Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Flow of nanofluid towards a Riga surface with heat and mass transfer under the effects of activation energy and thermal radiation

This paper numerically simulates the nanofluid flow over a thermally expanding Riga plate. Buongiorno model for nanofluid is employed to investigate the contribution of Brownian motion and thermophoretic force on the nanoflow. Magnetohydrodynamics (MHD) of viscous nanofluid through a porous medium is characterized with the help of Darcy–Forchheimer’s model. In addition, the simultaneous effects of activation energy and chemical reaction have been incorporated. Moreover, highly nonlinear coupled differential equations are formulated which highlight the influence of viscous dissipation and heat generation. A numerical solution is achieved with the help of the Range–Kutta fourth-order (RK4) method combined with the shooting technique. Finally, the role of emerging parameters is studied via performing the numerical simulation which reveals that the momentum boundary layer of nanofluid shrinks due to the porous medium. Whereas, thermal boundary layer expands for all variables, except for the Prandtl number. Finally, mass transfer rated suffers due to Schmidt number.

3D Brownian Motion Thin Film Fluid spraying nanoparticles impact of Convective Heat Phenomena over Stretchable Rotating Surface: Numerical Computation

The purpose of this research is to examine 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 purpose solution. Variable thickness., Unsteadiness parameter., Prandtl number., Schmidt number., Brownian-motion parameter., and Thermophoretic parameter have all been seen to have an impact. Physically and statistically, the indispensable terms namely Nusselt as well as Sherwood numbers are also investigated. As the dimensionless factor \(S\) grows, the temperature field decreases. The momentum boundary layer is cooled when the parameter \(S\) is improved, and the opposite effect is observed for Nusselt number. A greater Schmidt number Sc reduces the Sherwood number by increasing the kinematic viscosity as well as Concentration of the chemical species. Further, the RK4 method is also validated with the HAM approach. Furthermore, we verified the acquired results by establishing a comparison with previous literature, and we discovered an outstanding match, confirming the accuracy of the current communication.

Heat Transfer From a Concentrated Tip Source in Falkner-Skan Flow

The Falkner-Skan flow over a wedge is classic in boundary layer theory. We consider the heat or mass transfer from a source at the vertex of the wedge. The interactions of thermal boundary layer and momentum boundary layer lead to nonlinear similarity equations which are integrated numerically. There exists a mixing index which depends on the Prandtl number and the wedge opening angle. Attention is paid to special cases such as forced convection in Blasius flow past a semi-infinite plate and the Hiemenz stagnation flow normal to a plate.

Computational analysis of water based Cu - Al2O3/H2O flow over a vertical wedge

Theoretical and numerical investigation of the fluctuating mixed convection of hybrid nanofluid flow over a vertical Riga wedge is considered in this analysis. Two kinds of solid nanoparticles with base fluid at vertical Riga wedge is studied. Thermal and velocity slip impacts on vertical Riga wedge are investigated in the current study. We discussed both the unsteady and steady cases. The water has low thermal conductivity. We added the nanoparticle [Formula: see text] and [Formula: see text] which increases the thermal conductivity of the base fluid. This phenomena increase the heat transfer rate at the surface Riga plate. Partial differential equations are reduced into an ordinary differential equation by means of dimensionless similarity variables. The resulting ordinary differential equations are further solved through numerical and perturbation methods. Thickness of momentum boundary layer is reduced because of the solid nanoparticle rises in all cases of [Formula: see text], [Formula: see text], [Formula: see text]and[Formula: see text]. Our results are more agreeing with the decay results of Bachok et al. and Yacob et al. when rest of the physical parameters dimensions.

Analysis of a Chemically Reactive Mhd Flow With Heat and Mass Transfer Over a Permeable Surface

This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip

In this article, an axisymmetric three-dimensional stagnation point flow of a nanofluid on a moving plate with different slip constants in two orthogonal directions in the presence of uniform magnetic field has been considered. The magnetic field is considered along the axis of the stagnation point flow. The governing Naiver–Stokes equation, along with the equations of nanofluid for three-dimensional flow, are modified using similarity transform, and reduced nonlinear coupled ordinary differential equations are solved numerically. It is observed that magnetic field M and slip parameter λ 1 increase the velocity and decrease the boundary layer thickness near the stagnation point. Also, a thermal boundary layer is achieved earlier than the momentum boundary layer, with the increase in thermophoresis parameter N t and Brownian motion parameter N b . Important physical quantities, such as skin friction, and Nusselt and Sherwood numbers, are also computed and discussed through graphs and tables.

The natural convective graphene oxide nanofluid flow in an upright squeezing channel

The 3-D flow of water based graphene oxide (GO-W) and ethylene glycol based graphene oxide (GO-EG) nanofluids amongst the binary upright and parallel plates is considered. The unsteady movement of the nanofluid is associated with the porous medium and the unbroken magnetic field is executed in the perpendicular track of the flow field. The basic governing equations have been altered using the Von Karman transformation, including the natural-convection in the downward direction. The solution for the modeled problem has been attained by means of optimal homotopy analysis method (OHAM). The influence of the physical parameters on the momentum boundary-layer, pressure and temperature fields is mainly focused. Moreover, the comparison of the GO-W and GO-EG nanofluids under the impact of physical constraints have been analyzed graphically and numerically. The imperative physical constraints of the drag force and heat transfer rate have been computed and conferred. The consequences have been validated using the error analysis and the obtained outcomes have been shown and discussed.

On the transient response of the turbulent boundary layer inception in compressible flows

The behavioural characteristics of thermal boundary layer inception dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the thermal boundary layer to be established is vital to optimize flow control strategies, as well as the thermal management of systems exposed to ephemeral phenomena, typically on the millisecond scale. This paper presents the time characterization of the momentum and thermal boundary layer development in transient turbulent compressible air flows. We present a new framework to perform such estimations based on detailed unsteady Reynolds averaged Navier–Stokes simulations that may be extended to higher fidelity simulations. First of all, the aerodynamic boundary layer initiation is described using adiabatic simulations. Additional numerical calculations were then performed by setting the isothermal wall condition to evaluate the additional time required by the thermal boundary layer to establish after the aerodynamic boundary layer reaches its steady state. Finally, full conjugate simulations were executed to compute the warm up effect of the solid during the blowdown of a hot fluid over a colder metallic test model. The transient performance of the turbulent thermal and momentum boundary layers is quantified through numerical simulations of air blowdown over a flat plate for different mainstream flow conditions. The effects of Reynolds number, free stream velocity, transient duration, test article length and free stream temperature were independently assessed, to then define a mathematical expression of the momentum boundary layer settlement. This paper presents a novel numerical correlation of the additional time required by the thermal boundary layer to be stablished after the settlement of the momentum boundary layer. The time scales of the aerodynamic and thermal boundary layers are presented as a function of relevant non-dimensional numbers, as well as the description of the response of the near wall flow to sudden free stream changes. The characterization of the boundary layer mechanisms discussed in this paper contribute to the establishment of an evidence-based foundation for advances in the field of flow control.