This paper, an effort has been made to examine the impact of some distinct parameters, namely magnetic field, porous parameter, reaction rate parameter and viscoelastic parameters of an unsteady convective diffusion through a rectangular channel. The momentum equation and concentration equation of the model have been derived by utilizing the perturbation technique and generalized dispersion model incorporated with BJ slip condition. To get an insight into various parameter of the problem on the velocity and dispersion coefficient has been analysed through different graphs.

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The effect of magnetic field on unsteady convective diffusion in a couple stress fluid (blood) is studied using a time dependent dispersion model. This model is used to calculate the mean concentration distribution of a solute, bounded by the porous layer and is expressed as a function of dimensionless axial distance and time. The magnetic field, arising as a body couple in the governing equations is shown to increase the axis dispersion coefficient. This is useful to the control of haemolysis caused by artificial organs implanted or extracorporeal. Dispersion coefficient and mean concentration are computed for different values of Hartmann number (M), Couple Stress Parameter (a) and Porous Parameter (σ).

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The simultaneous effect of electric field and couple stress on the generalized dispersion of an unsteady convective diffusion in a poorly conducting fluid through a channel is investigated. A two dimensional flow has been considered and the resulting partial differential equation have been solved analytically using the mixture theory together with a regular perturbation technique. The solutions are computed and the results show that the solute is dispersed relative to a plane moving with the mean speed of couple stress poorly conducting fluid as well as the mean speed of coagulation of aerosols with a relative unsteady dispersion coefficient. The graphs for velocity, mean concentration and dispersion coefficient are presented for different values of electric number and couple stress parameter. They show that the effect of couple stress is predominate only for small values.