THERMAL SCIENCE

International Scientific Journal

NEW SIMILARITY SOLUTION OF BOUNDARY LAYER FLOW ALONG A CONTINUOUSLY MOVING CONVECTIVELY HEATED HORIZONTAL PLATE BY DEDUCTIVE GROUP METHOD

ABSTRACT
A mathematical model is presented and analyzed for steady two-dimensional non-isothermal laminar free convective boundary layer flow along a convectively heated moving horizontal plate. New similarity transformations are developed using one parameter deductive group transformations and hence the governing transport equations are reduced to a system of coupled, nonlinear ordinary differential equations with associated boundary conditions. The reduced equations are then solved numerically by an implicit finite difference numerical method. The effects of pertinent parameters on the non-dimensional velocity, temperature, friction factor and heat transfer rates are investigated and presented graphically. It is found that friction factor decreases with the free convective parameter and rate of heat transfer increases with the convection-conduction parameter.
KEYWORDS
PAPER SUBMITTED: 2013-01-15
PAPER REVISED: 2013-11-27
PAPER ACCEPTED: 2014-01-01
PUBLISHED ONLINE: 2014-03-08
DOI REFERENCE: https://doi.org/10.2298/TSCI130115014U
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE 3, PAGES [1017 - 1024]
REFERENCES
  1. Jaluria, Y., Thermal processing of materials: from basic research to engineering, J. of Heat Transfer, 125 (2003), pp. 957-979.
  2. Sakiadis, B.C., Boundary layer behavior on continuous solid surfaces. II: The boundary layer on a continuous flat surface, AIChE J., 7 (1961), pp. 221-225.
  3. Jaluria, Y., Transport from continuously moving materials undergoing a thermal processing, Ann. Rev. Heat Transfer, 4 (1992), pp. 187-245.
  4. Grupka, J.L., Bobba, K.M., Heat transfer characteristics of a continuous stretching surface with variable temperature, J. Heat Transfer, 107 (1985), pp. 248-250.
  5. Karwe, M.V., Jaluria, Y., Experimental investigation of thermal a transport from a heated moving plate, Int. J. of Heat Mass Transfer, 35 (1992), pp. 493-511.
  6. Ferdows, M., Uddin, M.J., Afify, A.A., Scaling group transformation for MHD boundary layer free convective heat and mass transfer flow past a convectively heated nonlinear radiating stretching sheet, Int. J. of Heat and Mass Transfer, 56 (2013), pp.181-187.
  7. Weidman, P.D., Kubitschek, D.G. , Davis, A.M.J., The effect of transpiration on self-similar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44 (2006), pp. 730-737.
  8. Fang, T., Lee, C.F., A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate, Appl. Math. Lett.,18 (2005), pp. 487-495.
  9. Ishak, A., Nazar, R., Pop, I., Boundary layer on a moving wall with suction or injection, Chin. Phys. Lett., 8(2007), pp. 2274-2276.
  10. Daskalakis, J., Kafoussias, N., Lewkowicz, A., Williams, E.W., Similarity solution for free and forced convection hydromagnetic flow over a horizontal semi-infinite plate through a nonhomogeneous porous medium, Astrophys. Space Sci., 151(1989), pp.217-226.
  11. Fan, J.R., Shi, J.M., Xu, X.Z., Similarity solution of mixed convection over a horizontal moving plate, Heat and Mass Transfer, 32(1997), pp.199-206.
  12. Noshadi, V., Schneider, W., Natural convection flow far from a horizontal plate, J. Fluid Mech., 387 (1997), pp.227-254.
  13. Pretot, S., Zeghmati, B., Palec, G.L., Theoretical and experimental study of natural convection on a horizontal plate, Appl. Therm. Eng., 20(2000), pp.873-891.
  14. Datta, P., Subhashini, S.V., Ravindran, R. Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates, Appl. Math. Model., 33 (2009), pp.1285-94.
  15. Aziz, A., A similarity solution for laminar thermal boundary layer over flat plate with convective surface boundary condition, Commun. in Nonlin. Science and Numer. Simulat., 4 (2009), pp.1064-1068.
  16. Ishak, A., Similarity solutions for flow and heat transfer over permeable surface with convective boundary conditions, App. Math. and Comput., 217(2010), pp.837-842.
  17. Khan, W.A., Uddin, M.J., Ismail, A.I.M., Similarity solutions of MHD mixed convection flow with variable reactive index, magnetic field and velocity slip near moving horizontal plate: A group theory approach, Math. Probl. Eng., 2012 (2012), Article ID 183029.
  18. Aziz, A., Khan,W.A., Pop, I., Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms, Int. J. of Therm. Sci., 56 (2012), pp. 48-57.
  19. Uddin, M.J., Yusoff, N.H.M, Bég, O.A, Ismail, A.I.M., Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation, Phys. Scr., 87(2013), pp. 025401
  20. Moran, M.J., Gaggioli, R.A., A new systematic formalism for similarity analysis, with application to boundary layer flows, Technical Summary Report No. 918, US Army Math. Res. Cen., 1968.
  21. Moran, M.J., Gaggioli, R.A., A New systematic formalism for similarity analysis, J. of Eng. Math., 3(1969), pp.151-162.
  22. Seshadri, R., Na , T.Y., Group Invariance in Engineering Boundary Value Problems, Springer, New York, USA, 1985.
  23. Hill, J.M., Differential Equations and Group Methods for Scientists and Engineers, CRC Press, New York, USA, 1992.
  24. Abd-el-Malek, M.B., Kassem, M.M., Mekky, M.L., Similarity solutions for unsteady free-convection flow from a continuous moving vertical surface, J. of Comput. and Appl. Math., 164-165(2004), pp. 11-24.
  25. Kassem, M.M., Rashed, A.S., Group solution of a time dependent chemical convective process, Appl. Math. and Comput., 215(2009), pp. 1671-1684.
  26. Akgu, M.B., Sarı, G., Pakdemirli, M., Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid, J. Appl. Math., 2012(2012), Article ID 675287.
  27. Uddin, M.J., Khan, W.A., Ismail, A.I.M., MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition, PLos One, 7(2012), pp. e49499.
  28. Ariel, P.D., A numerical Algorithm for computing the stagnation point flow of second grade fluid with/ without suction, J. Comput. and Appl. Math., 59(1995), pp. 9-24.
  29. Kiwan, S., Al-Nimr, M.A., Investigation into the similarity solution for boundary layer flows in Microsystems, J. of Heat Transfer, 132 (2010), pp. 041011.
  30. Gill, W.N., Zeh, D.W., Del Casal, E., Free convection on a horizontal plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, 16(4) (1965), pp. 539-541.
  31. Schlichting, H, Boundary Layer Theory, 7th Edn, McGraw-Hill, New York, USA, 1979.

© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence