Generaleristics of unsteady MHD temperature boundary layer

•Results presented in manuscript are in area of general characteristics of unsteady MHD temperature boundary layer, presenting as a fluid in coupled magnetic and temperature fields.•Manuscript contains numerous graphical illustrations as results of analytical and numerical investigation interaction of different kinetic parameters of the coupled fields to the boundary fluid layer.

Unsteady temperature magnetohydrodynamic (MHD) boundary layer on the arbitrary shape body which temperature is function of time and longitudinal coordinate has been studied. A generalized similarity method is applied to solve the governing non-linear differential equations. Universal partial differential equations of the discussed problem are obtained using the method by which the equations are transformed in such a way that neither the equations nor the boundary conditions depended on particular data of the considered problem. These equations are solved numerically and the integration results are given for different values of introduced parameters. Those solutions permit, before their application to the particular cases (assigned free stream velocity), a generalized analysis of the effects of certain pertinent parameters to the development of the boundary layer. Obtained results are discussed in detail for different values of introduced parameters. Based on the given universal solutions result it is possible to calculate any particular problem for defined free stream velocity and body temperature distribution.