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Numerical study of peristaltic transport of heat and mass transfer for a couple stresses non-Newtonian nano fluid through porous media inside asymmetric channel was investigated. The system is stressed by an external uniform magnetic field. This model is solved numerically subjected to an approbate boundary conditions using a Rung-Kutta-Merson method under assumption of the long wave length and low range of Reynolds number. The velocity, temperature and concentration of nanoparticles are obtained as a function of the physical parameters of the problem. The effects of these parameters on these solutions are discussed numerically and illustrated graphically through some graphs It is clear that the effects of the physical parameters of the problem on these solutions play an important rule to control the obtained solutions. The velocity profile decreases when Hartmann number increasing. This seems realistic, because the magnetic field acts in the transverse direction to the flow and magnetic force resists the flow, The velocity increasing when the fluid material parameter increasing because fluid becomes less viscous, The variation of temperature increasing with increasing values of Brownain motion parameter and porosity parameter, The variation of Concentration decreasing with increasing of thermophoresis parameter and Radiation parameter inside the used channel.

The motion of viscoelastic nanofluid flow with heat and mass transfer over a permeable flat plate under the action of uniform magnetic field is discussed. The effects of Brownian motion, thermophoresis and viscous and ohmic dissipations are considered. The system of equations describes the motion is converted to ordinary non-linear differential equations by using suitable transformations, and then solved numerically by using fourth order Runge-Kutta method with shooting technique. The obtained solutions are functions of the physical parameters of the problem. The effects of these parameters on the obtained solutions are discussed numerically and illustrated graphical to show that the parameters controlled the solutions.

This paper deals with the mathematical examination of the arrangement of incomplete differential conditions which depict the peristaltic movement of a non‐Newtonian nanofluid with couple stress through a symmetric channel with flexible walls. The fluid used obeys a power‐law model. The system of the nondimensional form of momentum, heat, and concentration of the fluid flow is solved numerically by using a Rung–Kutta–Merson method with the appropriate boundary conditions after using the approximations of long wavelength and low Reynolds number. The obtained arrangements are elements of the physical boundaries of the problem. In this manner, the impacts of these boundaries on the velocity, temperature, and nanoconcentration distributions are concentrated mathematically and shown graphically through many figures. It is discovered that the physical boundaries play a significant role in controlling the arrangements, where the speed field diminishes with expansion of the attractive boundary, while it increments with expanding couple pressure and the non‐Newtonian parameter of the non‐Newtonian liquid. Additionally, the temperature and nanoconcentration changes with the Brownian parameter and thermophoresis. Moreover, the temperature distribution increases with increase of the magnetic parameter, Prandtl number, Eckert number, and heat source.

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