NUMERICAL STUDY OF MIXED CONVECTION FLOW OF A MICROPOLAR FLUID TOWARDS PERMEABLE VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION

Ch. RamReddy; T. Pradeepa; D. Srinivasacharya

doi:10.11948/2016021

2016 Volume 6 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2016 > 6(2): 254-270

Next Article Previous Article

Ch. RamReddy, T. Pradeepa, D. Srinivasacharya. NUMERICAL STUDY OF MIXED CONVECTION FLOW OF A MICROPOLAR FLUID TOWARDS PERMEABLE VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 254-270. doi: 10.11948/2016021

Citation:

Ch. RamReddy, T. Pradeepa, D. Srinivasacharya. NUMERICAL STUDY OF MIXED CONVECTION FLOW OF A MICROPOLAR FLUID TOWARDS PERMEABLE VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 254-270. doi: 10.11948/2016021

NUMERICAL STUDY OF MIXED CONVECTION FLOW OF A MICROPOLAR FLUID TOWARDS PERMEABLE VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION

Department of Mathematics, National Institute of Technology Warangal-506004, India

Abstract

Abstract

In this article, the mixed convective flow of a micropolar fluid along a permeable vertical plate under the convective boundary condition is analyzed. The scaling group of transformations is applied to get the similarity representation of the system of partial differential equations of the problem and then the resulting equations are solved by using Spectral Quasi-Linearisation Method. This study reveals that the dual solutions exists for certain values of mixed convection parameter. The outcomes are analyzed with dual solutions in detail. Effects of micropolar parameter, Biot number and suction/injection parameters on different flow profiles are discussed and depicted graphically.
- Mixed convection /
- micropolar fluid /
- convective boundary condition /
- spectral Quasi-linearization method /
- dual solutions
MSC: 76A05;76R99;76M22;76M60

FullText(HTML)

References

[1]	G. Ahmadi, Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Eng. Science, 14(1976), 639-646. Google Scholar
[2]	A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun Nonlinear Sci Numer Simulat, 14(2009), 1064-1068. Google Scholar
[3]	R.E. Bellman and R.E. Kalaba, Quasilinearisation and Non-linear Boundaryvalue Problems, Elsevier, New York, 1965. Google Scholar
[4]	G.W. Bluman and S.C. Anco, Symmetry and Integration Methods for Differential Equations, Springer-Verlag 2009. Google Scholar
[5]	C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods Fundamentals in Single Domains, Springer, Verlag, 2006. Google Scholar
[6]	V.A. Eremeyev, L.P. Lebedev and H. Altenbach, Foundations of Micropolar Mechanics, Springer, Heidelberg, New York, 2013. Google Scholar
[7]	A.C. Eringen, Theory of Micropolar Fluids, J. Math. and Mech., 16(1966), 1-18. Google Scholar
[8]	I.A. Hassanien and M.A.A. Hamad, Group theoretic method for unsteady free convection flow of a micropolar fluid along a vertical plate in a thermally stratified medium, Applied Mathematical Modelling, 32(2008), 1099-1114. Google Scholar
[9]	A. Ishak, Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition, Applied Mathematics and Computation, 217(2010), 837-842. Google Scholar
[10]	S. Jena and M. Mathur, Mixed convection flow of a micropolar fluid from an isothermal vertical plate, Camp. Maths. with Appls., 10(1984), 291-304. Google Scholar
[11]	R. Kandasamy, K. Gunasekaran and S.B.H. Hasan, Scaling group transformation on fluid flow with variable stream conditions, International Journal of Non-Linear Mechanics, 46(2011), 976-985. Google Scholar
[12]	G. Lukaszewicz, Micropolar fluids-Theory and Applications, Birkhauser, Basel, 1999. Google Scholar
[13]	O.D. Makinde and P.O. Olanrewaju, Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition, Journal of Fluids Engineering, 132(2010), 044502-1-4. Google Scholar
[14]	J.H. Merkin, Mixed convection from a horizontal circular cylinder, International Journal of Heat and Mass Transfer 20(1977), 73-77. Google Scholar
[15]	S.S. Motsa, P.G. Dlamini and M. Khumalo, Spectral relaxation method and spectral quasilinearization method for solving unsteady boundary layer flow problems, Advances in Mathematical Physics, 2014(2014). DOI:10.1155/2014/341964. Google Scholar
[16]	S.S. Motsa, P. Sibanda, J.M. Ngnotchouye and G.T. Marewo, A spectral relaxation approach for unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet, Advances in Mathematical Physics, 2014(2014). DOI:10.1155/2014/564942. Google Scholar
[17]	A.A. Mutlag, M.J. Uddin, M.A.A. Hamad and A.I.M. Ismail, Heat transfer analysis for falkner-skan boundary layer flow past a stationary wedge with slips boundary conditions considering temperature-dependent thermal conductivity, Sains Malaysiana, 42(2013), 855-862. Google Scholar
[18]	R. Nazar, N. Amin and I. Pop, Mixed convection boundary-layer flow from a horizontal circular cylinder in micropolar fluids:case of constant wall temperature, International Journal of Numerical Methods for Heat and Fluid Flow, 13(1)(2003), 86-109. Google Scholar
[19]	M. Pakdemirli and M. Yurusoy, Similarity transformations for partial differential equations, SIAM Review, 40(1998), 96-101. Google Scholar
[20]	D. Prakash and M. Muthtamilselvan, Effect of radiation on transient MHD flow of micropolar fluid between porous vertical channel with boundary conditions of the third kind, Ain Shams Engineering Journal, 5(2014), 1277-1286. Google Scholar
[21]	G.K. Ramesh and B.J. Gireesha, Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles, Ain Shams Engineering Journal, 5(2014), 991-998. Google Scholar
[22]	Ch. RamReddy, P.V.S.N. Murthy, J.A. Chamkha and A.M. Rashad, Soret effect on mixed convection flow in a nanofluid under convective boundary condition, International Journal of Heat and Mass Transfer, 64(2013), 384-392. Google Scholar
[23]	M.A. Seddeek, M.Y. Akl and A.M. Al-Hanaya, Thermal radiation effects on mixed convection and mass transfer flow on vertical porous plate with heat generation and chemical reaction by using scaling group, Journal of Natural Sciences and Mathematics 4(2010), 41-60. Google Scholar
[24]	T. R. Sekhar and V.D. Sharma, Similarity solutions for three dimensional Euler equations using Lie group analysis, Applied Mathematics and Computation, 196(2008), 147-157. Google Scholar
[25]	T. R. Sekhar and V.D. Sharma, Similarity analysis of modified shallow water equations and evolution of weak waves, Commun Nonlinear Sci Numer Simulat, 17(2012), 630-636. Google Scholar
[26]	D. Srinivasacharya and Ch. RamReddy, Mixed convection heat and mass transfer in a micropolar fluid with soret and dufour effects, Adv. Appl. Math. Mech., 3(4)(2011), 389-400. Google Scholar
[27]	D. Srinivasacharya and Ch. RamReddy, Mixed convection in a doubly stratified micropolar fluid saturated non-Darcy porous medium, Canadian J. Chemical Engineering, 90(2012), 1311-1322. Google Scholar
[28]	S.V. Subhashini, N. Samuel and I. Pop, Double-diffusive convection from a permeable vertical surface under convective boundary condition, Int. Commun. Heat and Mass Transfer, 38(2011), 1183-1188. Google Scholar
[29]	M.J. Uddin, W.A. Khan and A.I.M. Ismail, MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition, Plos One 7(2012), e49499. Google Scholar