Isothermal Boundary Conditions Research Articles

Topology of thermodynamic potentials using physical models: Helmholtz, Gibbs, Grand, and Null.

Thermodynamic potentials play a substantial role in numerous scientific disciplines and serve as basic constructs for describing the behavior of matter. Despite their significance, comprehensive investigations of their topological characteristics and their connections to molecular interactions have eluded exploration due to experimental inaccessibility issues. This study addresses this gap by analyzing the topology of the Helmholtz energy, Gibbs energy, Grand potential, and Null potential that are associated with different isothermal boundary conditions. By employing Monte Carlo simulations in the NVT, NpT, and μVT ensembles and a molecular-based equation of state, methane, ethane, nitrogen, and methanol are investigated over a broad range of thermodynamic conditions. The predictions from the two independent methods are overall in very good agreement. Although distinct quantitative differences among the fluids are observed, the overall topology of the individual thermodynamic potentials remains unaffected by the molecular architecture, which is in line with the corresponding states principle-as expected. Furthermore, a comparative analysis reveals significant differences between the total potentials and their residual contributions.

Magnetic field influence on Casson fluid flow in rotating convection

The stability of buoyant flow in an infinite extended vertical fluid layer bounded by impermeable conducting isothermal rigid walls, known as magnetic field influence on Casson fluid flow in rotating convection, is investigated. A system of governing equations (Navier–Stokes, heat, and induction ones) is solved with isothermal rigid boundary conditions. When the majority of electrically conducting fluids are extremely small, the stability of governing equations can be simplified by taking the smallness of magnetic Prandtl number into account. In linear stability, the Chebyshev collocation method is used to solve numerically the system of eigenvalue problems. The Casson fluid parameter, Chandrasekhar number, magnetic Prandtl number, and Taylor number all have destabilizing effects on the system's basic velocity and basic magnetic field, resulting in instability. The critical Rayleigh number (Rc), critical wave number (ac), and critical wave speed (cc) are calculated using the influence of governing parameters. The Casson fluid parameter and magnetic Prandtl number were found to stabilize stationary disturbances in neutral stability curves.

On the generation of near-wall dilatational motions in hypersonic turbulent boundary layers

Dilatational motions in the shape of travelling wave packets have been identified recently to be dynamically significant in hypersonic turbulent boundary layers. The present study investigates the mechanisms of their generation and their association with the solenoidal motions, especially the well-recognized near-wall self-sustaining process of the regeneration cycle between the velocity streaks and quasi-streamwise vortices. By exploiting the direct numerical simulation databases and orchestrating numerical experiments, we explore systematically the near-wall flow dynamics in the processes of the formation and transient growth of low-speed streaks. We conclude via theoretical ansatz that the nonlinearity related to the parallel density and pressure gradients close to the wall due to the restriction of the isothermal boundary condition is the primary cause of the generation of the dilatational structures at small scales. In fully developed turbulence, the formation and the existence of healthy dilatational travelling wave packets require the participation of the turbulence at scales larger than those of the near-wall regeneration cycles, especially the occurrence of the bursting events that generate vortex clusters. This is proven by the less intensified dilatational motions in the numerical experiments in which the Orr mechanism is alleviated and the vortical structures and turbulent bursts are weakened.

Combustion of a nanoparticles-laden chemical in a vented cavity

Mixed convective characteristics of the combustion of a nanoparticles-laden fuel (n-butanol nanofluid) in a vented cavity are investigated. The nanofluid and the oxidizer enter the cavity through the inlets on the left and right vertical walls, respectively. However, the resulting product produced from the oxidation process of the fuel exits the cavity through the outlet at the bottom wall. Heat generated from the oxidation process causes natural convection within the cavity. The conjugate effect of natural and forced convection finally gives rise to mixed convection phenomena. In this regard, a mathematical model for mixed convection flow in a vented cavity is formulated with no-slip and isothermal boundary conditions. Having transformed the model into a dimensionless form, the stream function-vorticity formulation is used. The resulting equations are then solved numerically using the finite difference method. Numerical results are illustrated with the streamlines, isotherms, and isolines of fuel and oxidizer concentrations. The maximum values of the stream function (ψmax) and the temperature (θmax) are found to increase with an increase in the Frank–Kamenetskii number (Λ), volume fraction of nanoparticles (φ), and stoichiometric ratio (χ). On the contrary, they decrease with the increase in the Reynolds number (Re). When the Grashof number (Gr) is increased, ψmax increases and θmax decreases. The remaining concentrations of fuel, (CF)min, and oxidizer, (CO)min, are higher for an increase in Gr, whereas the opposite is recognized for increasing Λ. With the increase in Gr and Λ, the steady-state flow in the cavity tends to be oscillating and then chaotic.

Towards an optimal frequency and time response of singe-tube pressure measurement systems under continuum-flow conditions

The pressure transmission tube, as part of a pressure measurement system, generally has a considerable influence on its dynamic characteristics. The paper deals with the mathematical modelling of the dynamic behaviour of pressure transmission tubes with the aim of providing guidelines for the optimal design of such systems in the frequency and time domains. The mathematical models used are based on linear wave theory and continuum flow mechanics with no-slip and isothermal boundary conditions. The frequency responses were evaluated in terms of frequency bandwidth and the transient step responses in terms of settling and rise times. Following a systematic analysis of these characteristic parameters, we derived an analytically formulated optimisation objective function defining the transition between the low-wavenumber and high-wavenumber pressure waves in the pressure transmission tubes. The demanded dynamic behaviour in the frequency and time domains can be achieved through an appropriate ratio between the actual tube radius and the so-called transition tube radius, which was derived as a function of the tube length, end volume and fluid properties.

High performance analysis and optimization of metal halide perovskite-based thermoelectric generators for sustainable energy harvesting

Metal halide perovskite-based thermoelectric materials have garnered considerable attention due to their ultralow thermal conductivities and decent electric transport properties, while the research into thermoelectric generators (TEGs) lag much behind the progress of materials. In this paper, a real-sized 3D finite element model of a metal halide perovskite-based TEG is established under iso-thermal and iso-heat flux boundary conditions. Compared with traditional PbTe-based TEGs, perovskite-based TEGs exhibit more promising TE performance with TE conversion efficiency reaching ∼12 % at a 104 W/m2 thermal input power. In addition, the geometric parameters as well as the thermal management parameters under the iso-heat flux boundary condition, are optimized and discussed. The Taguchi optimization combined with the analysis of variance (ANOVA) method is further employed to quantify the contribution and importance of these factors on the output performance of the perovskite-based TEG. The results demonstrate that changing the device geometry and thermal management parameters will affect the temperature distribution between the hot- and cold-side. The thermal input power and the height of the p-n legs are the dominant factors affecting the output power and the TE conversion efficiency of the perovskite-based TEG. Promisingly, the TE conversion efficiency can reach above 20 % (or 65 % of the corresponding ideal Carnot efficiency) for an optimized perovskite-based TEG. This work predicts and verifies the highly promising TE performance of new metal halide perovskite-based TEGs. The principles behind the analyses here provide new strategies for designing and optimizing TEGs for waste-heat harvesting and other sustainable energy conversion applications.

Thermochemical non-equilibrium hypersonic flow over a rectangular cavity embedded on a compression ramp

This paper reports a systematic computational investigation that elucidates the fundamental thermochemical non-equilibrium physics that occurs when air at Mach number of 11 encounters a rectangular cavity of aspect ratio L/D = 2.0 embedded on a 25° compression ramp. The mechanistic details of this highly complex flow phenomenon are obtained by solving the compressible form of the Navier–Stokes equations in two dimensions using a finite-volume open-source library. Chemical and thermal non-equilibrium processes are treated using a five-species, 12-reaction chemical kinetics, and a two-temperature model, respectively. Following a detailed validation and grid sensitivity study, two simulations are conducted, one with isothermal boundary conditions and the other with conjugate heat transfer (CHT) to identify the effect of energy transmission to the material on surface heat flux. Fast Fourier transforms and near-wall velocity profiles inside and in the neighborhood of the cavity are used to identify primary oscillatory modes and shear layer dynamics. Two new descriptive states defined as “states I and II,” representative of the minimum and maximum deflection of the shear layer, are used to discuss the dynamical behaviors in the cavity, including the separation region before the cavity, trailing edge effects, frequency analysis of probe data collected at several key locations, and the effect of CHT on surface heat flux. It is found that the flow features at the cavity's center strongly influence the separation upstream of the cavity, and the transrotational temperature near the cavity's trailing edge is strongly correlated with the oscillations of the shear layer.

Effect of variable viscosity, porous walls and mixed thermal boundary condition on the onset of Rayleigh-Bénard convective instability

In this paper, we have studied the criteria for the onset of instability in the Rayleigh-Bénard convection problem, by considering a fluid layer confined between two infinitely extended rough boundaries, which are subjected to mixed-type thermal boundary conditions, physically representing the imperfectly conducting boundaries. The rough boundaries are assumed to be shallow porous layers with different pore size, properties, and permeabilities. Mathematically, it is given by the Saffman type boundary condition. Therefore, we have two generalized forms of boundary conditions, one for the flow field and the other for the thermal field. The two limiting cases of the mixed-type thermal boundary condition correspond to a perfectly conducting boundary and to a perfectly insulating boundary, whereas the two limiting cases of the hydrodynamic boundary condition correspond to a no-slip condition and to a free-surface condition, depending upon the limiting values of the parameters involved in these two generalized boundary conditions. The linear and nonlinear energy stability analyses are performed, and the existence of the region of subcritical instability is checked. Through the principle of exchange of stability analysis, it is found that the instability occurs only in the stationary mode. The adiabatic boundary condition is found to be more restrictive than the isothermal boundary condition. Under given conditions, the instability is observed to be occurring in the infinite wavelength mode for the case of adiabatic boundaries. In the present work, the effect of temperature and pressure dependent viscosity on the stability of the system has been shown and found to be of destabilizing nature. However, the roughness of the boundaries is found to be of stabilizing nature.

Entropy formation due to conjugate natural convection in a cylindrical open cavity under isothermal boundary condition at inner wall

Entropy formation due to conjugate natural convection in a cylindrical open cavity under isothermal boundary condition at inner wall

Analytical solution of heat equation taking into account convection with isothermal boundary conditions

The problem of determining the distribution of heat through the reservoir constantly arises in the production of hydrocarbons. Changes of temperature affect the viscosity of oil and consequently the rate of its production. Taking into account the filtration process, additional terms appear in the classical heat conduction equation, including nonlinear ones. Various numerical schemes are used to solve the modified equations. The question of the convergence of such methods often arises. The task of this work is to obtain an analytical solution of the heat equation in cases where it is possible, in order to further compare numerical solutions with them.

Generalized mean state of the isothermal Darcy–Benard problem and its instability onset

Thermally-driven natural convection is theoretically explored in the present work within a porous layer with respect to the Darcy’s law. The usual non circulating basic cellular flow between two infinitely long horizontal Darcy porous plates leads to generalized basic state considering the isothermal boundary conditions leading to the Hadley flow configuration. Such a motion is governed by a circulatory flow together with a temperature both varying along the horizontal axis. Hence, besides the buoyancy Rayleigh parameter, yet another parameter appears dominating the evolution of basic cellular circulation and thermal progress. Instability onset of this basic state is targeted based on the linear stability analysis of small normal modes. The resulting 3D instability system of equations is treated numerically and the stationary modes leading to convective neutral stability are determined. The found eigenvalues are also justified to be those deviating from the well-known no-flow Darcy porous solution through an asymptotic perturbation method in the special circumstances. The bounds of neutral stability curves in regard to the longitudinal, oblique and transverse modes are thoroughly investigated and it is shown that longitudinal modes are always the most unstable ones, while the transverse and oblique modes having finite encapsulated zone of instability can undergo a complete stability after a threshold value of horizontal temperature gradient parameter.

Thermocapillary effects during the melting of phase change materials subjected to lateral heat flux in microgravity

We numerically investigate the melting dynamics of n-octadecane in a rectangular container that is subjected to a constant lateral flux and is open to air in microgravity. As the melting progresses, the temperature gradient existing at the open boundary drives thermocapillary flow within the liquid phase and modifies the phase change dynamics. We conduct a parametric study varying key dimensionless parameters — the Marangoni and Stefan numbers, and the aspect ratio — and compare the associated temporal dynamics with those observed in the (so-called) reference case, where heat is transferred solely by conduction, and with those driven by isothermal boundary conditions [1,2]. Compared to the isothermal case, where the overall effect of thermocapillary flows is to accelerate melting by a factor up to 20, the analogous contribution with lateral flux is about one order of magnitude smaller, with values up to 2.8. Finally, we perform spectral analyses of the oscillatory standing wave and hydrothermal traveling wave modes that eventually appear during melting for large applied flux. The critical Marangoni number (Macr) is estimated considering the characteristic dependence ∝(Ma−Macr)0.25 of the (so-called) oscillatory mode contribution.

Global stability of Bénard–Marangoni convection in an anisotropic porous medium

Surface tension is essential in many industrial applications, especially where the liquid surface is in contact with the environment, such as crystal growth, semiconductor manufacturing, and welding. The present article reports a numerical analysis of convection induced by the combined effects of buoyancy force and surface tension in an infinitely extended horizontal fluid-saturated anisotropic porous layer with high permeability. We assume that the bottom boundary is rigid and the top is exposed to the air. Biot numbers establish general thermal conditions at both ends instead of commonly used adiabatic and isothermal boundary conditions. The anisotropy of the porous structure results in thermal and mechanical anisotropy parameters while examining layer's stability. The Chebyshev Tau technique yields the critical Marangoni number, MaLc and MaEc, representing linear and energy stability boundaries. We compare the constraints obtained from linear and energy analyses and conclude that the energy bounds for the current problem are less than linear bounds, indicating subcritical instabilities may exist. It is also observed that thermal anisotropy and Biot numbers stabilize the system. In contrast, mechanical anisotropy and the Darcy number advance the onset of convection. The existing results of limiting cases of the present problem are recovered with remarkable accuracy.

Influence of symmetric/asymmetric boundaries on axisymmetric convection in a cylindrical enclosure in the presence of a weak vertical throughflow

The linear and nonlinear stability of axisymmetric convection of a viscous fluid in a cylindrical enclosure heated from below is investigated for various radius to height ratios. A weak vertical throughflow is imposed in a gravity-aligned or a gravity-opposing manner. Symmetric and asymmetric boundaries of free-free, rigid-rigid and rigid-free types are considered for lower and upper boundaries with isothermal temperature boundary condition. The side-walls are assumed to be rigid and adiabatic. A convergent Maclaurin series representation is considered for the finding of axial trial eigenfunctions. In order to corroborate the results of the present study with those of a previous investigation, the critical Rayleigh number and the number of radial rolls manifesting for any given aspect ratio are determined in the case of no throughflow and an exact match is found. Further, the influence of boundaries and the effect of throughflow on chaotic and periodic regimes of motion are studied with the help of a time series solution and the largest Lyapunov exponent as indicators of chaos. The novelty of the present study is the use of a Maclaurin series representation for the eigenfunctions of the linear problem and using the same in determining the solution with the convective mode.

Thermoconvective instability in a ferrofluid saturated porous layer

The Forchheimer-extended Brinkman’s Darcy-flow model was used to investigate the initiation of ferroconvection in a flat porous layer while accounting for effective viscosity. The rigid ferromagnetic, rigid paramagnetic and stress-free isothermal boundary conditions are the three categories. The eigenvalue issue can be properly addressed for stress-free boundaries; the Galerkin approach is utilized to find the critical stability constraints quantitatively for other barriers. It was discovered that the boundary types had a strong influence on the system’s stabilization. Ferromagnetic boundaries are less preferred than paramagnetic boundaries in control of convection. The dependence of many physical limitations on the linear stability of the system is intentionally given, and it is demonstrated that increasing the value of the viscosity ratio delays the beginning of convection.

Entropy Production Analysis in an Octagonal Cavity with an Inner Cold Cylinder: A Thermodynamic Aspect

Understanding fluid dynamics and heat transfer is crucial for designing and improving various engineering systems. This study examines the heat transfer characteristics of a buoyancy-driven natural convection flow that is laminar and incompressible. The investigation also considers entropy generation (Egen) within an octagonal cavity subject to a cold cylinder inside the cavity. The dimensionless version of the governing equations and their corresponding boundary conditions have been solved numerically using the finite element method, employing triangular mesh elements for discretization. The findings indicated that incorporating a cold cylinder inside the octagonal cavity resulted in a higher heat transfer (HT) rate than in the absence of a cold cylinder. Furthermore, using the heat flux condition led to a higher average Nusselt number (Nuavg) and a lower Bejan number (Be) than the isothermal boundary condition. The results also showed that HT and Egen were more significant in the Al2O3-H2O nanofluid than the basic fluids such as air and water, and HT increased as χ increased. The current research demonstrates that employing the heat flux condition and incorporating nanoparticles can enhance the rate of HT and Egen. Furthermore, the thermo-fluid system should be operated at low Ra to achieve greater HT effectiveness for nanofluid concerns.

The Rayleigh–Bénard problem for water with maximum density effects

Linear stability and weakly nonlinear stability analyses are developed for Rayleigh–Bénard convection in water near 3.98 °C subject to isothermal boundary conditions. The density–temperature relationship (equation of state) is approximated by a cubic polynomial, including linear, quadratic, and cubic terms. The continuity equation, the Navier–Stokes momentum equation, the equation of state, and the energy equation constitute the governing system. Linear stability analysis is used to investigate how the maximum density property of water affects the onset of convective instability and the choice of unstable wave number for four different types of boundary conditions. Then, a weakly nonlinear stability study is done using the spectral Fourier method for isothermal tangential stress-free boundary conditions to quantify the heat transport of the system and demonstrate the transition from regular/periodic convection to chaotic convection. A Stuart-Ginzburg–Landau equation is obtained using the multiscale expansion method. Streamlines and isotherms are presented and analyzed. The influence of maximum density has been shown to delay the onset of instability and is, therefore, a stabilizing mechanism for thermal instability. Due to the maximum density, the onset of chaotic convection is also delayed. Among four different boundaries, the impermeable rigid boundaries require the highest Rayleigh number for instability to begin. Increasing boundary temperatures advance the onset of chaotic convection and improve the heat transport situation.

Determination of diffusion coefficient and convective heat transfer coefficient for non-isothermal desorption-diffusion of gas from coal particles

Experiments investigating gas adsorption/desorption-diffusion in coal particles typically involve putting coal particles into a sample cell in a water bath to ensure a constant-temperature environment. Numerical simulations of such experiments have also been performed under isothermal condition. However, the coal particle temperature is not constant, and the influence of temperature variation on the diffusion coefficient back-calculation is often neglected. In this study, CO2 desorption-diffusion experiments are conducted with coal particles first, using the abovementioned water bath technique, and the coal particle temperature is monitored. Then, a coupled thermal-gas model for CO2 adsorption/desorption-diffusion in coal particle is proposed, in which the interaction between gas adsorption/desorption and coal temperature variation is considered. Finally, numerical simulations of the CO2 desorption-diffusion experiments are described, and the applied thermal boundary conditions are validated. The impacts of temperature variation on the desorbed-diffused gas amount and the diffusion coefficient back-calculation are also evaluated. The experimental results show that the coal particle temperature first decreases and then increases. Thus, setting an isothermal boundary condition for the particle surface will not lead to an accurate simulation of the temperature variation, which will ultimately also affect the accuracy of the diffusion coefficient back-calculation. Instead, adopting a convective heat boundary condition for the particle surface can better reproduce the evolution of desorbed-diffused gas and coal temperature changes, thereby improving the accuracy of the diffusion coefficient back-calculation. The results also indicate that the magnitude of coal diffusion coefficient and the size of coal particle both have significant effects on the temperature variation and the subsequent desorption-diffusion of adsorbed gas.

Heat transfer enhancement in turbulent dual jet and its thermal characterizations using large eddy simulation

Heat transmission is the prime aim of any thermal device that requires effective cooling. This requirement becomes significantly more vital for a turbulent jet, which is encountered quite often in industrial and engineering purposes. The present study investigates thermal and turbulence characteristics of a turbulent dual jet using Large Eddy Simulation (LES). The bottom surface is maintained at isothermal and isoflux boundary conditions and the flow Re is 7500. The profiles of Reynolds shear-stress, turbulence kinetic energy, wall friction coefficient, r.m.s. temperature, mean Nusselt number, bottom wall temperature, and turbulent heat fluxes are investigated and scaled using outer, thermal and inner parameters. Variations in Nusselt number and bottom wall temperature are also studied. A significant rise in Nusselt number is observed nearer to the jet exit which enriches the cooling rate. Overall, the finding shows that compared to the wall jet and parallel flowing offset jet, the inflection point in the mean temperature profile of the present dual jet scaled with the thermal variable and outer variable is higher. Further, it is also observed that the thermal transmission spreading out of the wall is quite efficient in the low-pressure area of the dual jet. Near-wall eddies and the development of roller-like structures are seen. The interaction occurring through the inner and outer layers increases the momentum transfer along with turbulent heat-flux and a large amount of heat is lost due to turbulent flow.

Heat transfer simulation of nanofluids heat transfer in a helical coil under isothermal boundary conditions using COMSOL multiphysics

In the current paper, a numerical model was designed using COMSOL Multiphysics software based on experimental results to predict Nusselt number of TiO2, ZnO and Ag water-based nanofluids in helical coil under isothermal boundary conditions. All Nusselt number data extracted from the model were compared with experimental data to validate the model and the results showed that the model gives good accuracy and the model could be used to predict non-experimental data. Root Mean Square Error (RMSE) was calculated to evaluate model accuracy and the results were 4.35, 2.40 and 2.53 for TiO2/water, Ag/water and ZnO/water respectively. The model was used to predict non-experimental data and the results were logically predicted compared with experimental data and the model was proven to be sufficient for predicting non-experimental data. Model results were compared with two types of artificial neural networks predicting Nusselt number Feed Forward Neural Network (FFNN) and Generalized Regression Neural Network (GRNN). The deviation between predicted data and experimental data was calculated and the results indicated that GRNN network has the highest accuracy with maximum deviations of +0.02% & −0.3% while the COMSOL model has a maximum deviation of +4.5% & −5.9% and finally FFNN network +8.9% & −5.7%.