**ABSTRACT**

This paper is devoted to the analysis of unsteady two-dimensional dynamic, thermal and diffusion magnetohydrodynamic laminar boundary layer flow over a horizontal circular cylinder of incompressible and electrical conductivity fluid, in a porous medium, in the presence of a heat source or sink, and chemical reactions. The present magnetic field is homogenous and perpendicular to the body surface. It is assumed that the induction of the outer magnetic field is the function of the longitudinal coordinate and time. Fluid electrical conductivity is constant. The outer electric field is neglected and the magnetic Reynolds number is significantly lower than one i. e. the considered the problem is in induction-less approximation. Free stream velocity, temperature and concentration on the body are arbitrary differentiable functions. The developed governing boundary layer equations and associated boundary conditions are converted into a nondimensional form using a suitable similarity transformation and similarity parameters. The system of dimensionless equations is solved using the finite difference method and iteration method. Numerical results are obtained and presented for incompressible fluid for different numbers, such as Sc, Pr, Ec and magnetic number, and the parameter of the porous medium, temperature parameters, thermal parameter, diffusion parameters and chemical reaction parameter. The solutions for the flow, temperature and diffusion transfer and other integral characteristics, boundary layer, are evaluated numerically for different values of the magnetic field. Transient effects of velocity, temperature and diffusion are analyzed. A part of obtained results is given in the form of figures and corresponding conclusions.

**KEYWORDS**

PAPER SUBMITTED: 2012-05-03

PAPER REVISED: 2012-06-25

PAPER ACCEPTED: 2012-07-05

**THERMAL SCIENCE** YEAR

**2012**, VOLUME

**16**, ISSUE

**Supplement 2**, PAGES [S311 - S321]

- Prandtl, L., Uber Flussigkeitsbewengung bei sehr kleiner Reibung, Verhandl, Verhandlungen des III. Internat. Math.-Kongr., Heidelberg, Germany, 1904
- Schlichting, H., Boundary Layer Theory, Verlag G., Braun-Karsluhe, Germany, 1982
- Blasius, H., Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. Math. Phys., 56 (1908), pp. 1-37
- Frossling, N., Calculating by Series Expansion of the Heat Transfer in Laminar, Constant Property Boundary Layers at Non Isothermal Surfaces, Archiv Fysik, 14 (1958), pp. 143-151
- Sparrow, M., Lee, L., Analysis of Mixed Convection About a Horizontal Cylinder, Int. J. Heat Mass Transfer, 19 (1975), pp .229-231
- Merkin, H., Mixed Convection From a Horizontal Circular Cylinder, Int. J. Heat Mass Transfer, 20 (1977), pp. 73-77
- Merkin, H., Pop, I., A Note on the Free Convection Boundary Layer on a Horizontal Circular Cylinder with Constant Heat Transfer, Warme-und Stoffubet, 22 (1988), pp. 79-81
- Ingham, B., Pop, I., Natural Convection About a Heated Horizontal Cylinder in Porous Medium, Fluid Mechanic, (1987), 184, pp. 157-181
- Anwar, I., et al., Mixed Convection Boundary Layer Flow of a Viscoelastic Fluid Over a Horizontal Circular Cylinder, Int. J. Nonlinear Mechanic, 4 (2008), pp. 814-821
- Terrill, M., Laminar boundary-layer flow near separation with and without suction, Phil.Trans., A253 (1960), pp. 55-100
- Salleh, Z., et al., Forced convection boundary layer flow at a forward stagnation point with Newtonian heating, Chem Eng Commun, (2009), 196, pp. 987-996
- Blum, E. J., Mihajlov, I.A., Heat transfer in electro conductive fluid in presence of transversal magnetic field., Magnetohydrodinamics, 5 (1966), pp. 2-18.
- Rajeswari, R., et al., Chemical reaction, heat and mass transfer on nonlinear MHD boundary layer flow through a vertical porous surface in the presence of suction, Applied Mathematical Sciences, 3 (2009), 20, pp. 2469-2480
- Saljnikov, V., et al., Polyparametrice Metode fur Berechnung der Instationaraaren MHD Grenzshichten, ZAAM, 68 -5 (1988), pp. 346-349
- Obrović,B., Parametric method in the Boundary-Layer theory of ionized gas whose Electroconductivity is a function of the longitudinal velocity gradient, Acta Mechanica, 147 (2001), 1-4, pp. 35-44
- Boričić, B .Z., et al., Generalized similarity method in unsteady two-dimensional MHD boundary layer on the body witch temperature varies with time, International Journal of Engineering, Science and Technology, 1 (2009), pp. 206-215
- Saljnikov,N.V., et al., Generalized similarity solutions for 3-D laminar compressible boundary layer flows on swept profiled cylinder, Acta Mechanica, 4., Springer - Verlag , (1994), pp. 389-399
- Sharma, P.R., Singh, G., Effects of variable thermal conductivity and heat source/sink on MHD flow near stagnation point on a linearly stretching sheet, Journal of Applied Fluid Mechanics, 2, (2009), 1, pp. 13-21.
- Boricic, B.Z., et al., Universal Solutions of Unsteady Two-Dimensional MHD Boundary Layer on the Body with Temperature Gradient along Surface, WSEAS Transactions on Fluid Mechanics, 4 (2009), 3, pp. 97-106.
- Nikodijević, D.D., et al., Parametric method for unsteady two-dimensional MHD boundary layer on the whose temperature varies with time, Archives of Mechanics, 63 (2011), 1, pp. 57-76
- Boričić, B.Z., et al., Unsteady plane MHD boundary layer flow of a fluid of variable electrical conductivity, Thermal Science, Vol 14 Supplement (2011), pp. 155-169
- Savić,R.S., et al. The influence of the magnetic field on the ionized gas flow adjacent to the porous wall, Thermal Science, 14 (2010), Suppl., pp. 183-196
- K.A.Yih., Effect of uniform blowing/suction on MHD natural covection over a horizontal cylinder: UWT or UHT, Acta Mechanica, 144 (2000) , pp. 17-27
- Nazar, R., et al., Mixed convection boundary layer flow from a horizontal circular cylinder a constant surface heat flux, Heat and Mass Transfer, 40 (2004), pp. 219-227
- Luciano, M., De Socio., Laminar free convection around horizontal circular cylinder, In.J.Heat and Mass Transfer, 26, (1083), 11, pp. 1669-1677
- Aldoss, T.K., et al., MHD mixed convection from a horizontal circular cylinder, Numerical Heat Transfer, 30 (1996), pp .379-396
- Boričić, Z.A., et al., MHD dynamics and diffusion Boundary layer flow of variable electrical conductivity past a circular cilynder, SINTERM Proceeding, Soko Banja, Serbia, on CD, (2011), pp. 508-517
- Lojcjanski, L.G., Universal equation and parametric approximation in theory of laminar boundary layer, SSSR, Applied Mathematics and Mechanic, 29 (1965), pp. 70-87 Paper