Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition
 M. M. Rahman
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This paper presents heat transfer process in a twodimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperaturedependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the NachtsheimSwigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and noslip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or noslip at the boundary to obtain realistic results.
 Blasius H (1908) Grenzschichten in Flussigkeiten mit kleiner Reibung. Z Math Phys 56(1):1–37
 Howarth L (1938) On the solution of the laminar boundary layer equations. Proc R Soc Lond A 64:547–579
 Abussita AMM (1994) A note on a certain boundary layer equation. Appl Math Comput 64:73–77 CrossRef
 Wang L (2004) A new algorithm for solving classical Blasius equation. Appl Math Comput 157:1–9 CrossRef
 Cortell R (2005) Numerical solutions of the classical Blasius flat plate problem. Appl Math Comput 170:706–710 CrossRef
 Fang T, Fang G, Lee CFF (2006) A note on the extended Blasius equation. Appl Math Lett 19:613–617 CrossRef
 Fang T, Zhang J, Yao S (2009) Slip MHD viscous flow over stretching sheet—an exact solution. Commun Nonlinear Sci Numer Simul 14:3771–3737
 Kays WM, Crawford ME (1980) Convective heat and mass transfer. McGraw Hill, New York, pp 51–54
 Shu JJ, Pop I (1988) On thermal boundary layers on a flat plate subjected to a variable heat flux. Int J Heat Fluid Flow 19:79–84 CrossRef
 Bejan A (2004) Convective heat transfer, 3rd edn. Wiley, New York, pp 84
 Incropera FP et al. (2007) Fundamentals of heat and mass transfer, 6th edn. Wiley, New York
 Bataller RC (2008) Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface. J Mater Process Technol 203:176–183 CrossRef
 Cortell R (2010) Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a powerlaw fluid past an infinite porous plate. Chem Eng Res Des. doi:10.1016/j.cherd.2010.04.017
 Aziz A (2009) A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commun Nonlinear Sci Numer Simul 14:1064–1068 CrossRef
 Bataller RC (2008) Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition. Appl Math Comput 206:832–840 CrossRef
 Ishak A (2010) Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl Math Comput 217:837–842 CrossRef
 Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun Nonlinear Sci Numer Simul 16:752–760 CrossRef
 Yoshimura A, Prudhomme RK (1998) Wall slip corrections for Couette and parallel disc viscometers. J Rheol 32:53–67 CrossRef
 Hasimoto H (1958) Boundary layers slip solutions for a flat plate. J Aeronaut Sci 25:68–69
 Martin MJ, Boyd ID (2000) Blasius boundary layer with slip flow conditions. In: Bartel TJ, Gallis MA (eds) 22nd Rarefied gas dynamics symposium, Sydney, Australia, July 2000
 Martin MJ, Boyd ID (2006) Momentum and heat transfer in laminar boundary layer with slip flow. J Thermophys Heat Transf 20:710–719 CrossRef
 Martin MJ, Boyd ID (2010) FalknerSkan flow over a wedge with slip boundary conditions. J Thermophys Heat Transf 24:263–270 CrossRef
 Vedantam NK (2006) Effects of slip on the flow characteristics of a laminar flat plate boundary layer. In: Proceedings of ASME fluids engineering summer meeting, Miami, Florida, July 17–20, 2006, pp 1551–1560
 Fang T, Lee CF (2005) A moving wall boundary layer flow of slightly rarefied gas free stream over a moving flat plate. Appl Math Lett 18:487–495 CrossRef
 Andersson HI (2002) Slip flow past a stretching surface. Acta Mech 158:121–125 CrossRef
 Wang CY (2002) Flow due to a stretching boundary with partial slipan exact solution of the NavierStokes equations. Chem Eng Sci 57:3745–3747 CrossRef
 Wang CY (2006) Stagnation slip flow and heat transfer on a moving plate. Chem Eng Sci 61:7668–7672 CrossRef
 Wang CY (2009) Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonlinear Anal Real World Appl 10:375–380 CrossRef
 Aziz A (2010) Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition. Commun Nonlinear Sci Numer Simul 15:573–580 CrossRef
 Sahoo B (2010) Flow and heat transfer of a nonNewtonian fluid past a stretching sheet with partial slip. Commun Nonlinear Sci Numer Simul 15:602–615 CrossRef
 Szeri AZ, Rajagopal KR (1985) Flow of a nonNewtonian fluid between heated parallel plates. Int J NonLinear Mech 20:91–101 CrossRef
 Herwig H, Wickern G (1986) The effect of variable properties on laminar boundary layer flow. Wärme Stoffübertrag 20:47–57 CrossRef
 Pop I, Gorla RSR, Rashidi M (1992) The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate. Int J Eng Sci 30:1–6 CrossRef
 Elbashbeshy EMA, Bazid MAA (2000) The effect of temperature dependent viscosity on heat transfer over a continuous moving surface. J Phys D, Appl Phys 33:2716–2721 CrossRef
 Makinde OD (2001) Heat and mass transfer in a pipe with moving surface effect of viscosity variation and energy dissipation. Quaest Math 24:93–104 CrossRef
 Fang T (2004) Influences of fluid property variation on the boundary layers of a stretching surface. Acta Mech 171:105–118 CrossRef
 Mukhopadhyay S, Layek GC, Samad SkA (2005) Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int J Heat Mass Transf 48:4460–4466 CrossRef
 Ali E (2006) The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface. Int J Therm Sci 45:60–69 CrossRef
 Makinde OD (2006) Laminar falling liquid film with variable viscosity along an inclined heated plate. Appl Math Comput 175:80–88 CrossRef
 Yürüsoy M, Pakdemirli M, Yilbaş BS (2008) Perturbation solution for a third grade fluid flowing between parallel plates. Proc Inst Mech Eng Part C, J Mech Eng Sci 222:653–656 CrossRef
 Alam MS, Rahman MM, Sattar MA (2009) Transient magnetohydrodynamic free convective heat and mass transfer flow with thermophoresis past a radiate inclined permeable plate in the presence of variable chemical reaction and temperature dependent viscosity. Nonlinear Anal Model Control 14:3–20
 Chiam TC (1996) Heat transfer with variable conductivity in a stagnationpoint flow towards a stretching sheet. Int Commun Heat Mass Transf 23:239–248 CrossRef
 Chiam TC (1998) Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta Mech 129:63–72 CrossRef
 Datti PS, Prasad KV, Abel MS, Joshi A (2004) MHD viscoelastic fluid flow over a nonisothermal stretching sheet. Int J Eng Sci 42:935–946 CrossRef
 Prasad KV, Abel MS, Khan SK (2000) Momentum and heat transfer in viscoelastic fluid flow in a porous medium over a nonisothermal stretching sheet. Int J Numer Meth Heat Fluid Flow 10:786–802 CrossRef
 Abel MS, Prasad KV, Ali M (2005) Buoyancy force and thermal radiation effects in MHD boundary layer viscoelastic fluid flow over continuously moving stretching surface. Int J Therm Sci 44:465–476 CrossRef
 Prasad KV, Vajravelu K (2009) Heat transfer in the MHD flow of a power law fluid over a nonisothermal stretching sheet. Int J Heat Mass Transf 152:4956–4965 CrossRef
 Prasad KV, Pal D, Umesh V, Rao NSP (2010) The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet. Commun Nonlinear Sci Numer Simul 15:331–344 CrossRef
 Abel MS, Siddheshwar PG, Mahesha N (2009) Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a powerlaw fluid past a vertical stretching sheet in the presence of a nonuniform heat source. Int J NonLinear Mech 44:1–12 CrossRef
 Rahman MM, Salahuddin KM (2010) Study of hydromagnetic heat and mass transfer flow over an inclined heated surface with variable viscosity and electric conductivity. Commun Nonlinear Sci Numer Simul 15:2073–2085 CrossRef
 Rahman MM, Rahman MA, Samad MA, Alam MS (2009) Heat transfer in micropolar fluid along a nonlinear stretching sheet with temperature dependent viscosity and variable surface temperature. Int J Thermophys 30(5):1649–1670 CrossRef
 Rahman MM, Aziz A, AlLawatia M (2010) Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties. Int J Therm Sci 49:993–1002 CrossRef
 Rahman MM (2010) Convective hydromagnetic slip flow with variable properties due to a porous rotating disk. Sultan Qaboos Univ J Sci 15:55–79
 Ling JX, Dybbs A (1987) Forced convection over a flat plate submersed in a porous medium: variable viscosity case. ASME, Paper 87WA/HT23, ASME winter annual meeting, Boston, Massachusetts, pp 13–18
 Weast RC (1990) CRC handbook of chemistry and physics, 71st edn. CRC Press, Boca Raton
 Knezevic D, Savic V (2006) Mathematical modeling of changing of dynamical viscosity, as a function of temperature and pressure, of mineral oils for hydraulic systems. Facta Univ, Ser Mech Eng 6:27–34
 Yurusov M, Pakdemirli M (2002) Approximate analytical solutions for the flow of a thirdgrade fluid in a pipe. Int J NonLinear Mech 37:187–195 CrossRef
 Savvas TA, Markatos NC, Papaspyrides CD (1994) On the flow of nonNewtonian polymer solutions. Appl Math Model 18:14–22 CrossRef
 Helmy KA (1995) MHD boundary layer equations for power law fluids with variable electric conductivity. Meccanica 30:187–200 CrossRef
 GadelHak M (1999) The fluid mechanics of microdevices: The Freeman Scholar Lecture. J Fluid Eng 121:5–33 CrossRef
 Pantokratoras A (2002) Laminar freeconvection over a vertical isothermal plate with uniform blowing or suction in water with variable physical properties. Int J Heat Mass Transf 45:963–977 CrossRef
 Pantokratoras A (2004) Further results on the variable viscosity on flow and heat transfer to a continuous moving flat plate. Int J Eng Sci 42:1891–1896 CrossRef
 Nachtsheim PR, Swigert P (1965) Satisfaction of the asymptotic boundary conditions in numerical solution of the system of non linear equations of boundary layer type. NASA TND3004
 Alam MS, Rahman M, Samad MA (2006) Numerical study of the combined freeforced convection and mass transfer flow past a vertical porous plate in a porous medium with heat generation and thermal diffusion. Nonlinear Anal Model Control 11:331–343
 Pantokratoras A (2009) A common error made in investigation of boundary layer flows. Appl Math Model 33:413–422 CrossRef
 Title
 Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition
 Journal

Meccanica
Volume 46, Issue 5 , pp 11271143
 Cover Date
 20111001
 DOI
 10.1007/s1101201093722
 Print ISSN
 00256455
 Online ISSN
 15729648
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Convective flow
 Heat transfer
 Similar solution
 Slip flow
 Variable thermal conductivity
 Variable viscosity
 Industry Sectors
 Authors

 M. M. Rahman ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, AlKhod 123, Muscat, Sultanate of Oman