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

This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogeneous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i. e. considered problem is in inductionless approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multi-parametric (generalized similarity) method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.past an arbitrary shape surface has attracted the interest of many researchers in view of its important applications in many engineering problems.Recently the problem of magneto-hydrodynamic (MHD) flow over surfaces has become more important due to the possibility of applications in areas like nuclear fusion, chemical engineering, medicine, and high-speed, noiseless printing. Problem of MHD flow in the vicinity of plate has been studied intensively by a number of investigators [3][4][5][6][7]. Most of previous investigations were concerned with studies of the steady flow of fluid whose electrical conductivity is constant.The subject of the present research is to give an analytic investigation to the problem of unsteady laminar MHD boundary layer flow of a viscous incompressible fluid. The external magnetic field is homogeneous and perpendicular to the body. The fluid which forms the boundary layer is incompressible and its electrical conductivity is variable and can be assumed in the following form: