International Scientific Journal

Thermal Science - Online First

online first only

New method for calculating heat transfer in unsteady MHD mixed boundary layers with radiative and generation heat over a cylinder

This paper is devoted to the analysis of an unsteady two-dimensional MHD dynamic and thermal boundary layer over a horizontal cylinder in mixed convection, in the presence of suction/injection, heat source/sink, and heat radiation Fluid electrical conductivity is constant. The system of MHD equations of dynamic and temperature boundary layer, which describe complex non-auto model problems, has been solved by a new approach. New variables and sets of parameters were introduced and transformed equations were obtained, in which the influence of the magnitude Z was explicitly retained. In order to close the system of equations, to the equations of the boundary layers momentum equation was added. The solution of the obtained system of nonlinear differential equations was performed numerically using the finite difference method, with the simultaneous application of the iteration method. By replacing the derivatives in the system of equations with the corresponding relations of finite differences, a system of linear derivative algebraic equations is obtained, which is solved by the three-diagonal method. As a concrete example of the introduced method, the effects of heat transfer in the MHD boundary layers were considered, in the case of mixed convention, over a horizontal circular cylinder. The boundary conditions for temperature are defined by linear functions of longitudinal coordinates and time. Numerical results for different Ec, Sc and expanded Pr numbers and values: magnetic, dynamic, thermal parameters, temperature and buoyancy parameters were obtained and presented. The obtained results were analyzed through the diagrams of changes in velocity and temperature and the diagrams of integral and differential characteristics of boundary layers and the corresponding conclusions were given.
PAPER REVISED: 2023-05-12
PAPER ACCEPTED: 2023-05-29
  1. E. Blum, I. Mihajlov, Heat transfer in electro-conductive fluid in presence of transversal magnetic field, Magnetodohydrodinamics, 5 (1966), pp. 2-18.
  2. E. Sparrow, R. Cess, Effect of magnetic field on free convection heat transfer, Int.J.Heat and Mass Transfer, vol.3, pp. 267-274, 1961
  3. A. Mikhailov, A. Yu Heat and Mass Transfer in a Magnetic Field, Magnetohydrodynamics, 5 (1966), 1, pp. 3-10
  4. J. Rosow, On flow of electrically conducting fluid over a flat plate in the presence of a transverse magnetic field, Report No.1358, NASA, USA,1958
  5. Molokov, S. et al., Magnetohydrodynamics-Historical Evolution and Trends, Springer, Berlin, Germany, 2007
  6. R. Rajeswari, B. Jothiram, V. Nelson, 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, vol 3,N-20, pp. 2469-2480, 2009
  7. P. Sharma, G. Singh, 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, vol.2, N-1, pp.13-21, 2009
  8. Chen, C., Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with wall temperature and concentration, Acta Mechanica, v 172 (2004),pp 219-235
  9. Chamkha, A, Mujtaba, M., Quadri, M., Camille,I., Thermal radiation effects on MHD forced convection flow adjacent to a non- isothermal wedge in the presence of a heat source or sink, Heat and Mass transfer, v 39 (2003),pp 305-312.226
  10. Subhas, A., Prasad, K., Mahaboob, A., Buoyancy force thermal radiation effects in MHD boundary layer viscoelastic fluid over continuously moving stretching surface, Int,Journ. of Thermal Science, V 44 (2005), pp 465-476
  11. Miraj, A., Abdul, A., Sazzad A.,Conjugate effects of radiation and joule heating on MHD free convection flow along a sphere with heat generation, American Journal of Computational Mathematics, V 1(2011), pp 18-25
  12. Terill, R., Laminar boundary layer flow near separation with and without suction, Pfil.Trans.Roy.Soc. London, A253,No 1022, pp 55-100 (1960)
  13. Maurya,J., Singh,A., Shyam, L., Magnetohydrodinamic transient flow in a cirkular cylinder. Int.Journal of Dynamics and Control,V6, (2018) , pp 1477-1483
  14. Z. Boricic, D. Nikodijević, B. Blagojević, Ž.Stamenković, Universal Equations of Unsteady Two-Dimensional MHD Boundary Layer on the Body with Temperature Gradient along Surface, WSEAS Transactions on Fluid Mechanics, vol-4, pp. 97-106, 2009
  15. D. Nikodijević, V. Nikolić, Ž. Stamenković, A. Boričić, Parametric method for unsteady twodimensional MHD boundary layer on the whose temperature varies with time, Archives of Mechanics, vol 63,N-01, pp.57-76, 2011
  16. Savić, D., Obrović, B,. Gordić,D.,Jovanović,S., Investigation of the Ionized gas flow adjacent to porous wall in the case when electro conductivity is a function of the longitudinal velocity gradient, Thermal Science, Vol.14 (2010), No.1, pp 89-102.
  17. Boričić,Z.,Nikodijević,D.,Milenković,D.,Stamenković,Ž.,Universal solution unsteady twodimensional MHD boundary layer whose temperature varies with time, Theoretical and Appled Mechanics v 36, No 2 (2009), pp 119-135.
  18. D. Nikodijević, Ž. Stamenković, A. Boričić, M. Kocić, Active control of flow and heat transfer in boundary layer porous on the body of arbitrary shape, Thermal Science v 12, S 2, pp295-309, 2012,
  19. BoričićA.,Boričić,B., Application of the General Similarity Method to Research to Unsteady Dynamic,Temperature and Diffusoion Boundary Layer under te Effects Chemical Reaction and Heat Source/Sink, Proceedings 3in International Conference Mechanical Ingeenering in XXI Century, Serbia,Nish, (2015) pp 45-50
  20. K. Yih., Effect of uniform blowing/suction on MHD natural convection over a horizontal cylinder:UWT or UHT. Acta Mechanica, vol 144, pp. 17-27, 2000
  21. A. Boričić, M. Jovanović, B. Boričić, MHD effects on unsteady dynamic, thermal and diffusion Boundary layer flow a circular cilynder, Thermal Science, vol 12,S2, pp.295-309, 2012
  22. TK. Aldoss TK, YD. Ali. MHD mixed convection form a horizontal cylinder in a porous medium. JSME International Journal, Series B: Fluids and Thermal Engineering (1997), 40(2),pp.:290-295
  23. Amin, M., Combined effects of viscous dissipation and Joule heating on MHD forced convection over a nonisothermal horisontal cylinder embeded in a fluid saturated porous medium, Jour.of Magnetism and Magnetic Materials V 263 (2003), pp 337-343.
  24. Molla, M., Saha, S., Khan, M., MHD natural convection flow from an isothermal horizontal circular cylindar under consideration of temperature dependent viscosity., Enginering Computations, V 29, No 8 (2012), pp 875- 887 .
  25. Nazar, R., Amin, N., Pop, I., Mixed convection boundary layer flow from a horizontal circular cylinder a constant surface heat flux, Heat and Mass Transfer,(2004) V40, pp 219-227, 2004
  26. Ahmad,K.,Ishak,A., Magnetohdrodinamic flow and Heat transfer of a Jefrey fluid towards a stretchingg vertical surface, Thermal Science, V21, No1A, (2017), pp 267-277
  27. Javid, T., Mustafa,I.,Ahmad,H., Effect of thermal radiation on unsteady mixed convection flow near forward stagnation point over a cylinder of elliptic cross section, Thermal Science,V21,No1A(2017) pp-243-254
  28. Saleh, M., Mohamed, A., Bazid, 16A., Mahmoud, S., Heat and mass transfer in MHD visco-elastic fluid flow through a porous medium over a stretching sheet with chemical reaction, Applied Mathematics, V 1(2010),pp446-455
  29. Boričić,A., Universal methods in research of unstedy plane laminar flow of an incopressible conducting fluid in composite MHD dynamic,thermal and diffusion boundary layer, Ph.D. thesis, Faculty of Engineering, University of Nis, (1971)
  30. Boričić,A.,Jovanović, M.,Boričić,B., Unsteady Magnetohydrodynamic Thermal and Diffusion Boundary Layer from a Horizontal circular cylinder, Thermal Science,(2016), Vol. 20, Suppl. 5, pp. S1367-S1380
  31. Boričić,B.,Boričić,A., Unsteady Magnetohydrodynamic Mixed Convection Flow with Heat and Mass Transfer over a Horizontal Circular Cylinder embedded in a Porous Medium,Thermal Science, (2016) Vol. 20, Suppl. 5, pp. S1381-S1390
  32. Boričić,A.,Jovanović,M., Integral equations of the MHD Dynamic, Temperature and Diffuson Boundary Layer and their Application to Researched Concrete Flow, Proceedings 19th Int.Conference on Thermal Science and Engeering of Serbia - SIMTERM 2019,(2019), pp
  33. Ilyas Khan, Significance of ramped temperature in the dynamics of unsteady viscoelastic fluid subjected to lorentz force. Front. Physiol. 10:924910. doi: 10.3389/fphy.2022.924910.