Abstract
This paper examined the hydromagnetic mixed convection stagnation point flow towards a vertical plate embedded in a highly porous medium with radiation and internal heat generation. The governing boundary layer equations are formulated and transformed into a set of ordinary differential equations using a local similarity approach and then solved numerically by shooting iteration technique together with Runge-Kutta sixth-order integration scheme. A representative set of numerical results are displayed graphically and discussed quantitatively to show some interesting aspects of the pertinent parameters on the dimensionless axial velocity, temperature and the concentration profiles, local skin friction, local Nusselt number and local Sherwood number, the rate of heat and mass transfer. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases.
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Abbreviations
- g :
-
gravitational acceleration
- G T :
-
thermal Grashof number
- (x,y):
-
Cartesian coordinates
- C w :
-
plate surface concentration
- C ∞ :
-
free stream concentration
- C :
-
fluid chemical species concentration
- D :
-
diffusion coefficient
- f :
-
dimensionless stream function
- Nu :
-
Nusselt number
- T ∞ :
-
free stream temperature
- \(\tilde{K}\) :
-
porous media permeability
- G c :
-
solutal Grashof number
- Sh :
-
Sherwood number
- K :
-
permeability parameter
- T :
-
fluid temperature
- Pr :
-
Prandtl number
- T w :
-
plate surface temperature
- S :
-
heat generation/absorption parameter
- k :
-
thermal conductivity coefficient
- Sc :
-
Schmidt number
- (u,v):
-
velocity components
- Q :
-
volumentric heat generation/absorption rate
- K′:
-
mean absorption coefficient
- Ra :
-
thermal radiation parameter
- B 0 :
-
magnetic field of constant strength
- β ∗ :
-
coefficient of expansion with concentration
- β :
-
coefficient of thermal expansion
- μ :
-
coefficient of viscosity
- ρ :
-
density of fluid
- ϕ :
-
dimensionless concentration
- θ :
-
dimensionless temperature
- η :
-
dimensionless variable
- υ :
-
kinematic viscosity
- Ψ:
-
stream function
- σ ∗ :
-
Stefan-Boltzmann constant
- σ e :
-
fluid electrical conductivity
References
Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, New York
Kumari M, Takhar HS, Nath G (2001) Mixed convection flow over a vertical wedge embedded in a highly porous medium. Heat Mass Transf 37:139–146
Chamkha AJ, Quadri MMA (2001) Heat and mass transfer from a permeable cylinder in a porous medium with magnetic field and heat generation/absorption effects. Numer Heat Transf, Part A, Appl 40:387–401
Seddeek MA (2002) Effects of magnetic field and variable viscosity on forced non-Darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing. J Appl Mech Tech Phys 43:13–17
Stuart JT (1959) The viscous flow near a stagnation point when the external flow has uniform vorticity. Aerosp Sci Technol 26:124–125
Tamada K (1979) Two-dimensional stagnation-point flow impinging obliquely on a plane wall. J Phys Soc Jpn 46:310–311
Ali F, Nazar R, Arifin N, Pop I (2011) Effect of Hall current on MHD mixed convection boundary layer flow over a stretched vertical flat plate. Meccanica 46(5):1103–1112
Hayat T, Hameed MI, Asghar S, Siddiqui AM (2004) Some steady MHD flows of the second order fluid. Meccanica 39:345–355
Ishak A, Nazar R, Pop I (2006) Mixed convection boundary layers in the stagnation-point flow toward a stretching surface. Meccanica 41:509–518
Ishak A, Nazar R, Pop I (2008) Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet. Meccanica 43:411–418
Hiemenz K (1911) Die Grenzschicht in einem in den gleichformingen Flussigkeitsstrom eingetauchten gerade Kreiszylinder. Dinglers Polytech J 326:321–410
Singh G, Sharma PR, Chamkha AJ (2010) Effect of volumentric heat generation/absorption on mixed convection stagnation point flow on an iso-thermal vertical plate in porous media. Int J Ind Math 2(2):59–71
Sparrow EM, Cess RD (1978) Radiation heat transfer. Hemisphere, Washington. Augmented edition
Chamkha AJ, Issa C, Khanfer K (2002) Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation. Int J Therm Sci 41:73–81
Makinde OD, Ogulu A (2008) The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field. Chem Eng Commun 195(12):1575–1584
Bestman AR, Adiepong SK (1988) Unsteady hydromagnetic free-convection flow with radiative heat transfer in a rotating fluid. Astrophys Space Sci 143:73–80
Naroua H, Ram PC, Sambo AS, Takhar HS (1998) Finite-element analysis of natural convection flow in a rotating fluid with radiative heat transfer. J Magnetohydrodyn Plasma Res 7:257–274
Ouaf MEM (2005) Exact solution of thermal radiation on MHD flow over a stretching porous sheet. Appl Math Comput 170(2):1117–1125
Raptis A, Perdikis C, Leontitsis A (2003) Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field. Heat Mass Transf 39:771–773
Magyari E, Pantokratoras A (2011) Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows. Int Commun Heat Mass Transf 38(5):554–556
Na TY (1979) Computational methods in engineering boundary value problems. Academic Press, New York
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Makinde, O.D. Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation. Meccanica 47, 1173–1184 (2012). https://doi.org/10.1007/s11012-011-9502-5
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DOI: https://doi.org/10.1007/s11012-011-9502-5