On the Analysis of Variable Thermophysical Properties of Thermophoretic Viscoelastic Fluid Flow past a Vertical Surface with nth Order of Chemical Reaction
The objective of this study is to consider the flow of temperature dependent viscosity and thermal conductivity of free convective heat and mass transfer of viscoelastic fluid over a stretching surface with nth order of chemical reaction and thermophoresis. The effect of the temperature dependent dynamic viscosity and thermal conductivity together with modified thermal and solutal Grashof numbers are properly accounted for in order to enhance the transport phenomenon. Similarity transformations are used to convert and parameterize the non-linear partial differential equation to a system of coupled non-linear ordinary differential equation. The approximate analytical solutions of the corresponding BVP are obtained through Optimal Homotopy Analysis Method (OHAM). The effect of some pertinent parameters is tested on velocity, temperature, concentration profiles. It is observed from the computation that, the thickness of the velocity and thermal boundary layer increases with an increase in temperature dependent variable viscosity and thermal conductivity parameters when modified thermal and solutal Grashof numbers and are less than zero. It is also observed that the concentration layer becomes thinner with increasing thermophoresis parameter when the chemical reaction parameter is greater than zero for both cases of first and second order of chemical reaction i.e. when n=1,2.
Cite this paper
Koriko, O. K. , Oreyeni, T. and Oyem, O. A. (2018). On the Analysis of Variable Thermophysical Properties of Thermophoretic Viscoelastic Fluid Flow past a Vertical Surface with nth Order of Chemical Reaction. Open Access Library Journal, 5, e4271. doi: http://dx.doi.org/10.4236/oalib.1104271.
Prandtl, L. (1905) Uber Flussigkeigsbewegung bei sehr kleiner Reibung. In: Verhandlungen des dritten internationalen Mathematischen Kongresses, Heidelberg, Teubner Verlag, Leipzig, 484-491.
Gangadhar, K. and Reddy, N.B. (2013) Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate in a Porous Medium with Suction. Journal of Applied Fluid Mechanics, 6, 107-114.
Ibrahim, S.Y. and Makinde, O.D. (2010) Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate with Suction. Scientific Research and Essays, 5, 2875-2882.
Krishnamurthy, M.R., Prasannakumara, B.C. and Gireesha, B.J. (2016) Effect of Chemical Reaction on MHD Boundary Layer Flow and Melting Heat Transfer of Williamson Nanofluid in Porous Medium. Engineering Science and Technology, an International Journal, 19, 53-61. https://doi.org/10.1016/j.jestch.2015.06.010
Bhukta, D., Dash, G.C. and Mishra, S.R. (2014) Heat and Mass Transfer on MHD Flow of a Viscoelastic Flow through Porous Media over a Shrinking Sheet. International Scholarly Research Notices, 11 p. https://doi.org/10.1155/2014/572162
Gbadeyan, J.A., Idowu, A.S., Ogunsola, A.W., Agboola, O.O. and Olanrewaju, P.O. (2011) Heat and Mass Transfer for Soret and Dufour's Effect on Mixed Convectioin Boundary Layer Flow over a Stretching Vertical Surface in a Porous Medium Filled with a Visco-elastic Fluid in the Presence of Magnetic Field. Global Journal of Science Frontier Research, 11, 97-114.
Venkateswarlu, B. and Narayana, P.V.S. (2015) Mhd Visco-Elastic Fluid Flow over a Continuously Moving Vertical Surface with Chemical Reaction. Walailak Journal of Science and Technology, 12, 775-783.
Das, U.J. (2014) Soret and Dufour Effects on Steady Free Convective Mhd Viscoelastic Fluid Flow Confined between a Long Vertical Wavy Wall and Parallet Flat Wall. Thammasat International Journal of Science and Technology, 19, 9-21.
Choudhury, R. and Das, S.K. (2014) Visco-Elastic Mhd Free Convective Flow through Porous Media in Presence of Radiation and Chemical Reaction with Heat and Mass Transfer. Journal of Applied Fluid Mechanics, 7, 603-609.
Standford, S. (2013) A New Numerical Approach to MHD Flow of a Maxwell Fluid Past a Vertical Stretching Sheet in the Presence of Thermophoresis and Chemical Reaction. Boundary Value Problems, 2013, 196.
Hayat, T. and Qasim, M. (2010) Influence of Thermal Radiation and Joule Heating on MHD Flow of a Maxwell Fluid in the Presence of Thermophoresis. International Journal of Heat and Mass Transfer, 53, 4780-4788. https://doi.org/10.1016/j.ijheatmasstransfer.2010.06.014
Alam, M.S., Rahman, M.M. and Sattar, M.A. (2007) Similarity Solutions for Hydromagnetic Free Convective Heat and Mass Transfer Flow along a Semi-Infinite Permeable Inclined Flat Plate with Heat Generation and Thermophoresis. Nonlinear Analysis: Modelliing and Control, 12, 433-445.
Coleman, B.D. and Noll, W. (1990) An Approximation Theorem for Functionals with Application in Continuum Mechanics. Archive for Rational Mechanics and Analysis, 6, 355.
Charraudeau, J. (1975) Influence de gradents de properties physiques en convection force application au cas du tube. International Journal of Heat and Mass Transfer, 18, 87-95. https://doi.org/10.1016/0017-9310(75)90011-3
Talbot, L., Cheng, R.K. and Scheffer, R.W. (1980) Thermophoresis of Particles in a Heated Boundary Layer. Journal of Fluid Mechanics, 101, 737-758. https://doi.org/10.1017/S0022112080001905
Batchelor, G.K. and Shen, C. (1985) Thermophoretic Deposition of Particles in Gas Flowing over Cold Surface. Journal of Colloid and Interface Science, 107, 21-37.
Mills, A.F., Hang, X. and Ayazi, F. (1984) The Effect of Wall Suction and Thermophoresis on Aerosol-Particle Deposition from a Laminar Boundary Layer on a Flat Plate. International Journal of Heat and Mass Transfer, 27, 1110-1114. https://doi.org/10.1016/0017-9310(84)90127-3
Tsai, R. (1999) A Simple Approach for Evaluating the Effect of Wall Suction and Thermophoresis on Aerosol Particle Deposition from a Laminar Flow over a Flat Plate. International Communications in Heat and Mass Transfer, 26, 249-257. https://doi.org/10.1016/S0735-1933(99)00011-1
Oyem, O.A. and Oreyeni, T. (2017) Homotopy Analysis of Magnetic Field Effect on Free Convection Flow Past a Semi-Infinite Flat Plate. Annals of Faculty Engineering Hunedoara—International Journal of Engineering, 4, 103-110.
