#### Research article of American Journal of Scientific Research and Essays

**Effects of Radiation and Heat Generation on Magnetohydrodynamic Free Convection Flow along a Horizontal Cylinder with Conduction**

**K. M. Safiqul Islam ^{1}, M. A. Alim^{2} and Md. Rezaul Karim^{3}**

^{1}Department of Mathematics, Gowripur Govt. College, Mymensingh

^{2}Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka -1000, Bangladesh.

^{3}Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh

In this paper, the flow characteristics and the heat transfer process due to natural convection and conduction along a horizontal cylinder in presence of radiation, magnetic and heat generation effects are examined. The effects of radiation, magnetic and heat generation on electrically conducting fluid in natural convective flow along a non-linear system of partial differential equations is reduced to local non-similar horizontal cylinder with conduction have been studied in this paper. The governing boundary layer equations for this phenomenon are transformed into a non-dimensional form and the resulting partial differential forms by adopting appropriate suitable transformations. The transformed boundary layer equations are then solved numerically by using the implicit finite difference method. Numerical results of the velocity profiles and temperature distribution, coefficient of local skin friction and local rate of heat transfer distribution for the Prandtl number, radiation, magnetic and heat generation parameters are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters. Significant effect is found in heat transfer distribution for Prandtl number and radiation parameter. The thermal boundary layer thickness of Prandtl number is clearer than radiation parameter. Important effect is found in heat transfer distribution in Heat Generation effect. An excellent graph is found in magnetic effect for heat transfer profile, which is as like as a spiral situation.

**Keywords:** stream function, free convection, cylinder, Prandtl number, Grashof number

**How to cite this article:**

A. K. M. Safiqul Islam, M. A. Alim and Md. Rezaul Karim. Effects of Radiation and Heat Generation on Magnetohydrodynamic Free Convection Flow along a Horizontal Cylinder with Conduction. American Journal of Scientific Research and Essays, 2021 6:2.

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