Finite Element Study of Bio-Convective Stefan Blowing Ag-MgO/Water Hybrid Nanofluid Induced by Stretching Cylinder Utilizing Non-Fourier and Non-Fick’s Laws

In the present framework, an analysis on nanofluid magneto-transport phenomena over an extending cylinder influenced by gyrotactic behavior of algal suspension, is made using the Cattaneo–Christov heat flux (non-Fourier) and mass flux (non-Fick’s) concept in modified Buongiorno’s model. Two dimensional incompressible MHD hybrid nanofluid which comprises chemically reactive hybrid nanomaterials (Ag-MgO NPs) and Stefan blowing effect along with multiple slips is considered. The experimental correlations with their dependency on initial nanoparticle volume fraction are used for viscosity and thermal conductivity of nanofluids. Similarity transformation is used to convert the governing PDE’s into non-linear ODE’s along with boundary conditions, which are solved using the Galerkin Finite Element Method (GFEM). The mesh independent test with different boundary layer thickness (ξ∞) has been conducted by taking both linear and quadratic shape functions to achieve a optimal desired value. The results are calculated for a realistic range of physical parameters. The validation of FEM results shows an excellent correlation with MATLAB bvp5c subroutine. The warmth exhibitions are assessed through modified version of Buongiorno’s model which effectively reflects the significant highlights of Stefan blowing, slip, curvature, free stream, thermophoresis, Brownian motion and bio-convection parameters. The present study in cylindrical domain is relevant to novel microbial fuel cell technologies utilizing hybrid nanoparticles and concept of Stefan blowing with bioconvection phenomena.

Nonlinear Radiative Treatment of Hydromagnetic Non-Newtonian Fluid Flow Induced by a Nonlinear Convective-Boundary-Driven Curved Sheet With Dissipations and Chemical Reaction Effects

This study investigates the flow of heat and mass transport of an incompressible MHD Cross fluid over a nonlinear curved stretching sheet. Heat transport incorporates viscous dissipation, radiative flux, and surface heating, whereas the fluid concentration is distressed with the first-order chemical reaction. A radially varying applied magnetic field is considered to examine the effect of Lorentz force and Ohmic heating. The rheology of the fluid is theoretically modeled and constitute a novel work for the completeness of shear thinning and thickening fluids over curved structure. Similarity method is utilized to reduce the governing system of PDE’s into ODE’s. Numerical computation through Runge-Kutta fourth order with shooting technique is implemented by the first initialized higher-order system into the first ODEs. The behaviors of the flow quantities—velocity, temperature, and concentration—are graphically analyzed against the parameters, including radius of curvature, fluid rheology, radiation, and rate of reactions. The numerical results are validated in comparison with the published results. Studies of Newtonian fluids on flat and curved surfaces are the special cases of this work. The results are useful in material processing and polymer dynamics involving stretchable materials.

Soret and Dufour Effects on MHD Nonlinear Convective Flow of Tangent Hyperbolic Nanofluid Over a Bidirectional Stretching Sheet with Multiple Slips

The purpose of the present analysis is to investigate the Soret and Dufour effects on steady and incompressible MHD nonlinear convective flow of tangent hyperbolic nanofluid over a permeable stretching surface with multiple slip conditions at the wall. Also, nonlinearly varying thermal radiation, heat generation and chemical reaction along with a vanishing nanoparticle mass flux condition at the surface are taken into account. Further, Rosseland’s approximation for an optically thick and grey medium is used to approximate heat flux due to radiation. Suitable similarity transformations are employed to transform governing PDEs into a system of ODEs. The resulting nonlinear equations are then solved numerically using the shooting technique based on the Runge-Kutta Cash-Karp method. The upshots of various physical parameters on velocity, temperature and concentration distributions are illustrated and displayed through figures. The variations in coefficients of local skin friction, Nusselt and Sherwood numbers are explained and presented in tabular form. The obtained results are validated with the previously reported results for a particular case of the present fluid flow problem, and an outstanding correlation is noticed from the comparison. Graphical results reveal that the nonlinear convection parameters for both temperature and concentration accelerate the primary flow. However, the Dufour number diminishes the fluid temperature near the wall, and the Soret number uplifts the concentration profile within the boundary layer.

Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (∂1u1,∂1b1), (∂2u2,∂2b2) and (∂3u3,∂3b3) in anisotropic Lorentz space.