Journal of Applied and Computational Mechanics
Variable Thermal Conductivity and Thermal Radiation Effect on the Motion of a Micro Polar Fluid over an Upper Surface
Document Type : Research Paper
Authors
1 Department of Applied Mathematics, Sri Padmavati Mahila University, Tirupati,Andhra Pradesh -517502, India
2 Department of Mathematics, SAS, VIT, Vellore,Tamil Nadu-632014, India
3 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
Abstract
The intent of this analysis is to explore the influence of thermal radiation paired with variable thermal conductivity on MHD micropolar fluid flow over an upper surface. The novelty of the present model is to consider the fluid flow along an upper horizontal surface of a paraboloid of revolution (uhspr) with the porous medium. This physical phenomenon is described by a set of coupled non-linear ODEs by using suitable scaling analysis. The ODEs along with the boundary conditions are solved numerically. Influence of various flow parameters on momentum, thermal and concentration boundary layers is discussed graphically. It is noticed that the variable thickness of the surface has a leading consequence on the boundary layer progression along the surface. Moreover, the results of this study are not only useful for industrial applications but also present a basic understanding of the physical model.
Keywords
Main Subjects
[1] B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two dimensional and axis symmetric flow, AIChE Journal, 26 (1961) 221-227.
[2] L.J. Crane, Flow past a stretching plate, Journal of Applied Mathematics and Physics, 21 (1970) 645-647.
[3] Ishak, R. Nazar and I. Pop, Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet, Meccanica, 43 (2008) 411-418.
[4] E.M.A. Elbashbeshy, D.M. Yassmin and A.A. Dalia, Heat transfer over an unsteady porous stretching surface embedded in a porous medium with variable heat flux in the presence of heat source or sink, African Journal of Mathematics and Computer Science Research, 3(5) (2010) 68-73.
[5] M. Waqas, M. Farooq, M.I. Khan, A. Alsaedi, T. Hayat and T. Yasmeen, Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition, International Journal of Heat and Mass Transfer, 102 (2016) 766-772.
[6] N. Abbas, S. Saleem, S. Nadeem, A.A. Alderremy, and A.U. Khan, on stagnation point flow of a micro polar nanofluid past a circular cylinder with velocity and thermal slip, Results in Physics, 9 (2018) 1224-1232.
[7] S. Nadeem, Z. Ahmed, S. Saleem, The effect of variable viscosities on micro-polar flow of two nanofluids, Zeitschrift für Naturforschung A, 71(12) (2018) 1121–1129.
[8] S. Nadeem and S. Saleem, Analytical study of third grade fluid over a rotating vertical cone in the presence of nanoparticles, micropolar liquid due to nonlinear stretched sheet with convective condition, International Journal of Heat and Mass Transfer, 85 (2015) 1041-1048.
[9] L.L. Lee, Boundary layer over a thin needle, Physics of Fluids, 10 (1967) 822-828.
[10] M.M. Khader and A.M. Megahed, Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity, The European Physical Journal Plus, 128 100 (2013).
[11] M.M. Khader, M.M. Babatin, A. Eid and M. Megahed, Numerical study for simulation the MHD flow and heat-transfer due to a stretching sheet on variable thickness and thermal conductivity with thermal radiation, Applied Mathematics, 6 (2015) 2045-2056.
[12] Y.S. Daniel, Z.A. Aziz, Z. Ismail, F. Salah, Thermal stratification effects on MHD radiative flow of nanofluid over nonlinear stretching sheet with variable thickness, Journal of Computational Design and Engineering, 2 (2018) 232–242.
[13] T. Cebeci, and T.Y. Na, Laminar free-convection heat transfer from a needle, Physics of Fluids, 12 (1969) 463-465.
[14] Md Tausif .Sk, K. Das and P. K. Kundu, Consequences of nanoparticle diameter and solid–liquid interfacial layer on the SWCNT/EO nanofluid flow over various shaped thin slendering needles, Chinese Journal of Physics, in press, Doi: 10.1016/j.cjph.2018.06.016.
[15] R. Ahmad, M. Mustafa, S. Hina, Buongiorno's model for fluid flow around a moving thin needle in a flowing nanofluid: A numerical study, Chinese Journal of Physics, 55 (2017), 1264-1274.
[16] J.L.S. Chen, Mixed convection flow about slender bodies of revolution, J. Heat Transf., 109 (1987) 1033-1036.
[17] S.L. Lee, T.S. Chen and B.F. Armaly, Mixed convection along vertical cylinders and needles with uniform surface heat flux, Journal of Heat Transfer, 109 (1987) 711-716.
[18] C.Y. Wang, Mixed convection on a vertical needle with heated tip, Physics of Fluids, 2 (1990) 622-625.
[19] S. Ahmad, N.M. Arifin, R. Nazar and I. Pop, Mixed convection boundary layer flow along vertical thin needles: assisting and opposing flows, International Communications in Heat and Mass Transfer, 35 (2008) 157-162.
[20] R.T. Davis and M.J. Werle, Numerical solutions for laminar incompressible flow past a paraboloid of revolution, American Institute of Aeronautics and Astronautics, 10 (2015) 1224–1230.
[21] I.L. Animasaun and N. Sandeep, Buoyancy induced model for the flow of 36 nm alumina-water nanofluid along upper horizontal surface of a paraboloid of revolution with variable thermal conductivity and viscosity, Power Technology, 301 (2016) 858-867.
[22] O.D. Makinde and I.L. Animasaun, Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution, International Journal of Thermal Sciences, 109 (2016) 159-171.
[23] M. Gnaneswara Reddy and N. Sandeep, Computational modelling and analysis of heat and mass transfer in MHD flow past the upper part of a paraboloid of revolution, The European Physical Journal Plus, 132 222, (2017).
[24] O.K. Koriko, I.L. Animasaun, B. Mahantesh, S. Saleem, G. Sarojamma and R. Sivaraj, Heat transfer in the flow of blood-gold Carreau nanofluid induced by partial slip and buoyancy, Heat Transfer-Asian Research ,47(6) (2018) 806-823.
[25] Z. Li, M. Sheikholeslami, A. Shafee, S. Saleem, A.J. Chamkha, Effect of dispersing nanoparticles on solidification process in existence of Lorenz forces in a permeable media, Journal of Molecular Liquids, 266 (2018) 181-193.
[26] S. Mamatha Upadhya, C.S.K.Raju, S. Saleem, A.A. Alderremy, Mahesha, Modified Fourier heat flux on MHD flow over stretched cylinder filled with Dust, Graphene and silver nanoparticles, Results in Physics, 9 (2018) 1377-1385.
[27] P.V. Venkateswarlu and S. Narayana, Chemical reaction and radiation absorption effects on the flow and heat transfer of a nanofluid in a rotating system, Applied Nanoscience, 5 (2015) 351-360.
[28] M. Sheikholeslami, A. Ghasemi, Z. Li, A. Shafee, S. Saleem, Influence of CuO nanoparticles on heat transfer behavior of PCM in solidification process considering radiative source term, International Journal of Heat and Mass Transfer, 126(A) (2018) 1252-1264.
[29] P.V. Satya Narayana, S.M. Akshit, J.P. Ghori and B. Venkateswarlu, Thermal radiation effects on an unsteady MHD nanofluid flow over a stretching sheet with non-uniform heat source/sink, Journal of Nanofluids, 8 (2017) 1-5.
[30] Z. Li, M. Sheikholeslami, A.J. Chamkha, Z.A. Raizah, S. Saleem, Control Volume Finite Element Method for nanofluid MHD natural convective flow inside a sinusoidal annulus under the impact of thermal radiation, Computer Methods in Applied Mechanics and Engineering, 338 (2018) 618-633.
[31] K. Sreelakshmi G. Sarojamma, Heat transfer analysis in the non-orthogonal flow of a non-Newtonian nanofluid with non-linear thermal radiation, Transactions of A. Razmadze Mathematical Institute, 172 (2018) 606–618.
[32] O.K. Koriko and I.L. Animasaun, New similarity solution of micropolar fluid flow problem over an uhspr in the presence of quartic kind of autocatalytic chemical reaction, Frontiers in Heat and Mass Transfer, 26 (2017) 1-13.
[33] W.M. Kays, Convective heat and mass transfer, New York: McGraw-Hill, (1966).
[34] M. Arunachalam and N.R. Rajappa, Thermal boundary layer in liquid metals with variable thermal conductivity, Applied Scientific Research, 34 (1978) 179-187.
[35] S. Rosseland, Astrophysik und Atom-Theoretische Grundlagen, Springer Verlag, Berlin, (1931) 41-44.
[36] T. Fang, J.I. Zhang and Y. Zhong, Boundary layer flow over a stretching sheet with variable thickness, Applied Mathematics and Computation, 218 (2012) 7241-7252.
[37] I.L. Animasaun, Double diffusive unsteady convective micropolar flow past a vertical porous plate moving through binary mixture using modified Boussineq approximation, Ain Shams Engineering Journal, 7 (2016) 755-765.
[38] N.A. Shah, I.L. Animasaun, R.O. Ibraheem, H.A. Babatunde, N. Sandeep and I. Pop, Scrutinization of the effects of Grashof number on the flow of different fluids driven by convection over various surfaces, Journal of. Molecular Liquids, 249 (2018) 980-990.
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