resonant porous penetrative convection. Proc R Soc A Math Phys Eng Sci 460(2050):2913–2927MathSciNetMATH
55.
Canuto C, Hussaini MY, Quarteroni AM, Zang TA (1988) Spectral methods in fluid dynamics. Springer, Berlin, HeidelbergMATH
Metadata
Title
Effects of spatially varying gravity, temperature and concentration fields on the stability of a chemically reacting fluid layer
Authors
Amit Mahajan
Vinit Kumar Tripathi
Publication date
29-10-2020
Publisher
Springer Netherlands
Published in
Journal of Engineering Mathematics / Issue 1/2020
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-020-10068-1

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