**ABSTRACT**

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.

**KEYWORDS**

PAPER SUBMITTED: 2023-04-04

PAPER REVISED: 2023-05-12

PAPER ACCEPTED: 2023-05-29

PUBLISHED ONLINE: 2023-09-02

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