MHD peristaltic flow of radiating fourth-grade hybrid nanofluid with Joule heating under initial stress

Abstract

ABSTRACT The main goal of this work studies the effectiveness of two composed hybrid nanoparticle materials (Cu-TiO2) in the peristaltic flow of fourth-grand non-Newtonian nanofluids under the Joule heating and initial pressure in addition to the effectiveness of the magnetic field and heat transfer. On the other hand, this study depended on governing equations by transforming from PDEs into ODEs and solving this equation by using fourth-order Runge–Kutta with shooting technique and trapping methods is addressed graphically. Furthermore, the effects of all physical parameters on the distributions of velocity and temperature of hybrid nanoparticle inside the fluid, distribution of pressure gradients and the distribution of magnetic force are retained. Represent the result graphically and in tables. Comparing by graph the effectiveness of hybrid nanoparticles in velocity and temperature is also seen effectiveness of several parameters in heat transfer and velocity in pure fluid and nanofluid with the effect of this parameter in various in pressure. All these results are displayed by graphs to show the effects of the external new parameters that indicate the strong impact on the phenomenon. The two nanoparticles and , where is volume particle of (Cuo) and is volume particle of (TiO2) the velocity profile f'(η) has a comparable influence for both hybrid nanofluid and nanofluid. The larger quantity of the factors , M and Deborah number Γ.