Convective Boundary Condition Research Articles

MHD radiative Gr-Ag-TiO2/H2O ternary hybrid nanofluid flow upon a permeable movable wedge with irreversibility analysis

ABSTRACT The mass-based ternary hybrid nanofluid model is applied for the magnetohydrodynamic (MHD) flow over a moving wedge with wall permeability, thermal radiation, and convective boundary condition. The masses of the nanoparticles and the base fluid are considered instead of the volumetric concentration of the first, the second, and the third nanoparticles. In the base fluid of water, three types of nanoparticles such as titania, silver, and graphene have been embedded. A similarity method is used to reduce variables and also to turn prominent equations of ternary hybrid nanofluid flow into a simplified form. The shooting technique with the Runge-Kutta-Felhberg method has been used to numerically solve the converted boundary layer equations. The largest Nusselt number is related to the ternary hybrid nanofluid, in which a heat transfer enhancement of 6.55% has been obtained in comparison with regular fluid. The Nusselt number for five shapes of the third nanoparticles is obtained (when both the first and second nanoparticles are spherical), and when the third nanoparticle has the shape of the disk, the most heat transfer has occurred. The highest entropy generation is related to the stagnation point case (m = 1) and the lowest belongs t the downhill case (m = –0.0825).

Thermal Boundary Layer over a Vertical Plate in Porous Medium with a Convective Surface Boundary Condition

Thermal Boundary Layer over a Vertical Plate in Porous Medium with a Convective Surface Boundary Condition

Thermal Spreading/Constriction From an Isothermal Source Into a Multilayer Orthotropic Semi-Infinite Flux Tube

Abstract Thermal spreading and constriction have been widely studied due to relevance in heat transfer across interfaces with imperfect contact and problems such as microelectronics thermal management. Much of the past work in this field addresses an isoflux source, with relatively lesser work on the isothermal source problem, which is of much relevance to heat transfer across rough interfaces. This work presents an analytical solution for thermal spreading/constriction resistance that governs heat flow from an isothermal source into a multilayer orthotropic semi-infinite flux tube. The mixed boundary condition due to the isothermal source is accounted for by writing a convective boundary condition with an appropriately chosen spatially-varying Biot number. A series solution for the temperature field is derived, along with a set of linear algebraic equations for the series coefficients. An expression for the nondimensional thermal spreading resistance is derived for Cartesian and cylindrical problems. It is shown that, depending on the values of various nondimensional parameters, heat transfer in either the thin film or the flux tube may dominate and govern the overall thermal spreading resistance. Results for a single-layered isotropic flux tube are derived as a special case of the general result, for which, good agreement with past work is demonstrated. An easy-to-use polynomial fit for this special case is presented. This work contributes a novel technique for solving mixed boundary problems involving an isothermal source, and may also help solve practical problems related to interfacial heat transfre and thermal management.

A numerical framework of magneto Williamson hybrid nanofluid over porous sheet; a classical keller box analysis

The current study intends to talk about the unsteady Williamson hybrid nanofluid flow with heat transport across a stretching surface comprising the magnetic hydrodynamic, thermal radiative, suction/injection, and convective boundary condition effects respectively. The study focused on the hybrid Williamson nanofluid, comprising of an EG ethylene glycol (C2H6O2) and two types of nano-solid particles, c zinc oxide and molybdenum disulphide ZnO-MOS2. To accomplish this goal, the modelled expressions are transmitted into dimensionless ODE by making use of several highly established transformations. The aim of the numerical result of the current exploration is studied through Keller Box Analysis (KBA). Tabular data and statistical bar plots are used to compare this strategy. The impact of physical variables such as Magnetic field parameter γ, Williamson fluid variable We, Porous media β, Thermal radiation Rd, Biot number Bi and Prandtl number Pr are analyzed through plots and tables. An augmentation in the strength of the magnetic field and Williamson fluid parameter results in a reduction in velocity. However, a temperature rise is observed for higher values of the Williamson fluid parameter and magnetic parameters. The surface friction drag is diminished by the Forchheimer and Weissenberg values. The rate of mass transfer is strongly positively correlated with both the Schmidt number and chemical reaction. The present study has a remarkable agreement with the results that were previously published, which confirms the application and validation of the Keller-Box scheme.

Pool Fires Within a Large Under-Ventilated Environment: Experimental Analysis and Numerical Simulation Using OpenFOAM

Experimental analyses and numerical simulations are carried out on a test case involving an heptane pool fire within a large under-ventilated environment. During the experiments, the temperature history at several locations within the room is monitored by means of thermocouples, and the fire radiative heat transfer estimated through a plate thermocouple. The experimental layout is then replicated numerically and tested using OpenFOAM CFD code. The study is a preliminary analysis performed for code validation purposes on a full-scale fire scenario. The results of the simulations are compared to the experimental results and critically analysed, finding a reasonable agreement overall. Critical issues in fire modelling are also highlighted. In fact, due to the problem complexity and the limitations of the numerical models available some important aspect that can significantly influence the outcome of the simulations must be calibrated a posteriori, somewhat limiting the general predictive applicability of the fire models. Primarily, these are the heat release rate history, the combustion efficiency, and, to a lesser extent, the convective heat transfer boundary condition at the wall.

Time-dependent Darcy–Forchheimer flow of Casson hybrid nanofluid comprising the CNTs through a Riga plate with nonlinear thermal radiation and viscous dissipation

Abstract Carbon nanotubes (CNTs) are gaining popularity due to their expanding uses in industrial and technical processes, such as geothermal reservoirs, water and air filters, coatings, solar collection, ceramic material reinforcement, electrostatic dissipation, etc. In addition, the CNTs have superior electrical conductivity and biocompatibility. Based on the aforementioned applications, the current work examines the time-dependent and Darcy–Forchheimer flow of water/glycerin-based Casson hybrid nanofluid formed by single-walled CNTs and multi-walled CNTs over a Riga plate under velocity slip. The energy expression is modeled through nonlinear thermal radiation and viscous dissipation impacts. The incorporation of convective boundary condition into the current model improves its realism. By employing suitable variables, the governing models are re-framed into ordinary differential equations. The bvp4c and the homotopy analysis method are used to find the computational results of the re-framed equations and boundary conditions. The novel characteristics of a variety of physical parameters on velocity, temperature, skin friction coefficient (SFC), and local Nusselt number (LNN) are discussed via graphs, charts, and tables. It is found that the fluid velocity decays when enriching the Forchheimer number, unsteady and porosity parameters. The radiation parameter plays an opposite role in convective heating and cooling cases. The modified Hartmann number enhances the surface drag force, and the Forchheimer number declines the SFC. The unsteady parameter develops the heat transfer rate, and the Forchheimer number suppresses the LNN. The simulated flow problem has many applications in engineering sectors, including ceramic manufacture, heating and cooling systems, energy storage units, thermodynamic processes, and other fields.

Influence of boundary conditions on non-equilibrium heat transport under ultrafast laser action based on the lattice Boltzmann method

Based on the lattice Boltzmann method, this paper simulated the non-equilibrium heat transfer process in nano-silicon thin film under ultrafast laser irradiation. The influence of boundary conditions on heat transport was investigated. Results show that under rebound and diffuse boundary conditions, the energy distribution within the film is non-uniform due to interface effects. However, the specular boundary condition is equivalent to eliminating the interface, resulting in a smooth energy distribution. Under convective boundary conditions, the thermal wave phenomenon disappears owing to the open interface. When the energy tends to be stable, the energy density under convective boundary conditions is reduced to 50% of that under adiabatic boundary conditions. As the film size decreases, the differences between boundary conditions become more significant. Particularly when the film size is smaller than the phonon mean free path, the influence of boundary conditions cannot be neglected. Therefore, boundary conditions and size effects are important for the design of nanodevices. Furthermore, compared with the results obtained by the Cattaneo-Vernotte model, it is found that at smaller Knudsen numbers, the Cattaneo-Vernotte model has a better match with the lattice Boltzmann method.

Study of the Carreau fluid over a linearly curved stretching sheet: A numerical approach

Carreau fluid flow over a linearly curved stretching surface has significant applications in manufacturing industries. This study focuses on the impact of various parameters on the velocity, temperature, pressure skin friction, and heat transfer coefficient of a 2D Carreau flow. Both shear thinning (pseudoplastic) and shear thickening (dilatant) behaviors are considered. The parameters include suction, non-dimensional radius of curvature, Weissenberg number, magnetic parameter, power-law index, Eckert number (viscous dissipation parameter), and Prandtl number. The effects of viscous dissipation, magnetic field, convective boundary conditions, and suction are also taken into account. The study reveals that the flow velocity decreases with increasing magnetic parameter, curvature factor, and suction, but increases with the Weissenberg number and power law index. The heat transfer rate is reduced by the curvature factor, Weissenberg number, suction, power-law index, and Prandtl number, while the magnetic parameter has the opposite effect. The boundary value problem is simplified through appropriate similarity transformation and solved numerically using the shooting method and Matlab’s built-in function bvp4c. The results obtained from these two methods show good agreement. The findings also align well with existing literature in some limiting cases, confirming the validity of the study.

Analytical solutions of triple‐diffusive magnetohydrodynamic fluid flowing through a stretching/shrinking sheet

AbstractThe aim of this article is to investigate the dual nature solutions of the triple diffusive magnetohydrodynamic flow due to stretching/shrinking surfaces. The system of nonlinear partial differential equations is transformed into nonlinear ordinary differential equations with the help of compatible transforms. Analytical dual solutions are obtained for every unknown velocity, temperature, and concentration profile in terms of known physical parameters. Heat and mass transfer analyses have been carried out in the presence of convective boundary conditions. The graphic interpretation of the possible dual solutions of dimensionless velocity, temperature, concentration, skin‐friction coefficient, and Nusselt and Sherwood numbers is analyzed under the influence of different known physical parameters. The obtained results are validated against previously published results for a special case of the problem.

Irreversibility scrutiny of SWCNT and MWCNT nanofluid convective flow using Darcy-Forchheimer rule in an upright microchannel with variable thermal conductivity and Brownian motion and thermophoresis

Carbon nanotubes are used to attain greater thermal transfer rates in a various of enormous applications in the field of microsystem, emission, conductive polymers, fibers, and fabrics. Hence the aim of this article is to explore the entropy generation analysis of single wall carbon nanotubes and multiwall carbon nanotubes flow in an upright micro channel with variable thermal conductivity. The exponential heat source and non-linear thermal radiation were considered. The micro channel retains the no slip and convective boundary conditions. The Buongiorno model was used in this study, which emphasizes the light on Brownian motion and thermophoresis phenomena that occur during the fluid flow. Darcy- Forchheimer model is also taken into account. The governing equation numerically solved by employing Runge-Kutta Fehlberg's fourth-fifth order. The repercussion of this study upholds that the inflates of variable thermal conductivity magnify the thermal field. Entropy production inflates at right wall of the channel with augmented Brownian parameter and exhibits exactly opposite behavior at left wall of the channel. One of the important tasks of the investigation was to compare SWCNT and MWCNT. The findings confirmed that multiwall carbon nanotubes exhibit more magnificent heat and mass transfer than single wall carbon nanotubes.

Numerical simulations of Williamson fluid containing hybrid nanoparticles via Keller box technique

In this investigation, a Williamson hybrid nanoliquid flow over a stretchy surface has been considered. Furthermore, the convective boundary condition is incorporated for the analysis. In view of the practical applications thermal radiation is used to analyze the energy transfer phenomenon. The momentum and energy expressions are solved numerically by employing the KB approach (Keller Box Technique). The energy transfer rate has been discussed in the table. Further, velocity, temperature and Nusselt number impacts against thermal radiations are discussed in detail. This research portrayed that with the growth of suction/injection factor, the energy transmission and skin friction increase. Moreover, the heat transfer rate decreases for both (Al2O3+CuO)/SA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(Al}_{2}{O}_{3}+CuO)/SA$$\\end{document} and Al2O3/SA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Al}_{2}{O}_{3}/SA$$\\end{document} the on the growth of Weissenberg parameter. In the same vain heat transfer rate improves for the increment in the convective parameter.

Dynamics of accelerating and decelerating flows: A boundary layer examination with non-similar approach and convective boundary condition

Moisture/air-flow over the aircraft wing and bonnet of a moving car in aerodynamical systems exhibit dynamic behavior characterized by accelerating and decelerating flows. These analysis is essential and applicable in various fields, including physics, engineering, and fluid mechanics. The present investigation aim to explore the dynamics of accelerating and decelerating flows within the framework of boundary layer examination. To achieve these objectives, a non-similar group of transformations is employed to convert the governing dimensional two-variable dynamical system into a dimensionless differential form, with η and ξ as the independent variables. To gain physical understanding of the mathematical equations governing the flow, an efficient bivariate spectral collocation method (BSCM) is employed for analyzing the flow dynamics. This method allows for a thorough investigation of the behavior and characteristics of the accelerating and decelerating Casson flows. Subject to the convergence and residual error analysis of the numerical results, the effects of pertinent parameters on the flow variables were investigated. The findings of this study show that the effects of flow parameters on decelerating and accelerating flows are not completely opposite. Additionally, the Biot parameter positively impacts the velocity and temperature profiles of the two dynamical flows. However, an increase in the Casson fluid parameter β has an opposing effect on the temperature and concentration profiles of both flows.

Darcy-Forchheimer nanofluid flow and heat transfer with convective boundary conditions: Insights from differential transform method

In this work, we use the sophisticated differential transform method (DTM) to derive solutions to the complicated momentum, heat, and mass transfer equations that characterize Darcy-Forchheimer nanofluid flow over a stretching surface with convective boundary conditions. The investigation includes the nuanced effects of heat sources and chemical reactions and also addresses the synergistic effects of Brownian motion and thermophoresis. By applying an appropriate similarity transformation, the governing partial differential equations (PDEs) are gracefully transformed into an elegant system of nonlinear coupled ordinary differential equations (ODEs), a problem that is ingeniously solved using DTM. The veracity of our results is underpinned by a careful validation against previous scientific work that illuminates the path to scientific clarity. As the mathematical tapestry unfolds, the enchanting interplay of physical parameters on fluid dynamics is revealed, manifesting in visually captivating graphs and illuminating tables. Of particular note is the transformative influence of the magnetic parameter, which stages a ballet in which an increase in skin friction and the Nusselt number causes a diminuendo. Meanwhile, the solutal concentration decreases as the Brownian motion, Lewis number, and chemical reaction parameters increase, while it waltzes in reverse harmony with the thermophoresis parameter. Beyond equations and diagrams, this investigation promises to cast a luminous beacon on practical realms, imparting invaluable insights for industries ensconced in the realm of heat exchangers, the alchemy of lubricant refining processes, and the grand tapestry of scientific and engineering domains.

Thermal radiative and Hall current effects on magneto-natural convective flow of dusty fluid: Numerical Runge–Kutta–Fehlberg technique

This research article intends to examine the consequences of Hall impact on the natural convection of magnetohydrodynamic (MHD) fluid flowing and the thermal characteristics of the fluid flow which containing dusty particles via a vertical stretchable sheet. Slip velocity and convective boundary conditions are taken into consideration in this research article. The flow is mathematically described by partial differential equations. The governing equations are renovated into a group of nonlinear differential equations with the use of similarity conversations, which are then resolved numerically by applying Runge–Kutta–Fehlberg. The behavior of these physical factors on the rapidity and temperature profiles of the dust and fluid phases are exposed graphically in this article. Furthermore, frictional force and heat transfer are also examined and discussed. According to the investigation, the existence of suspended particles in the fluid lead to increment in momentum and thermal boundary layer thickness. The temperature of the fluid seems can be controlled by the significant parameter, such as it seem to be increase due to the magnetic, radiation, and Hall parameters, while it is seen to have decreased due to the slip thermal parameter. While the radiation accelerates up the fluid velocity, the magnetic parameter is excellent at slowing it down. The fluid phase’s temperature and velocity profiles are almost usually higher than those of the dust phase. The outcomes contribute to a better understanding of the two-phase theory’s fluid flow phenomenon.

Peristaltic transport of nanofluid with temperature dependent thermal conductivity: A numerical study

Peristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices.

Numerical computations for Darcy–Forchheimer-based dual convection reactive flow considering Casson nanomaterial by convected permeable surface

The use of nanoparticles in heat transmission is an interesting research subject and many scholars have shown an interest in this topic. In accordance with the motivating relevance of nanomaterials, the current research advocates for an evaluation of Casson nanofluid using porous medium thermal analysis in conjunction with vibrant implementations of mixed convection through a chemical reaction. Additionally, a nonlinear suction/injection phenomenon is taken into consideration. A consistent flow pattern is created by the stretched porous structure. The extended Casson nanofluid model is used to identify the heat production of non-Newtonian fluids. The essential incentives for choosing the Casson nanofluid model are validated as it simultaneously achieves Casson fluid, nanofluid and porous medium outcomes. The convective transport of nanofluid has been addressed using convective temperature boundary conditions and convective flow. A dimensionless form with similarity variables is used to simplify the fundamental equations for the provided flow model. The fourth-order Runge–Kutta (RK) strategy is deployed to arrive at a numerical solution for simulated flow. The physical conveyance of flow variables is accessed visually. It is calculated from engineering quantities (i.e., skin friction, Nusselt number and Sherwood number) to generate the numerical values. The velocity declines with increasing porosity and material factors while opposite outcomes are witnessed for buoyancy factors (mixed convection and buoyancy ratio) and injection factor.

Thermodynamic analysis of EMHD ternary nanofluid flow with shape factor effects over a shrinking sheet: A non-Fourier heat flux model

The investigation of the flow characteristics of ternary hybrid nanofluids through a contracting sheet has considerable importance due to its potential for achieving exceptionally high rates of heat transfer. The ternary hybrid nanofluid then absorbs heat from the surface and carries it away. The objective of this study is to analyze the influence of couple stress and activation energy parameters on the flow of a ternary hybrid nanofluid ( H 2 O + MWCNT + ZnO + Al 2 O 3 ) through a contracting sheet with electric forces and convective boundary conditions. The heat flux model created by Cattaneo and Christov is utilized to examine the mechanism of heat transmission. The equations necessary to depict the problem have been transformed into a system, which has subsequently been resolved using the bvp4c solver (MATLAB built-in function). It is found that there is a rise in the Bejan number with the increase in the couple stress parameter. An increase in the volume percentage of multi-walled carbon nanotubes ( ϕ MW ) is observed to result in an augmentation of entropy generation . It has been observed that there is a fall in the friction factor when the couple stress parameter rises and at 0 ≤ Ed ≤ 0.6 , (electric field parameter), the friction factor is seen to rise at a rate of 0.638797 (Platelet) and (0.638784). A positive correlation is observed between the thermal relaxation parameter ( ϒ ) and fluid temperature, indicating that a rise in the former leads to an increase in the latter. It is discovered that, when 0 ≤ ϒ ≤ 0.3 , the Nusselt number rises by 0.022587 (Platelet) and 0.022275 (Cylinder). There is a negative correlation between the upsurge in the activation energy parameter ( Eg ) and the corresponding rise in the Sherwood number. At 0 ≤ Eg ≤ 3 , the Sherwood number is seen to decline at a rate of 0.0321 (Platelet) and 0.03208 (Cylinder).

Analyzing the influence of inertial drag on hybrid nanofluid flow past a stretching sheet with Mintsa and Gherasim models under convective boundary conditions

Analyzing the influence of inertial drag on hybrid nanofluid flow past a stretching sheet with Mintsa and Gherasim models under convective boundary conditions

Entropy generation analysis of micropolar fluid flow through a vertical microchannel under the combined effect of Joule heating, viscous dissipation, and thermal radiation with convective boundary conditions

ABSTRACT In this era of modern science, microfluidics has gained much importance in the field of research due to large-scale applications in science and engineering. Transfer of heat via nanofluids in microfluidics is the key concept of research. Therefore, here we have considered micropolar fluid for better heat transfer in vertical microchannel and discussed the influences of radiative heat flux, Joule heating, and uniform heat source/sink with viscous dissipation. The equations that govern the physical model are nondimensionalised by the application of suitable dimensionless parameters. Runge–Kutta–Fehlberg 4th−5th order method is applied for solving the non-dimensional governing ordinary differential equations, and precisely computed microrotation, velocity, and temperature profiles of micropolar fluid. The impacts of various factors on entropy generation and Bejan number are explored and analysed through graphs. It is investigated that a higher coupling number decelerates the fluid flow and reduces the temperature of the fluid. Further, minimum entropy generation can be attained by rising coupling number, Hartmann number, and radiation parameter.

3D flow of variable properties viscoelastic nanofluids with impacts of Arrhenius energy and Cattaneo–Christov double-diffusion

In several situations, particularly, flow of viscoelastic nanofluids, the dynamic viscosity and thermal conductivity should be considered as variables due to their roles in various practical applications. Therefore, this article aims applying the Cattaneo–Christov double-diffusion theory to investigate the three-dimensional (3D) forced flow of second-grade viscoelastic nanofluids over a permeable stretching surface. The properties of the mixture are considered to be variables where the dynamic viscosity is exponentially varied with temperature and the thermal conductivity and Brownian motion are linearly dependent on temperature and concentration, respectively. The included medium is isotropic porous, and both heat generation and thermal radiation impacts are assumed. At the surface, the nanoparticles are either active or passively controlled, and the convective boundary conditions are considered for the surface temperature. The solution methodology is based on similarity transformations, and the numerical technique is based on 4th-order Runge-Kutta method. The major outcomes revealed that the growth in thermal relaxation time δ e and viscoelastic parameter K causes gradually decreases in temperature and nanoparticles features. Also, constant dynamic viscosity gives higher velocity features compared to the variable case. Furthermore, the considered range of thermal conductivity coefficient ε 1 gives an enhancement in rate of the heat transfer by 5.26%.