Convective Boundary Condition Research Articles

A numerical study of the nanofluid flow over an exponentially stretching surface with Navier slip condition following Corcione model

The size of nanoparticles influences the viscosity and thermal conductivity of a nanofluid flow. In this exploration, the impacts of the dynamic viscosity and thermal conductivity of the Corcione model on the magneto-hydrodynamics (MHD) Cu-water nanofluid flow over an exponentially stretched surface are examined. It is pertinent to mention that the whole scenario is done at 300[Formula: see text]K and the freezing temperatures of 273.15[Formula: see text]K with a particle size of 25[Formula: see text]nm. The Navier slip and convective boundary conditions are assumed at the surface. A homogeneous single-phase model is adopted to formulate the problem. Nonlinear, coupled momentum, and energy balance nondimensionalized ordinary differential equations (ODEs) are constructed with suitable transformations. To solve these ODEs numerically, a renowned bvp4c technique of MATLAB software is employed. The effects of the arising parameters are represented graphically and numerically and are depicted in tables and graphs. It is witnessed that the velocity of the copper-water nanofluid declined with larger estimations of the volume fraction of nanoparticles, although the temperature distribution showed the reverse tendency. Moreover, at the surface for higher values of the slip parameter, the velocity profile reduces and the temperature of the fluid augments for higher values of the Biot number. The validation of the model is also executed by comparing it with the published result in the limiting case. An outstanding correlation is attained.

Dual solutions of radiative Ag-MoS_2/water hybrid nanofluid flow with variable viscosity and variable thermal conductivity along an exponentially shrinking permeable Riga surface: Stability and entropy generation analysis

ABSTRACT In this analysis, the Silver-Molybdenum disulfide ()/water hybrid nanofluid flow past a permeable exponentially shrinking Riga surface with thermal radiant energy is considered. The novelty of this work is to find out the effects of variable viscosity, variable thermal conductivity with hybrid nanofluid’s slip velocity, and convective thermal boundary conditions over a shrinking Riga surface on velocity, temperature, skin-friction coefficient, Nusselt number, and entropy generation. The MATLAB programming platform with a fourth-order method to solve boundary value problem (bvp4c) was employed to get a good account of all pertinent flow parameters before solving the controlling partial differential equations numerically. Here of Silver () and of Molybdenum disulfide () nanoparticles in the hybrid model are considered in the base fluid water. The basic achievement of this analysis is to explore the Nusselt number, skin friction coefficient along with entropy formation, and Bejan number. The irreversibility factor is calculated using the thermodynamics second law. The findings also point to the presence of dual-nature solutions in the shrinking sheet region for a given value of a high mass suction parameter, with a stable upper solution branch and unstable lower solution branch. Two solutions are found for the limited range of shrinking parameter when and the solutions terminate at in the shrinking region. Additionally, the first solution generates a positive minimum eigenvalue (), whereas the second solution generates a negative eigenvalue (), indicating the solution’s stability. Nusselt number is enhanced for variable viscosity parameter but diminished by variable thermal conductivity parameter for the stable solution. The entropy generation and the Bejan number both increase significantly with the increment of the thermal radiant-energy parameter, Biot number, and Eckert number. These results are crucial in the long term because they allow us to optimize heat transmission for cooling and heating applications. Hence, this investigation is incredibly significant in the present era, particularly in the automotive industry, home industry, paper plastics, ceramics, food packaging, food colorants, cancer treatment, cosmetics, pharmaceuticals, fabrics, paints, and soaps as well.

Entropy generation and thermal analyses of a Cross fluid flow through an inclined microchannel with non‐linear mixed convection

AbstractThe temperature difference of the various applications such as microchannel heat exchangers, microelectronics, solar collectors, automotive systems, micro fuel cells, and microelectromechanical systems (MEMS) is relatively large. The buoyancy force (mixed convection) modeled by the conventional Boussinesq approximation is inadequate since the density of the operating fluids fluctuates non‐linearly with the temperature difference. Therefore, the mixed non‐linear convective transport of the flow of Cross fluid through three different geometric aspects (horizontal, vertical, and inclined) of the microchannel under the non‐linear Boussinesq (NBA) approximation is investigated. Mechanisms of internal heat source, Rosseland radiative heat flux, and frictional heating are incorporated into the thermal analysis. The mathematical construction is proposed using the Cross fluid model for a steady‐state, and subsequent non‐linear differential equations are deciphered by the spectral quasi‐linearization method (SQLM). Graphical sketches were constructed and displayed that explore the stimulus of various key parameters on Bejan number, velocity, temperature, and entropy generation. It is found that the Bejan number and entropy production improved due to the non‐linear density temperature variation. The convective heating boundary conditions augment the entropy production. The pressure gradient accelerates the transport of fluid in a microchannel. Furthermore, among three different geometries, the velocity, entropy production, and temperature are the highest for the vertical microchannel.

Insights into stretching ratio and velocity slip on MHD rotating flow of Maxwell nanofluid over a stretching sheet: Semi-analytical technique OHAM

Main core part of the research is to develop a novel mathematical model of MHD-Maxwell nanofluid over a stretching and shrinking surface. The stretching ratio, velocity slip and convective boundary conditions are also incorporated. The PDE's with associative boundary conditions are deduced into coupled highly non-linear ODE's by utilizing suitable transformations. The deduced dimensionless sets of Ordinary differential equations are solved by Optimal-Homotopy Analysis Method (OHAM). Behavior of pertinent parameters on the velocity, temperature and concentration fields as well as important aspects skin friction, Nusselt number and Sherwood number are recorded in Table 2. Outcomes declared that role of stretching ratio plays a prominent role in stretching surfaces its clearly recorded in Table 1(a & b).

Heat Transfer Analysis of Silver-water Nanofluid Flow over Stretching Cylinder Subjected to Multiple Convective Conditions over Stretching Sheet and Stretching Cylinder

Tiny particles are essential in electronics, heat exchangers, nanotechnology, and materials science because of their exceptional thermal conductivity and unique properties. The study investigate the MHD flow over a stretching cylinder containing silver-water nanofluid in the presence of a magnetic field under multiple convective boundary conditions over stretching sheet and stretching cylinder. A system of PDEs is reduced to a solvable system of ODEs by applying a suitable similarity transformation. We employ the Runga Kutta method along with shooting procedure to solve the flow, heat, and mass transfer equations along with boundary conditions. The results obtained from MATLAB codes are compared with previously published results of the same nature in limiting case. In this model, we made a comparison between the stretching cylinder and a flat sheet and those are represented via graphically. Numerical results of skin-friction coefficient and local Nusselt are systematized in the form of tables for sheet and stretching cylinder. The plots illustrate the effect of different dimensionless parameters on velocity, temperature, and concentration profiles. Significant role of Biot number on temperature and concentration profile was observed. Nusselt number increases with Bi and Pr but decreases with M. The skin friction is enhanced with M but decrease with \(\lambda\)

Entropy Generation of Cu–Al2O3/Water Flow with Convective Boundary Conditions through a Porous Stretching Sheet with Slip Effect, Joule Heating and Chemical Reaction

Currently, the efficiency of heat exchange is not only determined by enhancements in the rate of heat transfer but also by economic and accompanying considerations. Responding to this demand, many scientists have been involved in improving heat transfer performance, which is referred to as heat transfer enhancement, augmentation, or intensification. This study deals with the influence on hybrid Cu–Al2CO3/water nanofluidic flows on a porous stretched sheet of velocity slip, convective boundary conditions, Joule heating, and chemical reactions using an adapted Tiwari–Das model. Nonlinear fundamental equations such as continuity, momentum, energy, and concentration are transmuted into a non-dimensional ordinary nonlinear differential equation by similarity transformations. Numerical calculations are performed using HAM and the outcomes are traced on graphs such as velocity, temperature, and concentration. Temperature and concentration profiles are elevated as porosity is increased, whereas velocity is decreased. The Biot number increases the temperature profile. The rate of entropy is enhanced as the Brinkman number is raised. A decrease in the velocity is seen as the slip increases.

Significance of thermal conductivity and heat transfer mechanism through copper nanofluid with convective condition via heated Riga plate

This study investigates the heat and mass transfer of magnetohydrodynamic nanofluids via the Riga plate subjected to convective boundary conditions, including the thermal radiation parameter. Utilizing variable thermal conductivity and mixed convection effects, the heat transfer process is investigated. The peculiarity of the flow model enables us to investigate the importance of thermophoresis and Brownian motion to the kinetics of Newtonian fluids. The governing partial differential equations are converted into non-dimensional ordinary differential equations using proper similarity transformations and numerically solved using bvp4c in Matlab. The graphs explore the effects of pertinent parameters on the transference of heat, mass and velocity profiles. As the Biot number [Formula: see text] increases, so does the thermal boundary layer. The Nusselt number intensifies with radiation parameter but decreases with intensifying magnetic field parameter [Formula: see text], Eckert number [Formula: see text] and Brownian motion parameter [Formula: see text]. The influence of several physical quantities is illustrated and displayed through graphs and tables. Furthermore, it is observed that the thickness of the temperature profile is increased by combining the Biot number, the thermal radiation parameter, the thermal conductivity parameter and the modified Hartmann number.

Buongiorno Modelled Nanoliquid Consequence of Thermal and Solutal Convection on the Magneto-Micropolar Fluid Inside an Inclined Porous Stretching Device

The objective of the present work is to investigate the chemically reacting micropolar nanofluid flow past an inclined permeable stretching sheet. The flow is exposed in the magnetic and thermally radiative environment and convective boundary conditions are taken into consideration to form the complete description of the flow model. The appropriate similarity invariants are used to obtain the system of the non-linear ordinary differential equation. The well-known Runge-Kutta fourth-order method is worked out with a shooting technique for numerical investigation. The behavior of fluid motion, temperature, concentration, and engineering quantities for arising physical parameters is sketched through graphs and discussed in detail. The tabular comparison is used to provide the validation of current work. Outputs demonstrate flow decrement, which is due to the produced Lorentz force that itself is the result of the enhancement in magnetic parameter and inclination of angle, and rise in the profiles of porosity index. The fluid temperature exceeds in conjunction with the accumulation of radiative heat, dissipation heat, as well as thermophoresis and Brownian motion. Physical engineering supporting forces like Skin friction and heat transfer rates are favorable for magnetic and material parameters but the mass transfer rate exhibits an opposite response.

Exploration of Radiative and Dissipative Heat on Williamson Nanofluid Flow in Conjunction with Convective Boundary Condition

Nanofluid has a wide range of uses in various fluid systems, because of its excellent growth in thermal conductivity. The current paper explores the transfer of heat and mass process in MHD nanofluid flow across a stretching sheet, considering the collective impacts of nonlinear thermal radiation, Joule heating, and binary chemical reactions with convective boundary conditions for Williamson nanofluid. The necessary transformations are carried out to alter the controlling PDE’s into a collection of linked ODE’s. The shooting approach, in conjunction with the fourth-order Runge–Kutta method, is employed to get solutions to highly nonlinear ODE’s. The impact of varied main factors on velocity, temperature, concentration, for Weissenberg number, Biot number along with other parameters are depicted graphically, whilst the change in the rate of heat and mass transfer is investigated via numerical data in tabular form. The acquired numerical data show that expanding the Eckert number diminishes the rate of mass transfer whereas expanding the thermal radiation parameter, expandsthe rate of heatand rate of mass transfer.

On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations

We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the hydrodynamic limit of some simple exclusion jump process. We show that the scheme admits a unique discrete solution, that the natural bounds on the solution are preserved, and that it encodes the second principle of thermodynamics in the sense that some free energy is dissipated along time. The convergence of the scheme is then rigorously established thanks to compactness arguments. Numerical simulations are finally provided, highlighting the overall good behavior of the scheme.

Buoyancy flow of nanohybrid fluid over a rotating sphere imperiled to convective and viscous heating

The thermal radiation and convective condition principles were working on specific functions like gas turbines, electrical fuel, renewable energy, projectiles, nuclear power plants, aerospace engineering, and thermal transportation. Considering the aforementioned functions, the present analysis inspected the stagnation point hybrid nanofluids movement over the rotating sphere on the behavior of viscous dissipation and thermal radiation. Silver and Ferrous nanoparticles including the host fluid water were held into affected the flow. The presence of convective boundary conditions is incorporated within the system. Applying appropriate correspondence factors, nonlinear governing equations were transformed with ordinary differential equations. This finite element method is applied to find the mathematical solutions to the boundary conditions and simplified equations. These outcomes convey to temperature was decreased about accelerated factor, although primary velocity was found into increased. The heat transfer was magnified by thermal Biot number, and that rate of development was greater about hybrid nanosuspension. The heat transport method was reduced by the Eckert number; also that reduction rate was similarly dull on hybrid.

Experimental and numerical analysis of transient thermal stresses on thick-walled cylinder

Thermal loading can be a significant source of stress, especially on pipelines, ducts, pressure vessels, and heat exchangers widely used in industry. Analytical and numerical studies of thermal stresses resulting from transient loads are restricted to simple geometries and simplified boundary conditions. Therefore, experimental data to confront these models are a necessity, particularly when analytical solutions are not available. This study aims at providing a mathematical model based on finite difference method to predict transient thermal stresses across a cylinder. To validate the model, experiments with strain gauges on the outer surface of a thick-walled cylinder were performed in a rig with controlled convective boundary conditions. Additionally, a numerical model based on Finite Element Method (FEM) was adjusted to reproduce the experimental and modeling results. Thermal stress evaluation occurs with temperature differences between the heat sink and source up to 70 °C, typical processing conditions of the oil and gas industry. Stresses are significant particularly during the startup and interruption of the production process. Peak thermal stress scales with mechanical stresses created by pressure difference of about 1050 bar. The agreement between experimental, finite difference method and numerical results paves the way to assess thermal processing equipment with complex geometry and boundary conditions.

Soret and Dufour aspect of viscoelastic fluid due to moving cylinder with viscous dissipation and convective boundary conditions

Owing to contribution of thermo-diffusion phenomenon in various engineering and industrial frame works, scientists have presented some exclusive investigations on this topic. In current research, the thermos-diffusion prospective of second grade material accounted by a moving cylinder have been predicted. The applications of Soret and Dufour effects based on the thermos-diffusion phenomenon is evaluated. The magnetic force and viscous dissipation effects are presented for the current flow model. Additionally, the improvement in thermal transport of viscoelastic fluid is suggested with radiative phenomenon. The convective boundary constraints are used to report the thermos-diffusion phenomenon. The system based on dimensionless form is obtained with interaction of new variables. The shooting technique is used for numerical observations by using MATLAB software. The physical impact of phenomenon in view of parameters is graphically attributed. It has been noted that increasing velocity profile is results due to curvature parameter and viscoelastic parameter. The enhancement in thermal profile is noted due to Dufour number and Eckert number.

Coupling characteristics and simplification analysis method of laminated cooling configuration between external and internal cooling

This study presents a method to decouple the cooling process of laminated cooling configuration and analyze the coupling characteristics between internal and external cooling. Based on it, two simplification methods of external cooling are developed to predict the coupled cooling performance and its distribution. Employing verified numerical method, five series of cooling process simulations are conducted under different blowing ratios. Results show that, the similar vortices structure among coupled, internal, and external cooling demonstrate that the decoupled method can effectively decouple the internal and external cooling and keep the same flow pattern. In laminated cooling, internal cooling contributes most of cooling performance and heat transfer capacity, and external cooling mainly influences the distribution characteristics due to its intensively regional cooling performance. While coupled cooling presents superposition characteristics of internal and external cooling, they will counteract about 17.88% cooling performance. The almost same local and overall cooling effectiveness and distribution under different blowing ratios demonstrate that simplifying external cooling to convective boundary condition and replacing with external cooling correlation formulas can effectively capture cooling performance and heat transfer characteristics with an average error of 12.91%. Further, the presented prediction formula can effectively predict area-averaged cooling effectiveness with maximum deviation of 8.8%.

Three dimensional nanofluid motion with convective boundary condition in presents of nonlinear thermal radiation via stretching sheet

In present work activation energy on 3D (“Three-Dimensional”) nanofluid (NFs) motion via stretching surface (SS) with slip condition: a statistical study. The slip velocity defined for NFs model are reduction in governing PDE’s were converted into a set of non-linear ODE’s by help of similarity transformations. Present Statistical model is taken three different systems: in which the statistical results are computed via R-K-F (“Range-Kutta-Fehlberg”) algorithm and tested these solutions with help of shooting technique and improved bvp 4th order analysis. Graphical comparisons and statistical (“Numerical”) tables are created to validation results for three different techniques. The emerging physical parameters on velocity (“axial and transverse directions”), θ(η) (“Temperature”) and φ(η) (“Concentration”). We found that, the θ(η) is more impact in NFs motion for enlarge statistical values of various physical parameters. Further, we compared statistical results of present study with previous results in up to six decimal places.

Significance of radiant-energy and multiple slips on magnetohydrodynamic flow of single-walled carbon nanotube-water, titanium dioxide–water, multiwalled carbon nanotube–water, graphene oxide–water nanofluids

The magnetohydrodynamic flow of nanofluid is studied in the present analysis by using two parallel, rotating, and stretchable disks with a porous medium. The thermal radiation effects along with velocity slips at the interface of fluid and disk are considered in this work. The water is taken as base fluid, and carbon nanotubes (CNTs), titanium dioxide (TiO[Formula: see text]), and graphene oxide (GO) are taken as nanoparticles. The corresponding equations are modeled in terms of partial differential equations and Von Karman similarity transformation approach is adopted. The resulting equations are solved by using a finite difference method-based ND Solver. The axial, radial, and tangential velocity profiles and temperature distribution are discussed with graphs and tables. Thermal radiation and convective boundary conditions are used in the heat transfer process. When the thermal Biot number of the lower disk rises, fluid temperature enhances, whereas, the fluid temperature falls with the rise in the thermal Biot number of the lower disk. It is observed that when the thermal Biot number of lower disk rises from 0.5 to 0.8, heat transfer at lower disk is increased by about 6.66% in hexagonal-shaped CNTs-based nanofluid and 6.66% in spherical shaped TiO[Formula: see text] and GO-based nanofluid. The impact of physical parameters such as skin friction coefficient and Nusselt number are computed for governing parameters and discussed in detail.

Activation energy on three-dimensional Casson nanofluid motion via stretching sheet: Implementation of Buongiorno’s model

In this work, the statistical (“Numerical”) modelling of activation energy and chemical reaction on non-Newtonian liquid motion via stretching sheet (SS) were performed, analysed statistically, employing the shooting technique. The convective boundary conditions are considered on Casson liquid (“non-Newtonian”) motion with couple stress SS. The behaviour of thermophoresis diffusion and Brownian motion via a special effect of non-linear thermal radiation are assuming in temperature equation for liquid motion. This analysis highly governing nonlinear system of D. Es of velocity, temperature, concentration and activation are simulated via iterative scheme encoded with MATLAB programming language. The geometric model is described bvp 4th order of R-K-F (“Range-Kutta-Fehlberg”) scheme. We found that, 35% of heat transfer rate produces in motion of couple stress Casson nanofluid and the activation energy released 28% of mass transfer rate at stretching surface. A comparative result of linear and nonlinear SS presented via various dimensionless parameters on graphs and tables.

Thermal efficiency appraisal of hybrid nanocomposite flow over an inclined rotating disk exposed to solar radiation with Arrhenius activation energy

The energy crisis forced the world to look for alternate energy solutions. Amongst these, solar energy is the first choice of scientists that convert solar radiation into heat or electricity to meet the energy deficit. Despite its marginally high installation cost, this renewable energy solution is long-lasting with minimum operating cost. Heading in the same direction, the attributes of the solar radiation towards the heat transfer rate of hybrid nanocomposite comprising paraffin wax amalgamated with copper-oxide, and cobalt-oxide (CuO-Co3O4) nanocomposites and thin-film spraying over an inclined rotating disk are discussed. The nanocomposites are considered in varied shapes. The model is supported by the Arrhenius activation energy in the concentration equation and the convective boundary condition at the surface. The model assumptions are translated into the system of partial differential equations which are then converted into differential equations with apposite similarity transformations. The numerical solution of the transformed system is obtained by the Keller box method. The obtained results are analyzed graphically. The maximum heat transfer rate is witnessed in the case of spherical-shaped particles. Furthermore, the hybrid nanocomposite fluid velocity is augmented when the width of the film is improved.

Three-dimensional rotating viscous flow past a permeable stretching/shrinking sheet with convective boundary condition

The study of three-dimensional rotating boundary layer flow approaching a stretching or shrinking surface under convective boundary conditions is presented in this paper. This study expands the scope of previous researchers' work to encompass broader scenarios, including situations involving mass transfer (suction) on the wall, the Biot number and cases featuring a shrinking surface. It is found that the increase of suction and rotating parameters leads to a noticeable rise in both the local skin friction coefficients and the local Nusselt number, and the solutions to the governing ordinary differential equations exhibit a dual-branch nature, comprising both upper and lower branch solutions, within a specific range of the governing parameters.

Exploring dual solutions and thermal conductivity in hybrid nanofluids: a comparative study of Xue and Hamilton-Crosser models.

Hybrid nanofluids show great potential for heat transport applications such as solar thermal systems, car cooling systems, heat sinks, and thermal energy storage. They possess better thermal stability and properties compared to standard nanofluids. In this study, a base fluid, methanol, is injected into an electrically conducting heat-generating/absorbing disk of permeable boundary, and dual solutions are obtained. Two alternative models, Xue and Hamilton-Crosser are considered, and their thermal conductivities are contrasted. Furthermore, thermal radiation and ohmic heating are also considered, and convective boundary conditions are utilized to simulate overall heat gains or losses resulting from conduction, forced or natural convection between nearby objects of nearly constant temperature. Using a similarity transform, the governing equations are obtained and numerically solved via bvp4c, a finite difference method. It is observed that the presence of a magnetic field and the shrinking of the disk elevate the energy transport rate and wall stress. Additionally, the skin friction coefficient and thermal distribution rate increase with wall transmission constraint while fluid flow and energy transport diminish. Furthermore, particle clustering and nano-layer creation suggest that the Hamilton-Crosser model exhibits better thermal conductivity than the Xue model.