In this paper, boundary layer flow over a moving flat plate with second-order velocity slip, injection and applied magnetic field is analyzed. The governing partial differential equations are converted in to a nonlinear ordinary differential equation through an appropriate similarity transformation. The resulting nonlinear equation is solved via homotopy analysis method (HAM). Errors ranging from 10–7 to 10–10 are reported for a relatively few terms. The effects of the pertinent parameters on the velocity and the shear stress are presented graphically and discussed. In the absence of magnetic field and the two slip parameters, the results are found to be in excellent agreement with the available results in the literature. It is expected that the results obtained will not only provide useful information for industrial applications but also complement the earlier works.

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An analysis of MHD flow and mass transfer of an upper-convected Maxwell fluid with homogeneousheterogeneous first-order chemical reactions is presented. The flow is driven by a stretching surface and homogeneous-heterogeneous reactions. The governing nonlinear partial differential equations are first cast into ordinary nonlinear differential equations. Then analytical solutions are obtained in series form by the homotopy analysis method (HAM). The obtained results are compared with the existing results in the literature for some special cases and the obtained results are found to be in good agreement. The physical significance of different parameters on the velocity and the concentration fields are presented graphically and discussed. Also, the residual errors of the solutions for several sets of the parameters are obtained and presented.

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A study of an upper-convected Maxwell (UCM) fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of an applied magnetic field is carried out. The governing non-linear coupled equations with appropriate boundary conditions are initially cast into dimensionless form by similarity transformations. Then the resulting non-dimensional equations are solved analytically by Optimal Homotopy Analysis Method (HAM). The effects of the pertinent parameters on the velocity and temperature fields are analyzed graphically. The analysis reveals that the effect of the magnetic field is to decrease the velocity normal to the wall, but the opposite effect is observed for the temperature field. The present study is relevant to the haemodynamic flow of blood in the cardiovascular system in the presence of uniform magnetic field.