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Prakash, Jyoti
- On the Characterization of Nonoscillatory Motions in Maxwell Fluid in a Porous Medium Heated from Below
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Authors
Jyoti Prakash
1,
Renu Bala
1
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171005, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 51-54Abstract
In the present paper condition for characterizing nonoscillatory motions which may be neutral or unstable in a horizontal layer of Maxwell fluid in a porous medium (modified Darcy-Brinkman-Maxwell Model) heated from below is obtained. It is proved that for a horizontal layer of Maxwell fluid in a porous medium heated from below an arbitrary neutral or unstable mode of the system is definitely nonoscillatory in character and in particular the ‘ principle of the exchange of stabilities’ is valid if (RλP_r)/4∏ ∧ 2≤ 1. The result is uniformly valid for all combinations of free and rigid boundaries.Keywords
Maxwell Fluid, Oscillatory Motions, Thermal Convection, Porous Media, Modified – Darcy - Brinkman – Maxwell Model.
References
- Benard H 1900 Les tourbillions cellulaires dans une nappe liquid. Revenue generale des Sciences pures et appliqués 11 1261-71 and 1309- 28
- Bezan A 2004 Convection Heat Transfer third ed. John Wiley and Sons New Jersey
- Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic stability Clarendon Oxford
- Chen F and Chen C F 1988 Onset of finger Convection in a horizontal porous layer underlying a fluid layer J. Heat Transf. 110(2) 403 – 09
- Drazin P and Reid W 1981 Hydrodynamic Stability Cambridge University Press Cambridge
- Fu C Zhang Z and Tan W 2007 Numerical simulation of thermal convection of a viscoelastic fluid in a porous square box heated from below Physics of Fluids 19 104107(1 – 12)
- Horton C and Rogers F 1945 Convection currents in a porous medium J. Appl. Phys. 16(6) 367-70
- Katto Y and Masuoka T 1967 Criterion for the onset of convective flow in a fluid in a porous medium Int. J. Heat mass Transf. 10(3) 297-309
- Laroze D, Martinez-Mardones J and Bragard J 2007 Thermal convection in a rotating binary viscoelastic liquid mixture Eur. Phys. J. Special Topics 146 291-300
- Li Z and Khayat R E 2005 Finite amplitude Rayleigh-Benard Convection and pattern selection for viscoelastic fluids J. Fluid Mech. 529 221- 51 M. H. Schultz, Spline Analysis, Prentice Hall, Englewood Cliffs, NJ, (1973).
- M. H. Schultz (1973) Spline Analysis Prentice Hall Englewood Cliffs NJ
- Malashetty M S and Swamy M 2007 The onset of convection in a viscoelastic liquid saturated anisotropic porous layer, Trans. Por. Med. 67 203 – 18
- Malashetty M S Swamy M and Kulkarni S 2007 Thermal convection in a rotating porous layer using a thermal nonequilibrium model Phys. Fluids 19 054102 (1-16)
- Mckibbin R and O’Sullivan M J 1980 Onset of convection in a layered porous medium from below J. Fluid Mech. 96(2) 375-93
- Pellew A and Southwell R V 1940 On the maintained convective motion in a fluid heated from below Proc. Roy Soc. A 176 312 – 43
- Rayleigh L 1916 On the convective currents in a horizontal layer of fluid when the higher temperature is on the upper side Phil. Mag. 32 529- 46
- Saravanan S 2009 Centrifugal acceleration induced convection in a magnetic fluid saturated anisotropic rotating porous medium Trans. Por. Med. 77 79 – 86
- Sokolov M and Tanner R I 1972 Convective stability of a general viscoelastic fluid heated from below The Phys. Fluids 15(4) 534 – 39
- Straughan B 2006 Global nonlinear stability in porous convection with a thermal non – equilibrium model Proc. Roy. Soc. A 462 409 – 18
- Tan W and Masuoka T 2007 Stability analysis of a Maxwell Fluid in a Porous medium heated from below Physics Letters A 360 454-60
- Vest C M and Arpaci V S 1969 Overstability of a viscoelastic layer heated from below J. Fluid Mech. 36 (3) 613 – 23
- Yin C Fu C and Tan W 2012 Onset of thermal convection in a Maxwell fluid saturated porous medium. The effects of hydrodynamic boundary and constant flux heating conditions Trans. Porous. Med. 91 777 – 90
- Yoon D Y Kim M C and Choi C K 2004 The onset of oscillatory convection in a horizontal porous layer saturated with viscoelastic liquid Trans. Por. Med. 55 275 – 84
- Zhang Z Fu C and Tan W 2008 Linear and non linear stability analysis of thermal convection for Oldroyd-B fluids in porous media heated from below Phys. Fluids 20 084103(1 – 12)
- On Linear Growth Rates in Thermohaline Convection with Viscosity Variations
Abstract Views :720 |
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Authors
Jyoti Prakash
1,
Kanu Vaid
1
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 140-143Abstract
In the present paper it is proved that the complex growth rate (where and are real and imaginary parts of p ) of an arbitrary oscillatory motions of growing amplitude, neutral or unstable, for thermohaline convection configuration of Veronis type (Veronis, G., J. Mar. Res., 23(1965)1), with the viscosity variations must lie inside a semicircle in the right half of the prpiplane whose centre is at the origin and radius equals . A similar theorem is also proved for thermohaline convection of Stern type (Stern, M.E., Tellus 12(1960)172). Furthermore the above results are uniformly valid for all combinations of rigid and free bounding surfaces. The results obtain herein, in particular, also yield sufficient conditions for the validity of the ‘principle of the exchange of the stabilities’ for the respective configurations.Keywords
Thermohaline Instability, Oscillatory Motions, Veronis Type, Stern Type, Variable Viscosity.References
- Banerjee M. B., Katoch D. C., Dube G. S. and Banerjee K., Bounds for growth rate of a perturbation in thermohaline convection, Proc. Roy. Soc. London. A 387(1981)301.
- Banerjee M. B., Gupta J. R. and Shandil R.G., Generalized thermal convection with viscosity variations, J. Math. Phys. Sc. 11(5)(1977)421.
- Brandt A. and Fernando H. J. S., Double Diffusive Convection, Am. Geophys. Union, Washington, (1996).
- Lighthill M. J., Introduction to Boundary Layer Theory in Laminar Boundary Layers, (Ed.: L. Rosenhead), Clarendon Press, Oxford, (1963).
- Prakash J., A Mathematical theorem for thermohaline convection of the Veronis type with viscosity variations, Ind. J. Pure Appl.Math., 26(8)(1995)813.
- Schultz M. H., Spline Analysis, Prentice Hall Ince., Englewood Cliffs. N.J., (1973).
- Stern M. E., The salt fountain and thermohaline convection, Tellus 12 (1960)172.
- Torrance K.E., and. Turcotte D.L., Thermal convection with large viscosity variation, J. Fluid Mech, 47(1971)113.
- Turner J. S., Double diffusive phenomena, Ann. Rev. Fluid mech. 6(1974)37.
- Veronis G., On finite amplitude instability in thermohaline convection, J. Mar. Res., 23(1965)1.
- On Exchange Principle in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations
Abstract Views :190 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN
2 Department of Physics, M.L.S.M. College, Sunder Nagar (H. P.), IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN
2 Department of Physics, M.L.S.M. College, Sunder Nagar (H. P.), IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 1-5Abstract
Linear stability of a triply diffusive fluid layer heated from below, which is kept under the effect of uniform vertical magnetic field, has been studied by considering variable viscosity. A sufficient condition for the occurrence of stationary convection is derived. These results are uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Variable Viscosity, Concentration Rayleigh Number, Stationary Convection, Chandrasekhar Number.- On Rotatory Hydrodynamic Triply Diffusive Convection in Porous Medium:Darcy Model
Abstract Views :188 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5, IN
2 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5, IN
2 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 19-22Abstract
Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable for triply diffusive convection in porous medium (Darcy model) in the presence of a uniform vertical rotation, are obtained. It is further proved that the result obtained herein is uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Porous Medium, Taylor Number, Concentration Rayleigh Number, Darcy Model.- Upper Limits to the Linear Growth Rate in Triply Diffusive Convection
Abstract Views :173 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 47-49Abstract
In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a triply diffusive fluid layer (with one of the component as heat with diffusivity κ) must lie inside a semicircle in the right half of the (Pr, Pi) - plane whose centre is at the origin and radius equals √(|R| + R1) where R and R1 are the thermal Rayleigh number and concentration Rayleigh number with diffusivities κ and κ_1. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Concentration Rayleigh Number.- A Characterization Theorem in Rotatory Thermohaline Convection of Veronis Type in Porous Medium
Abstract Views :266 |
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Authors
Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
Research Journal of Engineering and Technology, Vol 3, No 2 (2012), Pagination: 133-139Abstract
The present paper mathematically establishes that rotatory thermohaline convection of the Veronis type in porous medium cannot manifest itself as oscillatory motion of growing amplitude in an initially bottom heavy configuration if the thermohaline Rayleigh number Rs, the Lewis number , the Prandtl number p1, the porosity , satisfy the inequality Rs≤4π2 (1/P>l +τ/(E'∈p1 )) , where Pl and E' are constants which depend upon porosity of the medium. It further establishes that this result is uniformly valid for the quite general nature of the bounding surfaces.- On Rotatory Hydrodynamic Triply Diffusive Convection in Porous Medium
Abstract Views :200 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 113-117Abstract
Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for rotatory hydrodynamic triply diffusive convection in a porous medium is derived. It is analytically proved that the principle of the exchange of stabilities, in rotatory triply diffusive convection in a porous medium, is valid in the regime R1E1σ/2τ21π4 + R2E2σ/2τ22π4 + Ta/π2ΛDa-1 ≤ 1, where R1 and R2 are the concentration Raleigh numbers, and τ1 and τ2 are the Lewis numbers for the two concentration components respectively, Ta is the Taylor number, σ is the Prandtl number, Da is the Darcy number, E1 and E2 are constants.Keywords
Triply Diffusive Convection, Porous Medium, Darcy-Brinkman Model, the Principle of the Exchange of Stabilities, Taylor Number, Concentration Rayleigh Number.- Linear Stability Analysis of Multicomponent Convection
Abstract Views :236 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 118-122Abstract
Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for multicomponent convection is derived.Keywords
Multicomponent Convection, The Principle of the Exchange of Stabilities, Oscillatory Motions, Complex Growth Rate, Concentration Rayleigh Number.- On the Onset of Stationary Convection in Double-Diffusive Binary Viscoelastic Fluid Saturated Anisotropic Porous Layer
Abstract Views :180 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla 171005, IN
2 Department of Physics, M.L.S.M. College, Sunder-Nagar, Distt. Mandi (H.P.), IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla 171005, IN
2 Department of Physics, M.L.S.M. College, Sunder-Nagar, Distt. Mandi (H.P.), IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 223-226Abstract
Linear stability of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer has been studied analytically. A sufficient condition for the occurrence of stationary convection has been derived in terms of the parameters of the system alone. It is further proved the above result is uniformly valid for any combination of the bounding surfaces.Keywords
Double-Diffusive Convection, Viscoelastic Fluid, The Principle of the Exchange of Stabilities, Porous Medium.- A Characterization Theorem in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations
Abstract Views :398 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 81-86Abstract
The paper mathematically establishes that magnetohydrodynamic triply diffusive convection, with variable viscosity and with one of the components as heat with diffusivity κ, cannot manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R1 and R2, the Lewis numbers τ1 and τ2 for the two concentrations with diffusivities k1 and k2 respectively (with no loss of generality κ > κ1 > κ2), μmin (the minimum value of viscosity μ in the closed interval [0,1]) and the Prandtl number σ satisfy the inequality R1 + R2 ≤ 27π4/4{μmin+(τ1+τ2)/σ/1+τ1/τ22 provided D2μ is positive everywhere. It is further proved that this result is uniformly valid for any combination of rigid and/or free perfectly conducting boundaries.Keywords
Triply Diffusive Convection, Variable Viscosity, Concentration Rayleigh Number, Oscillatory Motion, Initially Bottom Heavy Configuration and Chandrasekhar Number.- An Energy Relationship in Multicomponent Convection Problem
Abstract Views :186 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 99-102Abstract
analogous to magnetohydrodynamic thermohaline convection problem of Veronis (1965) type has been established. It is shown that the total kinetic energy associated with a disturbance exceeds the sum of its total magnetic and concentration energies in the parameter regime Qσ1/π2 + R1σ/4τ21π4 + R2σ/4τ22π4 + ⋯+ Rn-1σ/τ2n-1π4 ≤ 1, where Q,σ,σ1,τ1,τ2,…,τn-1,R1,R2,…,Rn-1 represent Chandrasekhar number, Prandtl number, magnetic Prandtl number, Lewis number for first concentration component, Lewis number for second concentration component, Lewis number for (n − 1)th concentration component, concentration Rayleigh number for first component, concentration Rayleigh number for second component, concentration Rayleigh number for (n - 1)th component respectively. Further, this result is uniformly valid for any combination of rigid or free boundaries whether perfectly conducting or insulating.Keywords
Multicomponent Convection, Chandrasekhar Number, Lewis Number, Prandtl Number, Rayleigh Number.- Characterization of Magnetorotatory Thermohaline Instability in Porous Medium:Darcy Model
Abstract Views :202 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 32-36Abstract
The present paper prescribes upper bounds for oscillatory motions of neutral or growing amplitude in magnetorotatory thermohaline configurations of Veronis (Veronis, G., J. Mar. Res., 23(1965)1) and Stern types (Stern, M.E., Tellus 12(1960)172) in porous medium (Darcy model) in such a way that also result in sufficient conditions of stability for an initially bottom-heavy as well as initially top-heavy configuration.
Keywords
Thermohaline Instability, Oscillatory Motions, Initially Bottom-Heavy Configuration, Initially Topheavy Configuration, Porous Medium.- Upper Limits to the Complex Growth Rates in Triply Diffusive Convection in Porous Medium
Abstract Views :179 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
2 Department of Physics, MLSM College, Sundernagar, H.P., IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
2 Department of Physics, MLSM College, Sundernagar, H.P., IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-3Abstract
The paper mathematically establishes that the complex growth rate (pr,pi ) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer in porous medium (Darcy Model) with one of the components as heat with diffusivity , must lie inside a semicircle in the right- half of the (pr,pi)-plane whose centre is origin and radius equals √(R1+<R2)σ where R1 and R2 are the Raleigh numbers for the two concentration components with diffusivities k1 and k2 (with no loss of generality, k > k1> k2 ) and is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Porous Medium.- Upper Bounds for the Complex Growth Rate of Thermohaline Convection of Veronis and Stern Types with Viscosity Variations
Abstract Views :163 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-4Abstract
Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation which may be neutral or unstable of thermohaline convection of Veronis (G.Veronis, J.MarineRes., 23, (1965) 1-17) type with the viscosity variation effects included heated from below are obtained which in particular yield sufficient condition for the validity the "principle of the exchange of stabilities" for this configuration. Similar results are also obtained for thermohaline convection of Stern (ME Stern, Tellus, 12,(1960), 171-175) type with the viscosity variation effect included. The results obtained herein are uniformly valid for all combinations of dynamically free and rigid boundaries.
Keywords
Thermohaline Instability, Veronis Type, Stern Type, Oscillatory Motions, Variable Viscosity.- On the Characterization of Nonoscillatory Motions in Triply Diffusiveconvection in Porous Medium
Abstract Views :160 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-3Abstract
The present paper mathematically establishes that 'the principle of the exchange of stabilities' for triply diffusive convection in porous medium (Darcy model) is valid in the regime (R_1 σ)/(2〖ι_1〗^2 π^4 )+(R_2 σ)/(2〖ι_2〗^2 π^4)≤1, where R_1 and R_2 are the Rayleigh numbers for the two concentration components, ι_1 and ι_2 are the Lewis numbers for the two concentration components and σ is the thermal Prandtl number. It is further proved that the above result is uniformly valid for any combination of rigid and free boundaries.
Keywords
Triply Diffusive Convection, Nonoscillatory Motions, Principle of the Exchange of Stabilities, Concentration Rayleigh Number, Porous Medium, Darcy Model.- A Semi-Circle Theorem in Triply Diffusive Convection
Abstract Views :326 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-4Abstract
The paper mathematically establishes that the complex growth rate (Pr, Pi) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer with one of the components as heat with diffusivity k, must lie inside a semicircle in the right- half of the (Pr, Pi)-plane whose centre is origin and radius equals
√(R1+R2)σ-27/4π4τ22
where R1 and R2are the Rayleigh numbers for the two concentration components with diffusivities κ1and κ2(with no loss of generality, κ > κ1> κ2) and σ is the Prandtl number. The bounds obtained herein, in particular, yield a sufficient condition for the validity of 'the principle of the exchange of stability'. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Principle of the Exchange of Stability.- On Triply Diffusive Convection Analogous to Stern Type with Variable Viscosity
Abstract Views :155 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, IN
2 J.N. Government Engineering College, Sunder Nagar (H.P.), IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, IN
2 J.N. Government Engineering College, Sunder Nagar (H.P.), IN
Source
Research Journal of Science and Technology, Vol 9, No 1 (2017), Pagination: 111-114Abstract
The paper mathematically establishes that triply diffusive convection (analogous to Stern type), with variable viscosity and with one of the components as heat, cannot manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the thermal Rayleigh number |R|, the Lewis number τ2 for the second concentration component , μmin (the minimum value of viscosity μ in the closed interval [0,1]) and the Prandtl number σ satisfy the inequality |R| ≤ 27π4/4 τ2(μmin + 1/σ) provided D2μ is positive everywhere. It is further proved that this result is uniformly valid for the quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Variable Viscosity, Concentration Rayleigh Number, Oscillatory Motion, Initially Bottom Heavy Configuration.- On Double-Diffusive Convection in a Binary Viscoelastic Fluid Saturated Anisotropic Porous Layer
Abstract Views :148 |
PDF Views:3
Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla 171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla 171005, IN
Source
Research Journal of Science and Technology, Vol 9, No 1 (2017), Pagination: 123-126Abstract
In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a double diffusive binary viscoelastic fluid saturated anisotropic porous layer heated from below must lie inside a semicircle in the right half of the (Pr, Pi)-plane whose centre is at the origin and radius equals λ1PrDRaT+√PrD(λ12RaT2PrD+4Ras)/2, where RaT and Ras are the Darcy -Rayleigh number and the solute Rayleigh number respectively. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.Keywords
Double-Diffusive Convection, Viscoelastic Fluid, Porous Medium, Complex Growth Rate, Solute Rayleigh Number.- On Triply Diffusive Convection in Porous Medium:Darcy Brinkman Model
Abstract Views :149 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
2 Department of Physics, MLSM College, Sundernagar, H. P., IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
2 Department of Physics, MLSM College, Sundernagar, H. P., IN
Source
Research Journal of Science and Technology, Vol 9, No 1 (2017), Pagination: 127-130Abstract
The present paper deals with the problem of triply diffusive convection analogous to Stern type in porous medium using Darcy-Brinkman model. Bounds are obtained for the complex growth rate of an arbitrary oscillatory perturbation of growing amplitude, neutral or unstable for this configuration which is uniformly valid for any combination of bounding surfaces.Keywords
Triply Diffusive Convection, Concentration Rayleigh Number, Porous Medium, Darcy-Brinkman Model.- On the Occurrence of Stationary Convection in Triply Diffusive Convection in Porous Medium : Darcy Model
Abstract Views :134 |
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN