American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: Editor-in-chief: Apply for this position
Open Access
Journal Browser
American Journal of Mathematical Analysis. 2017, 5(1), 12-16
DOI: 10.12691/ajma-5-1-3
Open AccessArticle

Matehmatical Study of Thermosolutal Convection in Heterogeneous Vscoelastic Fluid in the Presence of Porous Medium

Anil Kumar1,

1Department Applied Sciences (Mathematics), Chandigarh Engineering College Landarn, Mohali, Punjab, India

Pub. Date: March 17, 2017

Cite this paper:
Anil Kumar. Matehmatical Study of Thermosolutal Convection in Heterogeneous Vscoelastic Fluid in the Presence of Porous Medium. American Journal of Mathematical Analysis. 2017; 5(1):12-16. doi: 10.12691/ajma-5-1-3


The present paper a thermo-solutal convection in Walters B' heterogeneous visco-elastic fluid through Brinkman permeable effect is investigated. The investigation of thermosolutal convection is proposed by its complexities of double diffusive dissemination and importance of geophysics and nuclear physics. The results are investigation of the oscillatory modes exists under different conditions and non-oscillatory modes are unstable.

Thermosolutal Convection Heterogeneous Walters B’ Viscoelastic Fluid Porous Medium Linear Stability Theory dispersion

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Chandrasekhar, S.. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford, UK, 1961.
[2]  Veronis, G.. On Finite Amplitude Instability in Thermohaline Convection. J. Marine Res. 23. pp. 1-17. 1965.
[3]  Tabor, H. and Matz, R.. Solar Pond Project, Solar Energy. 9. pp. 177-182. 1965.
[4]  Shirtcliffe, T.G.L.. Thermosolutal Convection: Observation of an Overstable Mode. Nature (London). 213. pp. 489-490. 1967.
[5]  Lister, P.E.. On the Thermal Balance of a Mid-Ocean Ridge. Geophys. J. Roy. Astr. Soc. 26. pp. 515-535. 1972.
[6]  [McDonnel, J.A.M.. Cosmic Dust. John Wiley and Sons, Toronto. p. 330. 1978.
[7]  Vest, C.M. and Arpaci, V.S.: Overstability of a Viscoelastic Fluid Layer Heated From Below. J. Fluid Mech. 36. pp. 613-619. 1969.
[8]  Bhatia, P.K. and Steiner, J.M.: 1972. Convective Instability in a Rotating Viscoelastic Fluid Layer. Zeitschrift fur Angewandte Mathematik und Mechanik. 52. pp. 321-327. 1972.
[9]  Sharma, R.C. and Sharma, K.C.. Thermal Instability of a Rotating Maxwell Fluid Through Porous Medium. Metu J. Pure Appl. Sci. 10. pp. 223-229. 1977.
[10]  Sharma, R.C.: Thermal Instability in a Viscoelastic Fluid in Hydromagnetics. Acta Physica Hungarica. 38. pp. 293-298. 1975.
[11]  Oldroyd, J.G.: Non-Newtonian Effects in Steady Motion of Some Idealized Elastico-Viscous liquids. Proc. Royal Society London. A245. pp. 278-297. 1958.
[12]  Walters, K.. The Motion of Elastico-Viscous Liquid Contained Between Coaxial Cylinders. J. Mech. Appl. Math. 13. pp. 444-453. 1960.
[13]  Walters, K.: The Solution of Flow Problems in Case of Materials With Memory. J. Mecanique. 1. pp. 469-479. 1962.
[14]  Chakraborty, G. and Sengupta, P.R.. MHD Flow of Unsteady Viscoelastic (Walters Liquid B’) Conducting Fluid Between Two Porous Concentric Circular Cylinders. Proc. Nat. Acad. Sciences India. 64. pp. 75-80.1994.
[15]  Sharma, R.C. and Kumar, P.. On the Stability of Two Superposed Walters Elastico-Viscous Liquid B’. Czech. J. Phys. 47. pp. 197-204. 199 1997.
[16]  Sharma, R.C. and Kumar, P.. Rayleigh- Taylor Instability of Two Superposed Walters B’ Elastico-Viscous Fluids in Hydromagnetics. Proc. Nat. Acad. Sci. India. 68. pp.151-161. 1998.
[17]  Kumar, P.. Effect of Rotation on Thermal Instability in Walters B’ Elastico-Viscous Fluid. Proc. Nat. Acad. Sci. India. 71, pp. 33-41. 2001.
[18]  Kumar, P., Mohan, H. and Singh, G.J.. Stability of Two Superposed Viscoelastic Fluid-Particle Mixtures. Z. Angew. Math. Mech. 86. pp. 72-77. 2006.
[19]  Pawan Preet Kaur, SP Agrawal and Anil Kumar (2014). Analysis of heat transfer in hydrodynamic rotating flow of viscous fluid through a non homogenious porous medium with constant heat source / sink, International J. of Engg. Research & Indu. Appls., Vol.7, No. I, pp 9-24.
[20]  Pawan Preet Kaur, SP Agrawal and Anil Kumar (2013). Finite Difference Technique for Unsteady MHD Periodic Flow of Viscous Fluid through a Planer Channel, American Journal of Modeling and Optimization, USA, Vol. 1, No. 3, 47-55.
[21]  Anil Kumar, CL Varshney and Sajjan Lal (2013). Perturbation technique of MHD free convective flow through infinite vertical porous plate with constant heat flux, International Journal of Mathematical Modeling and Physical Sciences, India Vol. 01, (02) pp 1-5, 2013.
[22]  Anil Kumar and S P Agrawal (2013). Mathematical and Simulation of lid driven cavity flow at different aspect ratios using single relaxation time lattice Boltzmann technique, American Journal of theoretical and Applied Statistics, USA vol 2 (3), pp 87-93.
[23]  Anil Kumar, R. K. Saket, C L Varshney and Sajjan Lal. Finite difference technique for reliable MHD steady flow through channels permeable boundaries, International Journal of Biomedical Engineering and Technology (IJBET) UK, Vol. 4(2) pp 101-110, 2010.