Purpose: The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid. Design/methodology/approach: Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter. Findings: It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid. Originality/value: The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.

In this study, we investigate a peristaltic transport of nano-hyperbolic tangent fluid in an inclined asymmetric channel with convective boundary conditions. Two types of nanoparticles are considered, namely, the copper and aluminum oxide. Mathematical modeling is carried out by using a long wavelength and low Reynolds number assumptions. The governing equations of the problem are solved analytically by a perturbation technique with small Weissenberg number. Through graphs, we analyze the effects of the nanoparticles volume fraction parameter, slip parameter, Biot number along with the other pertinent parameters on the stream function, axial velocity, pressure rise per wavelength, temperature and Nusselt numbers. It was found that the copper and aluminum oxide nanoparticles have almost insignificant effect on the axial velocity field and the heat transfer coefficients. However, the retrograde pumping rate decreases with increasing a,B and n while this behavior is reversed for the cases of peristaltic and copumping. Furthermore, the pressure rise per wavelength does not show a significant change with an increase in We in the presence of copper and aluminum oxide nanoparticles