Isothermal Boundary Conditions Research Articles

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%.

Flame Acceleration in Stoichiometric CH4/H2/air Mixtures with Different Hydrogen Blend Ratios in an Obstructed Channel

ABSTRACT Adding a certain percentage of hydrogen into the natural gas pipeline network is regarded as an efficient way to store and transport hydrogen. CH4-H2 binary fuel is also considered to be an important means of hydrogen utilization. In this paper, flame acceleration (FA) in stoichiometric CH4/H2/air mixtures with various hydrogen blend ratios (i.e., Hbr = 0%, 20%, 50%, 80%, and 100%) was studied experimentally and numerically. In the experiments, high-speed photography was used to record the FA process. In the numerical simulations, the two-dimensional, fully-compressible, reactive Navier-Stokes equations were solved using a high-order algorithm on a dynamically adapting mesh. The chemical reaction and diffusive transport of the mixtures were described by a calibrated chemical-diffusive model. The numerical predictions agree reasonably with the experimental measurements. The results show that a larger hydrogen blend ratio leads to a faster FA. The difference in FA due to hydrogen blending mainly depends on the property change of the fuel mixtures, the increase of flame surface area and the interactions between flame and pressure waves, corresponding to three different stages. In addition, the heat loss to the channel walls and obstacle surfaces has an impact on the FA process, especially in the mixtures with low hydrogen blend ratios (i.e., Hbr ≤ 20%). This is related to the weakening of interactions between pressure waves and flame under isothermal boundary condition.

The Effects of Heat Transfer through the Ends of a Cylindrical Cavity on Acoustic Streaming and Gas Temperature

The longitudinal vibrational motion of a cylindrical cavity with gas, in which the acoustic streaming occurs, is considered. The motion is described by the system of equations for the dynamics and thermal conductivity of a viscous perfect gas, written in a cylindrical coordinate system associated with the cavity. The system of equations is solved numerically by the finite volume method with an implicit staggered grid scheme, while the convective–diffusion fluxes are approximated by the power law scheme. According to the boundary conditions, the lateral surface of the cavity is maintained at a constant equal initial temperature. The effects of heat transfer through the ends of the cavity are studied. Heat transfer is given by isothermal boundary conditions. The obtained solutions are compared with the solutions under adiabatic boundary conditions. It is shown for the first time that the effects of heat transfer manifest themselves with an increase in the nonlinearity of the process; when the frequency and amplitude of vibration increase, this is also facilitated by an increase in the radius of the cavity. The effects of heat transfer on the period average temperature, on the streaming velocity and on structure are established.

Performance of Heat Transfer in Micropolar Fluid with Isothermal and Isoflux Boundary Conditions Using Supervised Neural Networks

The current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. Generally, the explicit or analytical solutions for such nonlinear problems are hard to calculate. Therefore, we have designed a computer or artificial intelligence-based numerical technique. The reliability of neural networks using the machine learning (ML) approach is used with a local optimization technique to investigate the behaviours of different material parameters such as the Prandtl number, micropolar parameters, Reynolds number, heat index parameter, injection/suction parameter on the temperature profile, fluid speed, and spin/rotational behaviour of the microstructures. The approximate solutions determined by the efficient machine learning approach are compared with the classical Runge–Kutta fourth-order method and generalized finite difference approximation on a quasi-uniform mesh. The accuracy of the errors lies around 10−8 to 10−10 between the traditional analytical solutions and machine learning strategy. ML-based techniques solve different problems without discretization or computational work, and are not subject to the continuity or differentiability of the governing model. Moreover, the results are illustrated briefly to help implement microfluids in drug administering, elegans immobilization, and pH controlling processes.

EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER AND PRESSURE DROP CHARACTERISTICS FOR VERTICAL DOWNFLOW USING TRADITIONAL AND 3D-PRINTED MINI TUBES

In this study, an investigation on the influences of different manufacturing techniques on the heat transfer and pressure drop in the developing and fully developed regions of mini-tube under different flow regimes is introduced. The purpose of this research is to experimentally investigate the heat transfer and pressure drop characteristics using 3D-printed tubes and traditional stainless steel tubes in the vertical direction under isothermal and non-isothermal boundary conditions. Experiments are conducted using distilled water (Prandtl numbers varying from 4 and 7) at Reynolds numbers of 800-10000 with heat fluxes between 30 and 500 kW·m<sup>-2</sup>. Test tubes with inside diameters of 2 mm are used, and the average surface roughness is 1.6 μm and 15.3 μm, respectively. The results are compared with previous studies. It is verified that the heat transfer characteristics are almost the same for the traditional tube and the 3D-printed tube in the laminar region. The average deviation between these two tubes is 7.7%. However, for the turbulent region, the Nusselt numbers of 3D-printed tube in the turbulent region increases by an average of 45% as compared with a traditional tube. The friction factors under heating conditions also increased by an average of 209%. In addition, the 3D-printed tube enters the transition region earlier. The results show that the average critical Reynolds number of a traditional tube and 3D-printed tube is around 2300 and 2000, respectively. Correlations in the turbulent region are developed to predict the friction factors and heat transfer coefficients with good accuracy.

Theoretical analysis of a two-dimensional multilayer diffusion problem with general convective boundary conditions normal to the layered direction

Theoretical analysis of transient thermal conduction in a two-dimensional multilayer structure has been limited to problems with isothermal or adiabatic boundary conditions along the walls normal to the layered direction. Due to mathematical difficulties pointed out in past work, an analytical solution has not been possible so far for the general case where each layer has a distinct convective boundary condition. This work presents an analytical technique to solve this general problem using Laplace transforms followed by derivation of a sufficient number of linear algebraic equations based on given boundary conditions to determine the coefficients of an eigenfunction-based series solution. This technique makes it possible to solve the problem when each layer may have a different convective heat transfer coefficient along the walls normal to the layered direction. Results from this general analysis are shown to correctly reduce to past work for the special cases of very small or very large Biot number. Good agreement with specific results presented in a past paper is also demonstrated. The technique is used to investigate the impact of key dimensionless parameters on the temperature field. This work significantly generalizes past work that was limited only to adiabatic or isothermal boundary conditions. Results presented here may help improve the theoretical understanding of multilayer diffusion problems, and make theoretical models much more representative of realistic conditions.

Effect of Electric Field Modulation on The Onset of Electroconvection in a Couple Stress Fluid

The problem of a convectional instability in a horizontal dielectric fluid layer with electric field modulation under couple stress fluid is examined. The horizontal dielectric upper boundary fluid layer is cooled, and the lower boundary is subjected to an isothermal boundary condition. The regular perturbation method based on the small magnitude of modulation is used to compute the critical Rayleigh number and the corresponding wavenumber. The solidity of the system is the characterised by a correction Rayleigh number, which is computed as a function of thermal, electric, and couple stress parameters and the frequency of electric field modulation. Some of the known findings are retrieved as specific cases in this study. It is demonstrated that the onset of the convection may be advanced or delayed by the proper regulation of different regulation parameters. The outcomes of this study have potential implications for the control of electroconvection with a time-dependent electric field.

Entropy analysis of hybrid nanofluid flow in a porous medium with variable permeability considering isothermal/isoflux conditions

The presented article deals with the mixed convection flow of a hybrid nanofluid comprising of copper and silver nanoparticles flowing in a porous medium having variable permeability. The porous medium is embedded in a parallel plate inclined channel where the plates are subjected to isothermal–isoflux conditions. Two cases are considered where the isothermal–isoflux conditions are interchanged: isothermal–isoflux and isoflux–isothermal conditions. Moreover, variation in permeability of the porous medium is taken for two cases where the permeability increases along the width of the channel for one case and the permeability decreases along the width of the channel for the other case. The homotopy analysis method is utilised to solve the nonlinear differential equation governing the flow of the nanofluid. To verify the solution, a reduced form of the governing equation is solved analytically and the answers were compared. Entropy generation analysis is then conducted in a manner that the flow parameters are varied individually. An interesting observation is that the isothermal–isoflux condition is more sensitive towards the variation in the parameter values. Another noteworthy observation is that the case of decreasing the permeability parameter of the porous medium leads to a higher entropy generation for all parameter values presented in the study. • Hybrid nanofluid flowing in a porous medium having non – uniform permeability is investigated using entropy generation analysis. • Two thermal boundary conditions are considered: isothermal – isoflux and isoflux – isothermal conditions. • Entropy generated in the flow was found to be maximum near the upper part of the wall. • Isoflux – isothermal boundary condition was found to generate more entropy for all cases of the investigation.

A high order moving boundary treatment for convection-diffusion equations

In this paper, a new type of inverse Lax-Wendroff boundary treatment is designed for high order finite difference schemes for solving general convection-diffusion equations on time-varying domain. This new method can achieve high order accuracy on Dirichlet boundary conditions with moving boundary. To ensure stability of the boundary treatment, we give a convex combination of the boundary treatments for the diffusion-dominated and the convection-dominated cases. A group convex combination of weights is carefully designed to avoid zero denominator, resulting in a unified algorithm for pure convection, convection-dominated, convection-diffusion, diffusion-dominated and pure diffusion cases. In order to match the time levels when constructing values of ghost points in the two intermediate stages of the third order Runge-Kutta method, we propose a new approximation to the mixed derivatives at the boundaries to ensure high order accuracy and to improve computational efficiency. In particular, we extend the boundary treatment to the compressible Navier-Stokes equations, which satisfies the isothermal no-slip wall boundary condition at any Reynolds number. We provide numerical tests for one- and two-dimensional problems involving both scalar equations and systems, demonstrating that our boundary treatment is high order accurate for problems with smooth solutions and also performs well for problems involving interactions between viscous shocks and moving rigid bodies.

Experimental Investigation of the Isothermal Pressure Drops in Mini-Elbows

An experimental setup was built in this study to measure the pressure drop for the horizontal mini-scale elbows under the isothermal boundary condition. Six stainless steel mini-elbows with various bending angles (45° and 90°) and inner diameters (0.6 mm to 4.5 mm) were used as the test section. The experimental setup was verified by comparing the current horizontal straight tube data with the well-known correlations. The Reynolds number range for this study was around 800 to 10,000. The experimental results clearly showed the effect of diameter and angle on the loss coefficient for the 45° and 90° elbows in the entire Reynolds number range. A critical region was shown to be obvious in the 45° elbows than that in the 90° elbows. Basically, the traditional fixed loss coefficient and the 2-K and 3-K methods did not predict the loss coefficients of the 45° and 90° mini-elbows with good accuracy. Therefore, an accurate correlation was developed for different diameters and angles of mini-elbows and the majority of loss coefficients data was predicted within an accuracy of ±20%.

Turbulent kinetic energy evolution in turbulent boundary layers during head-on interaction of premixed flames with inert walls for different thermal boundary conditions

The statistical behaviour of turbulent kinetic energy, and its transport in turbulent boundary layers during premixed flame-wall interaction for isothermal and adiabatic chemically inert walls have been analysed using a Direct Numerical Simulation (DNS) database. The terms due to the mean velocity gradient (commonly known as the production term) and viscous dissipation remain leading order contributors to the turbulent kinetic energy transport when the flame is away from the wall, similar to that in the corresponding non-reacting turbulent boundary layer, but in addition to these terms, the pressure dilatation and pressure transport contributions play leading order roles when the flame interacts with the wall. It has been found that the gradient hypothesis-based Reynolds stress closures in the context of the k−ε model may yield an inaccurate prediction of the mean velocity gradient term due to the counter-gradient behaviour of Reynolds stresses in the premixed flame cases considered in this analysis. The thermal boundary condition at the wall does not have a major influence apart from a higher wall friction velocity for adiabatic boundary condition than in the case of isothermal boundary condition. The assumption of local equilibrium of production and dissipation of turbulent kinetic energy has been found to be rendered invalid when the flame is either near to the wall or interacting with the wall. This invalidates the conventional log-law for mean streamwise velocity variation, and the wall functions derived based on production-dissipation balance equipped by the usual gradient hypothesis in the context of the standard k−ε model for premixed flame-wall interaction in turbulent boundary layers. Therefore, improved wall functions are necessary for Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction in turbulent boundary layers.

Fluid-structure interaction model of blood flow in abdominal aortic aneurysms with thermic treatment

Hyperthermia is one of the non-invasive therapy of an Abdominal Aortic Aneurysm (AAA), which is achieved by applying a heat source upon the AAA without surgical operation. This research paper considers laminar flow and heat transfer in a heated abdominal aortic aneurysm using an isothermal boundary condition. Heat is added to explicate the thermal treatment of a diseased artery. The blood is assumed as a non-Newtonian fluid based on the shear-thinning Carreau model. Two unequal aneurysms are assumed in the lower wall to simulate bulges or a disordered artery. Flexible wall segments are assumed in the upper wall and opposing to each aneurysm. The transient momentum and energy equations are solved based on the fluid–structure interaction (FSI) using the Arbitrary-Lagrangian–Eulerian (ALE) method. It is found that the shear stress is much higher for a higher index of the power-law fluid governing the blood viscosity and hence, it is strictly recommended to reduce the viscous nature of the blood in diseased vessels. It is found also that the thermal energy can be greatly transported across the blood at a higher Reynolds number, this means that the hyperthermia therapy becomes effective when blood flows violently through the aortic.

Kaviteye Yerleştirilen Açılı Kare Silindirden Doğal Ve Zorlanmış Taşınım

In this work, mixed convection from an inclined square cylinder in a cavity is numerically investigated. A commercial CFD solver Ansys Fluent is used to solve the problem. First, the inclined square cylinder is located at the center of the cavity, then the location of the cylinder is changed along the x-axis. The cavity walls are assumed to be adiabatic and the cylinder walls are assumed to be isothermal boundary condition. The Reynolds number, Re varies from 100 to 300 and the Grashof numbers, Gr range from 103 to 105 throughout the work. The working fluid is chosen as air at Prandtl number, Pr = 0.7. The Nusselt number, Nu variations, the distributions of velocity and isotherms are presented in Tables and Figures.

A similarity solution for laminar forced convection heat transfer from solid spheres

A new analytical solution, based on scale analysis and similarity transformation, is presented to solve a linearized form of the energy equation for the laminar forced convection over a sphere in a spherical coordinate system. Compact expressions for temperature, wall heat flux, and Nusselt number are developed as a function of the Reynolds number (ReD) and Prandtl number (Pr) for both isothermal and isoflux boundary conditions. A blending method is used to extend the range of the present analytical expression to cover 0<ReD<105 and 0.7<Pr<∞. The present analysis reveals that the theoretical averaged-Nusselt numbers for the laminar forced convection over isoflux (constant wall heat flux) and isothermal (uniform wall temperature) spheres are identical. The proposed model is verified by comparing the analytical expression with the available experimental data over various Reynolds and Prandtl numbers.

Combined particle image velocimetry and thermometry of turbulent superstructures in thermal convection

Turbulent superstructures in horizontally extended three-dimensional Rayleigh–Bénard convection flows are investigated in controlled laboratory experiments in water at Prandtl number ${Pr}=7$ . A Rayleigh–Bénard cell with square cross-section, aspect ratio $\varGamma =l/h=25$ , side length $l$ and height $h$ is used. Three different Rayleigh numbers in the range $10^{5} &lt; {Ra} &lt; 10^{6}$ are considered. The cell is accessible optically, such that thermochromic liquid crystals can be seeded as tracer particles to monitor simultaneously temperature and velocity fields in a large section of the horizontal mid-plane for long time periods of up to 6 h, corresponding to approximately $10^{4}$ convective free-fall time units. The joint application of stereoscopic particle image velocimetry and thermometry opens the possibility to assess the local convective heat flux fields in the bulk of the convection cell and thus to analyse the characteristic large-scale transport patterns in the flow. A direct comparison with existing direct numerical simulation data in the same parameter range of $Pr$ , ${Ra}$ and $\varGamma$ reveals the same superstructure patterns and global turbulent heat transfer scaling ${Nu}({Ra})$ . Slight quantitative differences can be traced back to violations of the isothermal boundary condition at the extended water-cooled glass plate at the top. The characteristic scales of the patterns fall into the same size range, but are systematically larger. It is confirmed experimentally that the superstructure patterns are an important backbone of the heat transfer. The present experiments enable, furthermore, the study of the gradual evolution of the large-scale patterns in time, which is challenging in simulations of large-aspect-ratio turbulent convection.