Computational Framework of Magnetized MgO-Ni/Water-Based Stagnation Nanoflow Past an Elastic Stretching Surface: Application in Solar Energy Coatings

In this article, motivated by novel nanofluid solar energy coating systems, a mathematical model of hybrid magnesium oxide (MgO) and nickel (Ni) nanofluid magnetohydrodynamic (MHD) stagnation point flow impinging on a porous elastic stretching surface in a porous medium is developed. The hybrid nanofluid is electrically conducted, and a magnetic Reynolds number is sufficiently large enough to invoke an induced magnetic field. A Darcy model is adopted for the isotropic, homogenous porous medium. The boundary conditions account for the impacts of the velocity slip and thermal slip. Heat generation (source)/absorption (sink) and also viscous dissipation effects are included. The mathematical formulation has been performed with the help of similarity variables, and the resulting coupled nonlinear dimensionless ordinary differential equations have been solved numerically with the help of the shooting method. In order to test the validity of the current results and the convergence of the solutions, a numerical comparison with previously published results is included. Numerical results are plotted for the effect of emerging parameters on velocity, temperature, magnetic induction, skin friction, and Nusselt number. With an increment in nanoparticle volume fraction of both MgO and Ni nanoparticles, the temperature and thermal boundary layer thickness of the nanofluid are elevated. An increase in the porous medium parameter (Darcy number), velocity slip, and thermal Grashof number all enhance the induced magnetic field. Initial increments in the nanoparticle volume fraction for both MgO and Ni suppress the magnetic induction near the wall, although, subsequently, when further from the wall, this effect is reversed. Temperature is enhanced with heat generation, whereas it is depleted with heat absorption and thermal slip effects. Overall, excellent thermal enhancement is achieved by the hybrid nanofluid.

Numerical computation of 3D Brownian motion of thin film nanofluid flow of convective heat transfer over a stretchable rotating surface

This research examines the thin-film nanomaterial movement in three dimensions over a stretchable rotating inclined surface. Similarity variables are used to transform fundamental systems of equations into a set of first-order differential equations. The Runge–Kutta Fourth Order approach is utilized for numerical computations. The impact of embedded parameters (variable thickness, unsteadiness, Prandtl number, Schmidt number, Brownian-motion, and thermophoretic) is examined carefully. Physically and statistically, the indispensable terms namely Nusselt and Sherwood numbers are also investigated. Results indicated that, as the dimensionless parameter S raises, the temperature field decreases. In reality, as the values of S increases, heat transmission rate from the disc to the flowing fluid reduces. Internal collisions of liquid particles are physically hampered at a low rate. The momentum boundary layer is cooled when the parameter S is increased, as a consequence local Nusselt number rises. Sherwood number decreases as the parameter S increases because of inter collision of the microscopic fluid particles. Enhancing in the apparent viscosity and concentrations of the chemical reactions, a higher Schmidt number, Sc, lowers the Sherwood number. With increasing values of Prandtl number the Nusselt number decreases. For validation purpose, the RK4 method is also compared with homotopy analysis method (HAM). The results are further verified by establishing an excellent agreement with published data.

Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties

A mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno's two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter [Formula: see text], thermal conductivity parameter (c4), nano-particle mass diffusivity (c6), micro-organism species diffusivity (c8), thermophoresis parameter [Formula: see text], Brownian motion parameter [Formula: see text], Lewis number [Formula: see text], bioconvection Schmidt number [Formula: see text], bioconvection constant (σ) and bioconvection Péclet number [Formula: see text]. Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter ([Formula: see text] whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter ([Formula: see text] whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter ([Formula: see text]) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent ([Formula: see text] skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter ([Formula: see text]) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes.