Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes.

Convective phenomena in a nanofluid flow under the influence of gravitational and magnetic body forces is analyzed in this communication. Nanofluid is of viscoelastic nature that preserves viscosity as well as elasticity. In order to capture the more realistic behavior of the convective phenomena Caputo fractional derivative and fractional relaxation time are introduced in the Buongiorno nanofluid model. Fractional derivative and relaxation time are used for controlled flow mechanism and to overcome infinite propagation speed for the temperature and concentration. The proposed model will also help to understand the hereditary and memory properties of the viscoelastic nanofluid. In order to more closely analyze the buoyancy forces nonlinear convection is introduced in the mathematical modeling of the flow problem. Finite difference-finite element numerical computations are carried out for the governing nonlinear partial differential equations. Quantities of physical interest are computed and discussed for the fractional model. The proposed fractional model can be used to realistically simulate various flow problems in polymer and chemical industries.

In the current study, the bioconvective flow of Ree–Eyring through an expanding sheet with the porous medium is analyzed by considering the inclined magnetic field and gyrotactic microorganisms. Buongiorno's model, which defines the two major mechanisms; thermophoresis and Brownian motion is used to frame the mathematical model. The presence of motile cells helps in stabilizing the nanoparticle and avoids the sedimentation due to nanoparticles. The mathematical model with these assumptions is framed using partial differential equations (PDE) that are later remodeled to ordinary nonlinear differential equations by incorporating desirable similarity transformation. The equations so obtained shall be solved using DTM and the outcomes are described through graphs and tables. The graphs indicated that the velocity of the nanofluid flow reduces with the increase in the porosity and similarly, the higher values of Peclet number (Pe) are found to diminish the motile density. Whereas the increase in the thermophoresis parameter enhances the thermal and mass profiles of the nanofluid.