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In the present article, importance of double-diffusivity convection in nanofluids on peristaltic pumping of Carreau fluid in tapered channel with induced magnetic field and different waveforms has been theoretically discussed. Mathematical modeling of the two-dimensional and two-directional flow of a Carreau fluid are described in detail. A well-known assumption (long wave length and low Reynolds numbers) are employed in order to find the exact and analytical solution of the proposed problem. Exact solutions of temperature, concentration, and nanoparticle volume fraction are computed. Perturbation technique is used to calculate the solutions of highly nonlinear partial differential equations. With the help of Mathematica software and MATLAB, graphical results are displaced to see the behavior of temperature, concentration, nanoparticle volume fraction, pressure rise, pressure gradient, magnetic force function, and stream functions. It is observed that temperature and concentration profile increases with an increase in Nb, Nt, NCT, and NTC.

The present article deals with the effects of nanoparticles and magnetic field on the peristaltic flow of a couple stress fluid in an asymmetric channel with different wave forms. Mathematical modelling for 2-D and two directional flows of a couple stress fluid along with nanofluid are first given and then simplified under the assumptions of long wavelength and low Reynolds number approximation. After invoking these approximations we get coupled non-linear differential equations. The exact solutions of temperature distribution, the nanoparticle concentration, velocity, stream function and pressure gradient are calculated. Finally graphical results of various physical parameters of interest are discussed to examine the behavior of flow quantities.

Noteworthiness of double-diffusive convection with nanofluids by induced magnetic field and diverse wave shapes for peristaltic stream of Williamson fluid in a uniform channel has been theoretically examined. Mathematical formulation of two-directional and two-dimensional flow of a Williamson fluid model is explained in detail. The exact solutions of nanoparticles are described. Perturbation solutions of nonlinear PDEs are also calculated. Numerical and graphical results are displaced to see the conduct of temperature, concentration, nanoparticle volume fraction, pressure rise, pressure gradient, magnetic force function and stream functions. It is concluded that the profile of temperature increases and profile of concentration decreases by increasing values of Brownian motion parameter $$ N_{\text{b}} $$ , thermophoresis parameter $$ N_{\text{t}} $$ , Dufour parameter $$ N_{TC} $$ and Soret parameter $$ N_{CT} $$ .

Study the significance of double-diffusive convection and induced magnetic field on peristaltic flow of pseudoplastic nanofluid in a tapered asymmetric channel with different four wave forms have been investigated. Formulation and governing equations of this problem were deduced representing by highly partial differential equations. Hence, exact and analytical solutions of the resulting equations were deduced. Therefore, effects of pressure rise, pressure gradient, temperature, concentration, nanoparticle volume fraction, magnetic force function and stream functions were graphical represented and discussed. It was found that, on rising in the tapered asymmetric channel parameter, the pumping rate increases (decreases) in copumping region (in the retrograde pumping and free pumping regions). Further, the temperature distributions increase with growing in Brownian motion, Soret, Dufour and thermophoresis parameters while the concentration profile decreases with these parameters.