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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

MHD effects on unstedy dynamic, thermal and diffusion boundary layer flow over a horizontal circular cylinder