An axisymmetric viscous carbon nanotube (CNT) nanofluid flow exterior to a rotating circular cylinder of radius a ₀ along with viscous dissipation and magnetohydrodynamic (MHD) is considered here. The two-phased Buongiorno’s model is employed to observe the thermal energy transport in nanofluid with engine-oil as a background fluid and two distinct nanoparticles, i.e., single-walled (SWCNTs) and multi-walled (MWCNTs). The flow is driven because of the torsional motion and stretching of the cylinder along the z-direction, which constitutes the axial pressure gradient. It is seen that in the presence of a magnetic field, the axially dependent swirling motion of the cylinder creates a light transverse flow in the meridional plane, which is the principal cause for the wall jet phenomenon on the axial axis. The function computing the numerical solution is bvp5c, which is available in Matlab ^® . It is noted that for both SWCNTs/MWCNTs cases, thermal and mass transport coefficients are decreasing function of Prandtl and Schmidt numbers, respectively. However, they are augmented due to the presence of strong Lorentz force. The values for wall stress parameters (WSPs) are determined as a function of a magnetic parameter for 0.01 ≤ Re ≤ 10 ² (where Re is Reynolds number). It is also perceived that the axial WSP decreases due to an increase in values of Re, but an increase in numerical values of azimuthal WSP and Nusselt number is noticed.

The problem of Jeffrey’s nanofluid for a modification of Homann’s exterior potential flow in the stagnation region is modeled over a cylindrical disk. The characteristic of electrically conducting nanofluid flow with a time-independent free stream is noted as well. Due to this, a new family of asymmetric flows is created, which mainly depends on the viscoelastic parameter $k,$ magnetic parameter $M,$ and the stress-to strain rate ratio, i.e., $\gamma =\frac{b}{a}.$ By deploying Buongiorno’s model and Rosseland’s approximation, the outcomes of the Brownian diffusion, thermophoresis, and solar radiation on the mass and thermal boundary layer are also scrutinized. The conservation laws are remodeled by a similarity transformation, and the governing equations are solved by a builtin program bvp4c in Matlab. Furthermore, a comparison is made between the numerical outcomes and their large-γ asymptotics for wall stresses and displacement thicknesses. It is discovered that due to the impact of Jeffrey’s material parameters and magnetic field, when $\gamma$ reaches infinity, along the x-axis the two-dimensional displacement thickness and the coefficient of skin friction are closer to their asymptotic values; however, along the y-axis, they exhibit opposite trend. Moreover, the thermal and mass transport is enhanced due to significant contributions of nanofluid conductivity.

In this article, an investigation of the thermal and solutal energy transport in the 3 D flow of Maxwell nanofluid through a porous medium under the influence of the magnetic field is performed. The heat generation source and chemical reaction are also taken in account as a controlling agent for the heat and mass transport in the Maxwell liquid. A novel idea of Cattaneo-Christov theory and Buongiorno model for nanofluid is employed under the impact of Joule heating for the present analysis. The governing partial differential equations (PDEs) are transformed into a non-linear system of ordinary differential equations (ODEs) by using flow similarities. The solution of similar ODEs is constructed through a well known semi-analytical technique which is the homotopy analysis method. The results of the investigation are explored in the form of graphs. It is observed that higher values of magnetic field decline the flow field. The temperature and concentration distributions decrease with the higher magnitude of thermal and solutal relaxation time phenomena, respectively. Moreover, the temperature field enhances when the Brownian motion of nanoparticles increases in flow while the concentration profile decreases. Also, it is found that the increase in resistive heating boosts up the thermal energy transport in the fluid motion.

In this article, an analysis is conducted on the flow over a circular cylinder enduring torsional motion immersed in a viscous fluid. The thermal energy distribution is examined for constant and variable surface temperatures. The problem is formulated for an axisymmetric flow in the Cattaneo–Christov double diffusion theory, wherein the energy equation is modified. Note that the rotation of the cylinder is axially dependent, and the phenomenon of wall jet arises due to the axially dependent velocity component, mainly because of the axial pressure gradient. Using the appropriate variables, the dimensionless ordinary differential equations are developed by governing partial differential equations. To solve them, we implemented a built-in function in MATLAB, namely, bvp5c. It is perceived that the peak of the wall jet rises by enhancing the values of Reynolds number Re; however, the azimuthal velocity distribution reduces. The impact of pertinent parameters on thermal and solutal transport in viscous fluid flow is also studied. In general, it is seen that they reduce the heat and mass transfer rates according to their physical influence on the flow. Moreover, the axial and swirl wall-shear stresses are plotted as a function of Re over the range of 0.01 ≤ Re ≤ 10⁴.