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Effect of Nonlinear Temperature Gradient on the onset of Rayleigh-Benard Electro Convection with Internal Heat Generation and Radiation in a Micropolar Fluid
Current Issue
Volume 5, 2018
Issue 1 (February)
Pages: 1-8   |   Vol. 5, No. 1, February 2018   |   Follow on         
Paper in PDF Downloads: 64   Since Apr. 27, 2018 Views: 1066   Since Apr. 27, 2018
Authors
[1]
Nurul Afiqah Mohd Isa, Department of Mathematics, University Putra Malaysia, Kuala Lumpur, Malaysia.
[2]
Norihan Md Arifin, Department of Mathematics, University Putra Malaysia, Kuala Lumpur, Malaysia; Institute for Mathematical Research, University Putra Malaysia, Kuala Lumpur, Malaysia.
[3]
Norfifah Bachok, Department of Mathematics, University Putra Malaysia, Kuala Lumpur, Malaysia; Institute for Mathematical Research, University Putra Malaysia, Kuala Lumpur, Malaysia.
Abstract
In this article, we have examined Rayleigh-Benard convection in a micropolar fluid with electric field, internal heat generation and cubic temperature gradient for six possible boundaries combination. Galerkin technique was used to find the eigenvalue and linear stability analysis was present. The influence of internal heat generation and nonlinear temperature gradient is studied numerically. Three nonlinear temperature gradients were considered and their comparison effect on the convection was dissertated. Results show that the internal heat generation has a significant influence on the onset convection where increasing the internal heating will destabilize the fluid system.
Keywords
Rayleigh Benard Convection, Internal Heat Generation, Electric Field, Micropolar Fluid
Reference
[1]
Pranesh S., Tarannum S., and Baby R., Effects of Suction–Injection–Combination (SIC) on the onset of Rayleigh–Bénard Electroconvection in a Micropolar Fluid, Mapana J Sci 14, Pp 23-42, (2015).
[2]
Pranesh S. and Baby R., Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid, Applied Mathematics 3, Pp 442-450, (2012).
[3]
Azmi H. M. and Idris R., Effects of Controller and Nonuniform Temperature Profile on the Onset of Rayleigh-Bénard-Marangoni Electroconvection in a Micropolar Fluid, Journal of Applied Mathematics, Pp 1-8, (2014).
[4]
Joseph T. H., Manjunath S. R., and Pranesh S., Effect of Non-Uniform Basic Temperature Gradient on the Onset of Rayleigh-Bénard-Marangoni Electro-Convection in a Micropolar Fluid, Applied Mathematics 4, Pp 1180-1188, (2013).
[5]
Rudraiah N., Shankar B. M., and Ng C. O., Electrohydrodynamic Stability of Couple Stress Fluid Flow in a Channel Occupied by a Porous Medium, Special Topics & Reviews in Porous Media-int journal 2, Pp 11-22, (2011).
[6]
Siddeshwar P. G. and Radhakrishna D., Linear and nonlinear electroconvection under AC electric field, Commun Nonlinear Sci Numer Simulat 17, Pp 2883–2895, (2012).
[7]
El-Sayed M. F., Onset of electroconvective instability of Oldroydian viscoelastic liquid layer in Brinkman porous medium, Arch Appl Mech 78, Pp 211–224, (2008).
[8]
Douiebe A., Hannaoui M., Lebon G., Benaboud A., and Khmou A., Effects of a. c. Electric Field and Rotation on Bénard–Marangoni Convection Flow, Turbulence and Combustion 67, Pp 185–204, (2001).
[9]
Sparrow E. M., Goldstein R. J., and Jonsson, Thermal stability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature, J. Fluid Mech. 18, Pp 513-529, (1964).
[10]
Roberts P. H., Convection in horizontal layers with internal heat generation, Theory. J. Fluid Mech 30, Pp 33-49, (1967).
[11]
Char M. I. and Chiang K. T., Stability analysis of Benard-Marangoni convection in fluids with internal heat generation, Phys. D: Appl. Phys. 27, Pp 748-755, (1994).
[12]
Wilson S. K., The effects of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of fluid, Acta Mechanica 124, Pp 63-78 (1997).
[13]
Bachok N., Arifin N. M., and Ali F. M., Effects of Control on the Onset of Marangoni-Benard Convection with Uniform Internal Heat Generation, matematika 24, Pp 23–29, (2008).
[14]
Yekashi V., Pranesh S., and Bathul S., Effects of Gravity Modulation and Internal Heat Generation on the onset of Rayleigh-Bénard convection in a Micropolar Fluid, Journal of Advances in Mathematics 12, Pp 6270-6285, (2016).
[15]
Nanjudappa C. E., Shivakumara I. S., and Arunkumar R., Onset of Benard-Marangoni Ferroconvection with Internal Heat Generation, Microgravity Sci. Technol. 23, Pp 29–39, (2011).
[16]
Khalid I. K., Mokhtar N. F. M., and Arifin N. M., Uniform Solution on the Effect of Internal Heat Generation on Rayleigh Benard Convection in Micropolar, Fluid Int J. of Math, Comp, Phy, Elec and Comp Eng 7, Pp 440-445, (2013).
[17]
Eringen A. C., Theory of Micropolar Fluids, International Journal of Engineering Science 16, Pp 1-18, (1966).
[18]
Siddeshwar P. G. and Pranesh S., Effect of a non-uniform basic temperature gradient on Rayleigh-Benard convection in a micropolar fluid, International Journal of Engineering Science 36, Pp 1183-1196, (1998).
[19]
Pranesh S., Effect of Magnetic Field and Non Uniform Basic Temperature Gradient on The Onset of Rayleigh Benard Convection in Micropolar Fluid, MJS 6, Pp 1-33, (2007).
[20]
Dupont O., Hennenberg M., and Legros J. C., Marangoni–Bénard Instabilities under Non-steady Conditions Experimental and Theoretical results, International Journal of Heat and Mass Transfer 35, Pp 3237–3244, (1992).
[21]
Chiang K. T., Effect of a Non-Uniform Basic Temperature Gradient on the Onset of Bénard–Marangoni Convection: Stationary and Oscillatory Analyses, International Communication in Heat and Mass Transfer 32, Pp 192–203, (2005).
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