A Theoretical Study of Steady MHD mixed convection heat transfer flow for a horizontal circular cylinder embedded in a micropolar Casson fluid with thermal radiation

Document Type : Research Paper


1 Faculty Engineering, Department of Civil Engineering, Al-Balqa Applied University, Amman-Jordan

2 Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan

3 Faculty of art and science, Aqaba University of Technology, Aqaba-Jordan


In this study, an investigation is carried out for laminar steady mixed 2D magnetohydrodynamic (MHD) flow of micropolar Casson fluid with thermal radiation over a horizontal circular cylinder with constant surface temperature. In the present study, an investigation is carried out on the effects of physical parameters on Casson fluid non dimensional numbers. The governing nonlinear partial differential equations and the controlling boundary conditions are derived for this case study. Furthermore, these equations are solved numerically using finite difference technique known as Keller Box Method (KBM). The effects of non-dimensional governing parameters, namely Casson parameter, mixed convection parameter, magnetic parameter, radiation parameter on the Nusselt number and local friction coefficient, as well as temperature, velocity and angular velocity are discussed and shown graphically. It is noticed that the local skin friction and the local Nasselt number has decrement behaviors when increasing the values the Casson parameter. But the opposite happens when the mixed convection parameter λ increase. It is found that the results in this study are in good agreement with previous studies. This proves that calculations using KBM method and the chosen step size are accurate enough for this type of problems.


Main Subjects

[1] Abid, S., S. Islam, et al. "Magnetic hydrodynamic flow of unsteady second grade fluid between two vertical plates with oscillating boundary conditions." J. Appl. Environ. Biol. Sci 4(01): 0-01.
[2] Abolbashari, M. H., N. Freidoonimehr, et al. "Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface." Advanced Powder Technology 26(2): 542-552.
[4] Alkasasbeh, H. T., M. Z. Salleh, et al. (2014). "Numerical solutions of radiation effect on magnetohydrodynamic free convection boundary layer flow about a solid sphere with Newtonian heating." Applied Mathematical Sciences 8(140): 6989-7000.
[5] Animasaun, I. L. "Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-darcian MHD dissipative Casson fluid flow with suction and nth order of chemical reaction." Journal of the Nigerian Mathematical Society 34(1): 11-31.
[6] Ariman, T., M. A. Turk, et al. (1973). "Microcontinuum fluid mechanics—a review." International Journal of Engineering Science 11(8): 905-930.
[7] Blasius, H. (1908). "Grenzschichten in Flussigkeiten mit kleiner Reibung, 2. angew." Math. Phye 56.
Casson, N. (1959). "A flow equation for pigment-oil suspensions of the printing ink type." Rheology of disperse systems.
[8] Cebeci, T. and P. Bradshaw Physical and computational aspects of convective heat transfer, Springer Science & Business Media.
[9] Cortell Bataller, R. (2008). "Radiation effects in the Blasius flow." Applied mathematics and computation 198(1): 333-338.
[10] Eringen, A. C. (1966). "Theory of micropolar fluids." Journal of Mathematics and Mechanics: 1-18.
[11] Gaffar, S. A., V. R. Prasad, et al. "Magnetohydrodynamic free convection flow and heat transfer of non-Newtonian tangent hyperbolic fluid from horizontal circular cylinder with Biot number effects." International Journal of Applied and Computational Mathematics 3(2): 721-743.
[12] Gul, A. and M. Ullah "Thin Film Flow Analysis of a MHD Third Grade Fluid on a Vertical Belt With no-slip Boundary Conditions." J. Appl. Environ. Biol. Sci 4(10): 71-84.
[13] Haq, R., S. Nadeem, et al. "Convective heat transfer and MHD effects on Casson nanofluid flow over a shrinking sheet." Open Physics 12(12): 862-871.
[14] Ingham, D. B. (1978). "Free-convection boundary layer on an isothermal horizontal cylinder." Zeitschrift fأ¼r angewandte Mathematik und Physik ZAMP 29(6): 871-883.
[15] Khalid, A., I. Khan, et al. "Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium." Engineering Science and Technology, an International Journal 18(3): 309-317.
[16] Khonsari, M. M. and D. E. Brewe (1994). "Effect of viscous dissipation on the lubrication characteristics of micropolar fluids." Acta Mechanica 105(1-4): 57-68.
[17] Lukaszewicz, G. (1999). Micropolar fluids: theory and applications, Springer Science & Business Media.
[18] Mahdy, A. and S. E. Ahmed "Unsteady MHD convective flow of non-Newtonian Casson fluid in the stagnation region of an impulsively rotating sphere." Journal of Aerospace Engineering 30(5): 04017036.
[19] Malik, M. Y., M. Naseer, et al. "The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder." Applied Nanoscience 4(7): 869-873.
[20] Mehmood, Z., R. Mehmood, et al. "Numerical investigation of micropolar Casson fluid over a stretching sheet with internal heating." Communications in Theoretical Physics 67(4): 443.
[21] Merkin, J. H. (1976). Free convection boundary layer on an isothermal horizontal cylinder. American Society of Mechanical Engineers and American Institute of Chemical Engineers, Heat Transfer Conference, St. Louis, Mo., Aug. 9-11, 1976, ASME 5 p.
[22] Mohammad, N. F. (2015). Magnetohydrodynamic Flow Past a Sphere in a Viscous and Micropolar Fluids for Unsteady Free and Mixed Convective Boundary Layer, Universiti Teknologi Malaysia.
[23] Mukhopadhyay, S., K. Bhattacharyya, et al. "Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects." Chinese Physics B 22(11): 114701.
[24] Mukhopadhyay, S., K. Bhattacharyya, et al. (2013). "Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects." Chinese Physics B 22(11): 1-6.
[25] Mukhopadhyay, S., I. C. Mondal, et al. "Casson fluid flow and heat transfer past a symmetric wedge." Heat Transfer—Asian Research 42(8): 665-675.
[26] Mustafa, M., T. Hayat, et al. "Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate." Heat Transferï؟½Asian Research 40(6): 563-576.
[27] Nagendra, N., C. H. Amanulla, et al. "Mathematical Study of Non-Newtonian Nanofluid Transport Phenomena from an Isothermal Sphere." Frontiers in Heat and Mass Transfer (FHMT) 8.
[28] Nazar, R., N. Amin, et al. (2003). "Mixed convection boundary-layer flow from a horizontal circular cylinder in micropolar fluids: case of constant wall temperature." International Journal of Numerical Methods for Heat & Fluid Flow 13(1): 86-109.
[29] Prasad, V. R., A. S. Rao, et al. "Modelling laminar transport phenomena in a Casson rheological fluid from a horizontal circular cylinder with partial slip." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 227(4): 309-326.
[30] Pushpalatha, K., V. Sugunamma, et al. "Heat and mass transfer in unsteady MHD Casson fluid flow with convective boundary conditions." International Journal of Advanced Science and Technology 91: 19-38.
[31] Qasim, M. and S. Noreen "Heat transfer in the boundary layer flow of a Casson fluid over a permeable shrinking sheet with viscous dissipation." The European Physical Journal Plus 129(1): 7.
[32] Shehzad, S. A., T. Hayat, et al. "Effects of mass transfer on MHD flow of Casson fluid with chemical reaction and suction." Brazilian Journal of Chemical Engineering 30(1): 187-195.
[33] Subba Rao, A., V. Ramachandra Prasad, et al. "Heat Transfer in a Casson Rheological Fluid from a Semiâ€گinfinite Vertical Plate with Partial Slip." Heat Transfer—Asian Research 44(3): 272-291.
[34] Swalmeh, M. Z., H. T. Alkasasbeh, et al. (2018). "Heat transfer flow of Cu-water and Al2O3-water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller-box method." Results in Physics 9: 717-724.
[35] Venkatesan, J., D. S. Sankar, et al. "Mathematical analysis of Casson fluid model for blood rheology in stenosed narrow arteries." Journal of Applied Mathematics 2013.
Volume 50, Issue 1
June 2019
Pages 165-173
  • Receive Date: 25 March 2019
  • Revise Date: 14 April 2019
  • Accept Date: 16 April 2019