Mass Flux Boundary Conditions Research Articles

Effects of Brownian and thermophoresis on the nanofluid flow with zero nanoparticle mass flux and convective conditions through non-linearly expanding Riga plate

The present flow phenomena characterize the behavior of the Brownian motion and thermophoresis considering the Buongiorno model nanofluid through a non-linearly expanding Riga plate. The conjunction of thermal radiation with zero nanoparticle mass flux and convective boundary conditions enriches the thermal properties of the nanofluid. With the recent need in various industrial applications, the biomedical sector, for the design and development of the production process of various equipment, the role of nanofluid is vital. Further, the suitable variables leading to transformation rules are useful to get rid of the dimensional form of the governing equations. Traditional numerical technique with the help of shooting-based Runge–Kutta fourth-order technique is adopted for the solution of a transformed set of equations. The physical behavior of the characterizing components is presented and described briefly. Further, the important outcomes are the use of Hartmann number that overshoots the velocity profile, whereas the heat transfer retards significantly and enhanced thermophoresis attenuates the heat transfer rate.

Thermodynamic analysis for peristaltic flow of Carreau-Yasuda magneto nanofluid through a porous medium

Thermodynamic analysis for mixed convective peristaltic transportation of Carreau–Yasuda (CY) magneto nanofluid is presented. The assumed nanofluid is a mixture of graphene nano-powder and ethylene glycol. The Carreau–Yasuda model is considered to represent the non-Newtonian features of nanofluids. A mathematical model is developed under the effects of a porous medium, variable thermal conductivity, Brownian motion, viscous dissipation, magnetic field, thermophoresis, and Ohmic heating assumptions. Mass and heat transfer aspects are also considered. The flow and heat/mass transfer equations were made using Buongiorno’s model of nanofluids. No-slip and zero mass flux boundary conditions are entertained for velocity, thermal, and concentration profiles. A numerical solution via built-in technique is obtained for a coupled system of equations. Graphical outcomes predict that due to Ohmic heating characteristics temperature profile increases. The heat transfer rate at the wall decreases for higher thermal conductivity parameter. The irreversible rate can be controlled by maintaining Darcy’s number. The concentration of nanomaterials increases when the thermophoresis parameter is improved. Fluid velocity is slowed down by enhancing the Hartman number and it improves by enhancing the thermal Grashof number.

A numerical scheme for Darcy-Forchheimer flow of non-Newtonian nanofluid under the effects of convective and zero mass flux boundary conditions

This research aims to propose a numerical scheme for solving boundary value problems. It is a two-stage, third-order accurate scheme known as a predictorcorrector scheme. The two main results are finding the region of the scheme where it is stable and determining the stability criterion for a set of linearized first-order differential equations. In addition, a mathematical model for heat and mass transfer of Darcy-Forchheimer flow of non-Newtonian nanofluid over the sheet is presented. The similarity transformations reduce PDE into a system of ODE for easier manipulation. The results are compared with the past research and those obtained by MATLAB SOLVER BVP4C. The results show that the velocity profile slightly decays by enhancing the Weisenberg number.

Thermal performance analysis of Sutterby nanoliquid subject to melting heat transportation

In the recent years, nanotechnology has been widely used in several fields regarding its rapid developments which create a lot of prospects for researchers and engineers. More specifically, replacement of conventional liquid with nanofluid is considered as an innovative solution to heat transfer problems. Keeping aforesaid pragmatism of nanofluid in view, we considered a time-dependent mathematical model to formulate the heat sink-source based Sutterby nanofluid model under thermophoretic and Brownian movements. New mass flux and melting boundary conditions are used for heat/ mass transfer analyses. Moreover, Prandtl’s boundary-layer idea is employed for mathematical formulation. The leading nonlinear set of partial differential equations is transformed to nonlinear set of ordinary differential equations. Numeric outcomes are acquired through bvp4c algorithm, graphical results are found via MATLAB technique. Acquired numerical data shows that temperature of nanofluid boosts for greater thermophoretic and unsteady parameters. Intensification is measured in concentration distribution.

Interaction of Variable Fluid Properties with Electrokinetically Modulated Peristaltic Flow of Reactive Nanofluid: A Thermodynamical Analysis

In the present study, the interaction of variable fluid properties with electrokinetically regulated peristaltic transportation of a reactive nanofluid embedded in a porous space is studied. The nanofluid saturates the porous space/medium with inhomogeneous porosity, which changes with distance from the channel boundary. It is assumed that nanofluids are accompanied by variable thermal conductivity and viscosity. The impacts of magnetic field, Brownian motion, electric field, viscous dissipation, chemical reaction, mixed convection, and thermophoresis are incorporated. Moreover, the contribution of zero mass flux boundary condition is executed. The complexity of the equations describing the flow of a nanofluid is reduced by applying the lubrication theory. The fully non-linear equations are solved by utilizing a numerical technique. Particular attention is paid to the analysis of entropy optimization, since its minimization is the best measure to enhance the efficiency of thermal systems. These results demonstrate that a positively oriented external electric field contributes to an increase in nanofluid velocity. Temperature of nanofluid increases more rapidly due to an augmentation in Joule heating parameter. It is noticed that the temperature of water is comparatively lower than that of kerosene. The system’s energy loss can be reduced when the thermal conductivity parameter enhance. The magnitude of Bejan number is enhanced by increasing electroosmotic parameter. Further, a substantial decrement in concentration profile is perceived when the Schmidt number is augmented.

Nonsimilar modeling and numerical convective transport analysis of forced flow of radiative Carreau nanofluid with zero mass flux boundary condition

AbstractPresent research focuses on nonsimilar analysis of the flow of a non‐Newtonian Carreau nanofluid against different geometrical configurations affected by thermal radiations. The flow is induced by stretchable surface with the implementation of zero‐net mass‐flux conditions on the surface. This considered model is commonly known as Kuznetsov and Nield's proposed updated model for nanoparticles. The derived flow equations are first nondimensionalized by employing appropriate nonsimilar transformations. The transformed system is analytically tackled by employing the local nonsimilarity (LNS) approach up to the second‐truncation level in association with the numerical algorithm bvp4c. The consequences of appropriate parameters, such as the suction parameter, wedge angle parameter, Weissenberg number, Prandtl number, constant velocity parameter, temperature ratio, Brownian motion, Lewis number, thermophoresis and radiation parameters, on fluid velocity, thermal, and concentration profiles are calculated and graphed. Drag coefficient, Nusselt, and Sherwood numbers are also computed and presented in tabular form. It is observed that intensification in the suction parameter shows augmentation in the local skin friction coefficient. Enhancement in the wedge angle parameter increases both the Sherwood and Nusselt numbers. Enhancement in velocity profile of the nanofluids is noticed with the increasing estimations of suction parameter. Thermophoresis parameter enhances both thermal and concentration profiles, however increasing Lewis number leads to a decline in the concentration boundary layer. With judgment, a comparative assessment is made of the present and previous results. This research may be helpful for the researchers that are interested in studying prospective industrial and engineering nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, and many others.

Numerical analyses of a reference wing for combination of hybrid laminar flow control and variable camber

The objective of the LuFo VI-1 project CATeW (Coupled Aerodynamic Technologies for Aircraft Wings) consists in multifidelity analyses to assess the potential for aerodynamic efficiency increase by combined application of hybrid laminar flow control and variable camber technologies to the wing of a transonic transport aircraft. Individually, both technologies have proven to lead to major aerodynamic drag reductions. An evaluation of the coupled technologies is, therefore, expected to show an even higher potential due to synergy effects. To derive conclusions on system level, low-fidelity (LowFi) overall aircraft design methodologies will be applied for the analysis of a medium haul reference aircraft in the course of the project, while complex aerodynamic phenomena are modelled with high-fidelity (HiFi) computational fluid dynamics methods. The paper at hand presents results of aerodynamic analyses on both fidelity levels for the wing of the turbulent reference configuration CATeW-01, featuring the technology combination as a retrofit. Furthermore, this work encompasses adaptations and implementations performed within both the LowFi and HiFi toolchains. The LowFi toolchain already incorporates several modules for the proposed technology combination. A short presentation of the LowFi-toolchain is given, along with the modeling approach in the HiFi framework using mesh deformations and a mass flux boundary condition. Comparative studies of the turbulent flow field around the wing show good agreement of predicted load distributions in both numerical frameworks, studies based upon the HiFi approach attest the potential for efficiency increase due to the variable camber technology, incorporated by means of Adaptive Dropped Hinge Flap (ADHF) deflections. Considering the coupled application, four different constant suction mass flow rates are examined, where the maximum mass flow causes laminar flow extending over the entire suction panel, thus moving the transition location from the wing’s leading edge to the end of the suction panel. When being coupled with ADHF deflections, again the variable camber technology leads to a reduction of the wing’s pressure drag component with the simultaneous application of boundary layer suction further promoting drag reduction with increasing suction rate. While the combined application shows no mutual inhibition, major reciprocal effects are not directly observable when applying the combination as a retrofit to the reference configuration CATeW-01. This is mainly attributed to the limited extend of laminar flow, thus indicating the necessity for optimization in wing geometry and operating parameters, to achieve extensive areas of laminar flow and to promote the aspired synergy effects.

Electromagnetohydrodynamic boundary layer flow in hybrid nanofluid with thermal radiation effect: Numerical simulation

AbstractHybrid nanofluid boundary layer flow past a stretching surface with zero mass flux boundary condition is explored in this article. The main aim of this article is to analyze the electromagnetohydrodynamic role in a hybrid nanofluid containing silver and molybdenum disulfide nanoparticles. The self‐similar solution is embedded to reduce the governing partial differential equation into algebraic equations and a shooting algorithm is applied to obtain the solution of the resultant boundary value problem. Variation in momentum, energy, and nanoparticle concentration is explained through graphical profiles. Nusselt number and drag force coefficients are computed for various flow parameters and their impact on the nanofluid and hybrid nanofluid is computed and presented and explained in a comparative fashion. It is observed that the velocity profile shows the opposite nature with respect to the electric field and magnetic field. For electric field parameter velocity accelerates whereas for magnetic parameter velocity diminishes. Nusselt number increases with electric field parameter and nanoparticle volume fraction.

Peristaltic transportation of Carreau–Yasuda magneto nanofluid embedded in a porous medium with heat and mass transfer

Magnetohydrodynamic rheological pumping systems based on biological sources are finding new applications in modern energy systems. These systems combine the electrically conductive properties of flowing fluids with rheological behavior, biological geometry, and propulsion mechanisms. Further improvement of transport characteristics can be achieved with the use of nanofluids. In this study, all these aspects are combined to analyze the heat and mass transfer in mixed convective peristaltic conveyance of Carreau-Yasuda (CY) magneto nanofluid with mixture of ethylene glycol and graphene nano-powder. The Carreau-Yasuda model is utilized for nanofluid rheology and the Buongiorno's model for nanoscale effects. The deemed flow situation is modelled via temperature dependent heat generation/absorption, variable thermal conductivity, porous medium, activation energy, mixed convection, Brownian diffusion, magnetic field, thermophoresis diffusion, Ohmic heating and viscous dissipation assumptions. Fluid saturated porous medium is simulated by employing a modified Darcy's law. Zero mass flux and no-slip boundary conditions are taken for concentration, heat and velocity fields. Using the lubrication assumption, the governing system of equations for the fluid transfer problem is abridged and resolved employing built-in command NDSolve in Mathematica. Effects of different pertinent parameters are shown via graphs.

Numerical and sensitivity computations of three-dimensional flow and heat transfer of nanoliquid over a wedge using modified Buongiorno model

Numerical investigation of the three-dimensional flow and heat transfer of 36 nm Al2O3–H2O nanoliquid over a wedge surface is carried out by utilizing the modified Buongiorno model (MBM). The boundary layer approximation is assumed to be valid. The thermophysical properties of Al2O3–H2O nanoliquid are deliberated in the study by modeling them through the use of correlations based on experimental data. The thermal boundary layer equation comprises the Brownian motion and thermo-migration effects caused by nanoparticles. Zero mass flux boundary condition is also accounted. Optimization of the heat transfer rate of nanoliquid is made using the Response surface methodology (RSM). Two stream functions are used to derive the similarity transformations and they are employed to arrive nonlinear ordinary differential system from the governing partial differential system, and then the subsequent nonlinear problem is treated numerically using the Finite Element Method (FEM). The heat flow features are scrutinized using two-dimensional, surface, and streamline plots. The results of flow due to a moving wedge in the same direction of free stream velocity are compared with those of a moving wedge in the opposite direction of free stream velocity. The thermal layer and nanoparticles volume fraction layers are enlarged due to the chaotic movement of nanoparticles. The thermophoresis mechanism improves the thermal layer at the wedge surface. The high level of pressure gradient factor, high level of shear-to-strain rate and low level of Lewis number, were found to be the optimal operating condition that would maximize the heat transfer rate.

Multiplicity for idealized rotational detonation waves

Simulations of three-dimensional rotational detonation waves are conducted to understand the mechanisms of wave bifurcation. A compressible reacting Euler solver is developed within the framework of OpenFOAM, and a fixed mass flux boundary condition is developed to avoid complex injector dynamics. Influences of inflow mass flow rates and initiations of ignition spots are studied. As the inflow mass flow rate increases, one detonation wave is maintained. Constrained by the circumference of the combustor, the maximum fill height is achieved when the maximum post-shock pressure expansion is reached. Further increasing mass flow rates does not lead to wave bifurcation or higher mean fill height. By introducing multiple ignition regions, an identical number of stable waves are ignited and maintained, which signifies that wave numbers are not uniquely determined by the inlet boundary conditions. The minimum fill height (or largest velocity deficit) owing to either the lowest mass flow rate or the maximum wave number is obtained when the pressure expansion distance is comparable to the hydrodynamic thickness. The scaling of fill height is subsequently explained through a theoretical relation based on mass conservation. It is shown that neither increasing mass flow rates nor existence of multiple waves is a sufficient condition for wave bifurcation. The fill height is intrinsically connected with wave numbers, and both cannot be predicted solely based on boundary conditions. Future work will relax some idealizations in this work to further quantify the limit for the fill height.

Role of Cattaneo\u2013Christov heat flux in an MHD Micropolar dusty nanofluid flow with zero mass flux condition

This investigation aims to look at the thermal conductivity of dusty Micropolar nanoliquid with MHD and Cattaneo–Christov heat flux flow over an elongated sheet. The novelty of the envisioned mathematical model is augmented with the added impacts of the heat source/sink, chemical reaction with slip, convective heat, and zero mass flux boundary conditions. The salient feature of the existing problem is to discuss the whole scenario with liquid and dust phases. The graphical depiction is attained for arising pertinent parameters by using bvp4c a built-in MATLAB function. It is noticed that the thermal profile and velocity field increases for greater values of liquid particle interaction parameter in the case of the dust phase. An escalation in the thermal profile of both liquid and dust phases is noticed for the magnetic parameter. The rate of mass transfer amplifies for large estimates of the Schmidt number. The thickness of the boundary layer and the fluid velocity are decreased as the velocity slip parameter is augmented. In both dust and liquid phases, the thermal boundary layer thickness is lessened for growing estimates of thermal relaxation time. The attained results are verified when compared with a published result.

Evaporation and propagation of liquid drop streams at vacuum pressures: Experiments and modeling.

Evaporation of streams of liquid droplets in environments at vacuum pressures below the vapor pressure has not been widely studied. Here, experiments and simulations are reported that quantify the change in droplet diameter when a steady stream of ≈100 μm diameter drops is injected into a chamber initially evacuated to <10^{-8}bar. In experiments, droplets fall through the center of a 0.8 m long liquid nitrogen cooled shroud, simulating infinity radiation and vapor mass flux boundary conditions. Experimentally measured changes in drop diameters vary from ≈0 to 6 μm when the initial vapor pressure is increased from 10^{-6} to 10^{-3} bar by heating the liquid. Measured diameter changes are predicted by a model based on the Hertz-Knudsen equation. One uncertainty in the calculation is the "sticking coefficient" β. Assuming a constant β for all conditions studied here, predicted diameter changes best match measurements with β≈0.3. This value falls within the range of β reported in the literature for organic liquids. Finally, at the higher vapor pressure conditions considered here, the drop stream disperses transverse to the main flow direction. This spread is attributed to forces imparted by an absolute pressure gradient produced by the evaporating stream.

Effect of zero mass flux condition on heat and mass transfer analysis of nanofluid flow inside a cavity with magnetic field

The present paper examines steady natural convection of Buongiorno’s model nanofluid flow in a square cavity with enhanced mass flux boundary condition numerically. The impact of magnetic field, Brownian motion, radiation and thermophoresis is also considered in this analysis. The governing equations are represented in terms of stream function, temperature and concentration which are solved by utilizing finite difference method of second-order accuracy. The results are presented in the form of streamlines, temperature lines, concentration lines, local Nusselt number and Sherwood number for various values of influenced parameters, such as, Rayleigh number $$ \left( {100 \le {\text{Ra}} \le 10^{3} } \right) $$ , Magnetic parameter $$ \left( {0.1 \le {\text{M}} \le 0.5} \right) $$ , Buoyancy ratio parameter $$ \left( {0.1 \le {\text{Nr}} \le 1.0} \right) $$ , Radiation number $$ \left( {0.1 \le {\text{R}} \le 1.0} \right) $$ , Brownian motion number $$ \left( {0.1 \le {\text{Nb}} \le 0.7} \right) $$ , Thermophoresis number $$ \left( {0.1 \le {\text{Nt}} \le 1.0} \right) $$ and Lewis number $$ \left( {10 \le {\text{Le}} \le 20} \right) $$ are represented through graphs. The outcomes indicate that noticeable intensification in rate of heat transfer is perceived after suspending nanoparticles. Furthermore, increasing the values of both thermophoresis and Brownian motion parameters augments the values of Nusselt number inside the cavity.

Mixed convective nanofluid flow over a non linearly stretched Riga plate

The present article concentrates on the heat and mass transfer characteristics of a mixed convective flow of an electrically conducting nanofluid past a slender Riga plate in the presence of viscous dissipation and chemical reaction. The heat and mass transfer characteristics are analyzed by a zero nanoparticle mass flux and convective boundary conditions. The thermophoretic and Brownian aspects for nanoliquid are proposed using Buongiorno's relations. The similarity quantities are utilized to obtain dimensionless forms of flow field equations. The resulting coupled nonlinear equations associated with the constituted boundary assumptions analytically proceed via optimal homotopy analysis method (OHAM). Various parameters causing the change in distributions of velocity, temperature, and concentration are graphically explained with relevant physical references. One of the important observations of the present study is, for higher values of modified Hartmann number the velocity profile increases and temperature profile supreses and it is interesting to note that the contemporary numerical simulations offer confirmable accuracy in the existing literature, which authenticates the novelty of current investigation.

Microorganisms time-mixed convection nanofluid flow by the stagnation domain of an impulsively rotating sphere due to Newtonian heating

The present article delineates a numerical analysis of buoyancy-driven nanofluid flow of gyrotactic time-mixed bioconvection heat transfer in stagnation domain of an impulsively revolving sphere due to convective boundary condition. Zero mass flux boundary condition has been merged to gain physically realistic computations. Nanofluid has been expressed in terms of the impacts of Brownian movement and thermophoresis. The given system of partial differential equations depicting the flow are mutated into a dimensionless formulas. The solution methodology involved for the constituted equations is followed by implementing an implicit finite difference approach. The acquired computations are given in terms of surface shear stress, rate of heat transfer, the density rate number of the motile microorganisms, velocity, temperature, concentration and density of motile microorganisms fluctuations. Due to gained outcomes the rotation λ and time ξ parameters have a strong impact on the flow, heat and density of motile microorganisms transfer rates, λ and time lead to strengthen all of F″(ξ,0),-θ′(ξ,0) and -N′(ξ,0). Parameters, like rotation and mixed convection exert a vigor aspect on nanofluid velocity, temperature and microorganisms density and their fluctuations rate. The surface shear stress F″(ξ,0) is mightily influenced by magnetic field parameter M. Besides, comparison amid the earlier published data and the present numerical computations are evaluated for the limiting cases, which are noticed to be in an excellent agreement.

Zero mass flux and convection boundary condition effects on Carreau-Yasuda fluid flow over a heated plat

A mathematical study is analyzed to explore the impact of zero normal flux condition on boundary layer flow of Carreau-Yasuda nanofluid flow over a heated surface. In this case the mean flow does not give the analytical solution of the Navier-Stocks, temperature, and concentration equations, hence for high Reynold's number the flow of boundary-layer can be determined by non-similarity transformations. The converted boundary-layer equations along with appropriate boundary conditions are then solved numerically. The solution of the modelled differential equations is calculated by utilizing moderate and well-known numerical technique namely BVP4C method. Carreau-Yasuda fluid model is employed to explore the characteristics of shear thinning and thickening fluids. It is generalized form of Carreau-Yasuda fluid which is applicable for having small and infinite shear rates.

Numerical investigation of induced magnetic field and variable mass diffusivity on double stratified Jeffrey fluid flow with heat and mass flux boundary conditions

AbstractThe investigation explores the influence of the induced magnetic field and variable mass diffusivity on an unsteady incompressible mixed convective double stratified and chemically reactive flow of Jeffrey fluid through a porous medium with heat, and mass flux boundary conditions. The system of flow field nonlinear partial differential equations is reduced into coupled nondimensional ordinary differential equations using appropriate similar variables, then worked out a numerical solution via shooting technique along with Rung‐Kutta fourth‐order scheme. The results are analyzed for various physical flows, heat and mass transfers, induced magnetic field, and skin friction against disparate prominent parameters via graphs and tables. It is recognized that the temperate of the fluid is enhanced with thermal stratification; however, the concentration of the fluid is decreased with magnetic Reynold's number. The comparison of numerical values of skin friction with the existing literature for limiting sense.

Demonstrating a High‐Resolution Gulf of Alaska Ocean Circulation Model Forced Across the Coastal Interface by High‐Resolution Terrestrial Hydrological Models

AbstractWe demonstrate a linking of moderately high resolution (1 km) terrestrial hydrological models to a 3‐D ocean circulation model having similar resolution in the northern Gulf of Alaska, where a distributed line source of freshwater runoff exerts strong influence over the shelf's hydrographic structure and flow dynamics. The model interfacing is accomplished via mass flux boundary conditions through the ocean model coastal wall at all land‐ocean adjoining grid cells. Despite the high runoff volume and lack of a coastal mixing estuary, the implementation maintains numerical stability by prescribing depth invariant and surface‐intensified inflows at fast and slow discharge grid cells, respectively. Based on comparisons against in situ hydrographic data, the coastal sidewall mass flux boundary condition results in more realistic hindcast surface salinity and salinity gradient fields than models that distribute coastal runoff in the form of spatially distributed precipitation. Correlations with observed thermal and haline monthly anomalies reveal statistically significant hindcast temporal variability during the freshet season when the signal‐to‐noise ratio is large. Comparisons of ocean models forced by high‐ and low‐resolution hydrological models reveal differences in salinity, surface elevation, and velocity fields, highlighting the value and importance of accurate coastal runoff fields. The model results improve our understanding of the regional influence of runoff on sea level elevations and the distribution and fate of fresh water. Our approach has potential applications to biogeochemical modeling in regions where distributed line source freshwater coastal discharges deliver heat, momentum, and chemical constituents that may influence the marine carbon pump.

GFEM analysis of MHD nanofluid flow toward a power‐law stretching sheet in the presence of thermodiffusive effect along with regression investigation

AbstractIn the current study, we use Galerkin finite‐element simulation to analyze the concept of triple diffusive flow with magnetic field effect toward a power law stretching sheet. The fluid comprises dissolved solutal particles and nanoparticles in the base fluid. The three important mechanisms that are responsible for rise in phenomenon of convective transportation are diffusophoresis, thermophoresis along with Brownian motion have been considered. Recently, the proposed nanoparticles' mass flux and heat flux boundary conditions have been imposed. Nanoparticle mass transportation, solutal mass transportation with heat transportation for prominent physical parameters, such as stretching parameter, magnetic influence parameter, thermophoresis parameter, and Brownian motion parameter are calculated. To further verify and understand the strength of the relationship between heat transportation rate and controlling parameters, the multiple regression process is used. The finite difference approach was adopted to numerically solve the nonlinear governing equations and the linked boundary conditions. In the present study, we used MATLAB software for finding the final outcomes and relating the concluding results for with extant outcomes in the literature as a limiting case in the absence of the magnetic intensity parameter and an excellent agreement was noted. It was observed that the magnetic field has a positive effect on heat and mass transfer. This study also helps in understanding and thus controlling the velocity of the flow along with solutal depositions, which has a significant engineering application in the process of extrusion. The findings of the present study help to control the rate of heat and mass transfer, aiding manufacturing companies in obtaining the desired quality of product.