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Nanofluid bioconvective channel flow is an essential aspect of the recent healthcare industry applications, such as biomedical processing systems. Thus, the present work examined the influence of nth order chemical reaction in an unsteady nanofluid bioconvective channel flow in a horizontal microchannel with expanding/contracting walls. The suitable form of the similarity transformation is exercised to transform the governing boundary layer equations into a more straightforward form of system to ease the computation process. The Runge–Kutta method of fifth-order integration technique solved the reduced boundary layer system and generated the numerical results as the governing parameters vary. It is found that the destructive second-order chemical reaction enhances the mass transfer rate at the lower wall but deteriorates the mass transfer rate at the upper wall. The upper channel wall has a better heat transfer rate than the lower wall when the Reynolds number increases.

In this article, the three-dimensional Magnetohydrodynamics flow of a nanofluid over a horizontal non-linearly stretching sheet in bilateral directions under boundary layer approximation is addressed. A two-phase model has been used for the nanofluid. The influences of thermophoresis, Brownian motion and thermal radiation on heat and mass transfers are considered. Two different cases for the heat and mass transfers are studied. In the first case, uniform wall temperature and zero nanoparticles flux due to thermophoresis are considered. In the second case, prescribed heat and mass fluxes at the boundary are considered. By using the appropriate transformations, a system of non-linear partial differential equations along with the boundary conditions is transformed into coupled non-linear ordinary differential equations. Numerical solutions of the self-similar equations are obtained using a Runge–Kutta method with a shooting technique. Our results for special cases are compared with the available results in the literature, and the results are found to be in good agreement. It is observed that the pertaining parameters have significant effects on the characteristics of flow, heat and mass transfer. The results are presented and discussed in detail through illustrations.