Constant Temperature Boundary Condition Research Articles

Nanoscale investigation of surface wettability distribution on bubble nucleation with variable temperature boundary condition

Surface wettability plays an essential role in bubble nucleation. In this article, the molecular dynamics simulation method is conducted to study the bubble nucleation of liquid argon film on a copper substrate with hybrid wettability. Unlike the constant temperature boundary condition, the variable temperature boundary condition is adopted to simulate the bubble nucleation process. The temperature gradually increases from 86 K to 200 K, so the substrate temperature at the bubble nucleation time can be obtained. The potential energy, kinetic energy, total energy, and temperature during bubble nucleation are analyzed. The results show that bubble nucleation occurs when the kinetic energy exceeds the potential energy barrier. A method is used to capture the bubble nucleation process, described from the perspective of total energy. The initial nucleation time of the hybrid wettability surface gradually reduces with the rise of the proportion of the hydrophilic part. Compared with the pure hydrophilic surface, the hybrid wettability surface can achieve faster initial nucleation time and lower nucleation temperature by altering the proportion of wettability. The potential energy and temperature distribution reveal the microscopic mechanism of bubble nucleation. This study provides theoretical guidance for the design of cooling surfaces of micro/nanoelectronic devices.

Investigation of the role of electrohydrodynamic forces on the heat transfer enhancement and solid extraction during melting of paraffin wax under constant temperature boundary conditions

The melting enhancement of paraffin wax is studied experimentally under the effect of electrohydrodynamic (EHD). Paraffin wax was melted under constant temperature boundary conditions with different applied DC voltage magnitudes and polarities, and different temperature gradients. The role of EHD forces was investigated by applying DC and AC square waves with different frequencies and offset values.It was found that the melting enhancement rises nonlinearly with increasing the voltage magnitudes. The maximum effective thermal conductivity under -10 kV was found to be 0.95 W/m-K in comparison with the value of 0.2 W/m-K for the pure liquid paraffin wax, with an enhancement ratio of 4.75.The EHD solid extraction phenomenon investigation showed that the extraction was detected for all the applied DC voltages. Small dendrites were observed to be pulled out from the mushy zone melt front and rise upwards in a rotational manner. It is concluded that the Coulomb force is the primary force for extraction while the formation of electroconvection cells is the main driving mechanism for the motion of the suspended dendrites in the liquid bulk. In addition, the AC studies revealed that the dielectrophoretic force is negligible in this study.

Numerical Analysis of Flow and Heat Transfer Characteristics of Lattice-Based Compact Heat Sinks

Abstract Single unit cell thick lattice frame materials have applications in efficient heat exchangers. This study is focused on strut-based sandwich-type configurations obtained through reticulation of unit cell topologies of tetrakaidecahedron (TKD), octet, and rhombic dodecahedron (DDC) shapes at a porosity of 0.9 with water as the working fluid. Interfacial heat transfer coefficient values on struts and endwalls were determined by imposing constant temperature boundary condition. Averaged heat transfer coefficient on the endwall was the highest for tetrakaidecahedron lattice whereas rhombic dodecahedron lattice exhibited the highest average interfacial heat transfer coefficients on the struts. Flow analysis showed the presence of strong secondary flow features on planes normal to the mean flow direction that demonstrated the unique flow mixing capabilities of these lattices. Reported interfacial heat transfer coefficient at struts and endwall can be used in volume-averaged computations of metal foams (representative of lattices' flow and thermal properties) under local thermal nonequilibrium.

Lattice Boltzmann simulation of complex thermal flows via a simplified immersed boundary method

A simplified immersed boundary (IB) lattice Boltzmann method (LBM) is developed in this study for simulating incompressible flows with heat transfer. The no-slip and constant temperature boundary conditions are both enforced by correcting the distribution functions. Similar to the previous distribution function correction (DFC)-IB method (S. Tao et al., 2021 [59]), the kinetic nature of LBM has been retained in the present scheme, which directly modifies the distribution functions other than models the interface as a source of IB force in the boundary treatment. However, this study presents two improvements. First, we reduce the number of distribution functions that need to be modified, and hence the computation load of the method can be reduced significantly. Furthermore, the correction term can be determined directly and explicitly, replacing the calculation of a local position-related adjustment parameter in the previous DFC-IB method. As a result, the computed velocity and temperature at the interface are consistent with their desired counterparts, and hence the Dirichlet boundary conditions can be accurately specified. The present simplified DFC IB method is validated in the simulations with both stationary and moving boundaries, including the flow past a hot cylinder, mixed convection in a square lid-driven cavity, and sedimentation of a particle in a long channel. The results demonstrate the accuracy and efficiency of the method.

Parametric investigation of internal Y-shaped fin configurations under natural convection in a concentric annulus

Natural convection heat transfer inside concentric annular enclosures has been well researched for decades. Such enclosures have been employed as intermediate layers between fluid streams in heat exchangers, particularly in latent heat thermal energy storage applications. Convection heat transfer coefficients originating from natural convection are relatively low, which drives the need for heat transfer enhancements by using extended surfaces (e.g., fins, heat sinks). In this study, numerical simulations are performed to investigate the natural convection heat transfer inside a concentric annulus in the presence of Y-shaped fins. Each Y-shaped fin has four important geometric parameters: (i) length of the fin base a, (ii) length of the fin branches b (i.e., the V-section), (iii) primary fin spacing angle θ, and (iv) secondary fin angle or branch angle α. Steady-state simulations are conducted using COMSOL Multiphysics® with constant temperature boundary conditions to generate the laminar natural convection profiles in the enclosure filled with air. The average Nusselt numbers, calculated at both the inner and outer walls of the enclosure, are used to gauge the heat transfer. The model is built with thin layer approximated fins first and subsequently compared to a modified model with fins with finite thickness. The optimized case using the thick fin model is found to yield a percent increase in Nu of 358.8% compared to the case with no fins. Lastly, the entropy generation is considered to determine the second law efficiency of the system, which is approximately 91%.

Hygro-thermo-mechanical modeling of thin-walled photovoltaic laminates with polymeric interfaces

A three-dimensional hygro-thermo-mechanical computational framework for photovoltaic (PV) laminates as well as its numerical implementation are established in this work. Aiming at an efficient thermo-mechanical modeling of thin-walled structures with polymeric interfaces, the solid shell element, which incorporates the enhanced assumed strain (EAS) method and the assumed natural strain (ANS) method for the alleviation of locking pathologies, and the interface element with thermo-visco-elastic cohesive zone model using fractional calculus are formulated. Besides, the finite element (FE) implementation of moisture diffusion in the 3D setting along the polymeric interfaces is also derived with the consideration of spatial and temporal variation of diffusivity due to its temperature and material decohesion dependencies. Given the difference between the time scales of moisture diffusion and thermo-mechanical problems, a staggered scheme is proposed for the solution of the coupled hygro-thermo-mechanical governing equations. Specifically, the relative displacement and temperature fields are firstly solved from the thermo-mechanical analysis, and then projected to the FE model of moisture diffusion to determine the diffusion coefficient for its subsequent analysis. The proposed method is applied to the simulation of three international standard tests of PV modules, namely the damp heat test, the humidity freeze test, and the thermal cycling test, and numerical predictions are compared with analytical solution for the damp heat case with a constant temperature boundary condition, as well as experimental electroluminescence (EL) images obtained from the thermal cycling test with the cyclic temperature boundary condition. A very satisfactory consistency demonstrates the effectiveness and reliability of this modeling framework.

Numerical evaluation of thermal energy storage rate in planar and cylindrical phase change material composites

Efficient design of high-performance phase change material (PCM) composites remains challenging, due to a lack of understanding regarding the relationships between the performance characteristics, and relevant design parameters. In this work, we adopt the effective composite approximation, as justified through experimental validation, and numerically investigate the effects of individual design variables on the thermal energy storage rate into phase change material composites under a constant temperature boundary condition. We isolate and describe the impact of (1) geometry, (2) volume fraction of metal, (3) time, (4) material thermophysical properties, and (5) the magnitude of the thermal boundary condition on the heat absorption rate normalized by heated area, by volume, and by mass of the active composite PCM. Finally, we assess the accuracy of the quasi-steady state approximation, as well as a modified version of the quasi-steady state approximation, which incorporates a term for sensible heating. These results are used to illustrate key relationships and trends which affect the volume fraction of metal in a composite PCM which maximizes the thermal energy storage rate across different performance metrics.

Turbulent melting characteristics of hybrid nano-enhanced molten salt phase change material in rectangular enclosure

The turbulent melting characteristics of hybrid nano-enhanced phase change material (HNEPCM) in a three-dimensional rectangular enclosure has been numerically investigated. The lower and upper walls are partially heated and cooled using constant surface temperature boundary condition and the other surfaces are specified with adiabatic boundary condition. The rectangular enclosure is filled with molten salt phase change material (PCM) of potassium nitrate (KNO3) with melting temperature of 334 °C. The transient melting rates of PCM are investigated by dispersing hybrid mono-dispersed spherical nanoparticles of Aluminum oxide (Al2O3) combined with Silicon dioxide (SiO2), Titanium dioxide (TiO2) and Multi-walled carbon nanotubes (MWCNT). The Rayleigh number (Ra) and particle volume fraction (ϕ) are varied in the range of 106≤Ra≤1010 and 2%≤ϕ≤5%. The turbulent phase change process of PCM is modeled using enthalpy–porosity approach with Lam–Bremhorst k−ϵ turbulence model. The three-dimensional governing equations are discretized using Finite difference technique and computations are carried out using Fortran 90 in-house code. The stronger thermal buoyancy force accelerates the melting rate and the melting pattern indicates the accumulation of large quantity of molten metal in the upper regions of the rectangular enclosure. The average melting velocity and turbulent kinetic energy of pure KNO3 PCM is increased by 51.17% and 77.84% by the addition of Al2O3−MWCNT hybrid nanoparticles. The impact of hybrid nanoparticles on the melting rate and thermal performance of PCM is significant in higher Rayleigh number flows than transitional flows. The present results are validated and are in close agreement with the benchmark experimental results.

Transient flow and thermal transport characteristics of wall-bounded turbulent dual jet with heated undulated wall

The present computational study aims to investigate and improve the turbulent dual jet cooling performance on an undulated surface with varying profiles. This study also aims to highlight the flow and thermal features arising owing to an undulated surface having amplitude (UA) between 0.0 and 0.7. The transient RANS equations are considered to simulate the complex behaviour of turbulent dual jet. Four Reynolds-Averaged Navier-Stokes (RANS) turbulence models, namely, standard k-ω, shear-stress transport (SST) k-ω, renormalization group (RNG) k-ϵ, and realizable k-ϵ models, are used to predict the thermal performance and flow field of a turbulent dual jet for a fixed Reynolds number (Re) of 10,000 and offset ratio of 2. A constant wall temperature and constant wall heat flux boundary conditions are used. For the amplitude between 0.0 and 0.1, a periodic vortex shedding phenomenon near the jet exit is observed. However, two stable counter-rotating vortices are observed with no periodic vortex shedding for higher values of UA ≥ 0.3. The axial position of the merge point reduces with a rise in the amplitude. It is also observed that the velocity profile becomes self-similar and the inflection point in the velocity profile rises near the wall region with amplitude. The time series of U and V velocity signals unveil sinusoidal oscillations and display almost the same peak to peak amplitude for UA ≤ 0.1 at various times. The FFT of U velocity signals displays a solo peak dominant frequency which is the same as shown by V velocity in the FFT plot corresponding to the Strouhal number of the vortex shedding phenomenon. The average Nusselt number is increased up to 63.89% and 65.03% for higher amplitude for the constant heat flux and constant temperature boundary conditions. Correlations have been also proposed for the average Nusselt number, the average heat flux and the merge point. The outcomes of the present research can be implemented for better design in automobile industries and utilization of cooling or heating jets in electronics, metal, and material processing.

The Stefan Problem With Internal Heat Generation in Spherical Coordinates

Abstract A weakly time-dependent equation for the evolution of the solid–liquid interface in spherical coordinates, driven by internal heat generation, is derived for constant surface temperature boundary conditions. The derivation comes by making an assumption that the interface moves slowly compared to the changes in the temperature so that the technique of separation of variables may be applied for Stefan numbers less than one. Under this approximation, we can separate the nonhomogeneous heat diffusion equation into transient and steady-state terms, and then integrate to get the temperature relations. With the temperature equations in hand, the derivatives are inserted into the interface equation giving a first-order differential equation for the location of the solid–liquid interface as a function of time. The results are compared to a previously derived quasi-static solution and a numerical simulation generated using the method of catching of the front. This method allows for direct tracking of a moving boundary via the calculation of the time it takes to move from node to node in a discretized grid characteristic of classical finite difference methods. Plots of the interface evolution show excellent agreement between the three methods, especially for lower Stefan numbers. The quality of the approximation decreases as the Stefan number increases, but the model is more accurate than the previously studied quasi-static model. For the Stefan numbers St = 1.0 and 10.0, the weakly time-dependent solutions are in better agreement with the numerical results than the quasi-static solutions.

Analytic Solution to Steady Heat Conduction with Transverse Radiation Heat Transfer

A unique analytic solution to the problem of steady heat conduction with radiative heat transfer normal to the conduction heat flow is presented. The solution is unique, as it does not assume zero temperature of the surroundings and addresses all possible tip boundary conditions for in-space applications. The temperature profiles in the direction of heat conduction are produced for a constant-temperature boundary condition at the base and three different boundary conditions at the tip: adiabatic, constant temperature, and radiative heat transfer. Approximate solutions to the implicit exact solution are also developed. An extended solution that includes convection for the adiabatic-tip boundary condition is also presented and compares very well to experimental data.

Aligned Magnetohydrodynamics (MHD) Flow of Hybrid Nanofluid Over a Vertical Plate Through Porous Medium

The future research on hybrid nanofluids need to be done as there are many applications of hybrid nanofluids. Some of them are electro-mechanical, renewable energy and manufacturing process application and also the application in automotive cooling. Therefore, this numerical study is conducted to investigate the aligned magnetohydrodynamics (MHD) flow of hybrid nanofluid over a vertical plate through a porous medium. The base fluid (water), silver and copper oxide flowed over a vertical plate in the presence of MHD and porous medium with boundary conditions of constant wall temperature by taking a few types of parameters into consideration. By using similarity transformation, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. Keller Box method is applied to solve numerically the nonlinear ordinary differential equations and the system is solved by using Fortran programming. The results of the study are illustrated graphically to show the behavior of velocity and temperature also skin friction and Nusselt number of hybrids nanofluid affected by the parameters. It is found that the velocity profiles increase, and temperature profiles decrease when the angle of aligned magnetic field, the interaction of magnetic parameter and local Grashof number increase while the velocity profiles decrease, and temperature profiles increase when the porous parameter and volume fraction of nanoparticles parameter increase. Besides, the skin friction of Ag-CuO-water is less than CuO-water and Nusselt number of Ag-CuO-water is higher than CuO-water.

Investigation of the Role of Electrohydrodynamic Forces on the Heat Transfer Enhancement and Solid Extraction During Melting of Paraffin Wax Under Constant Temperature Boundary Conditions

Investigation of the Role of Electrohydrodynamic Forces on the Heat Transfer Enhancement and Solid Extraction During Melting of Paraffin Wax Under Constant Temperature Boundary Conditions

Simulations of convective heat transfer in rectangular microchannel using thermal lattice Boltzmann method

The microfluidics becomes an emerging field of interest due to the advent of micro electro mechanical system. In this work simulations were performed to investigate the heat transfer phenomena in microchannel using the 2-D D2Q9 model of thermal lattice Boltzmann method. It is applicable in the whole range of slip velocity. The slip boundary condition which is combination of bounce and specular reflection was applied along with constant temperature boundary condition. For Knudson number greater than 0.001 (slip flow) fluid show slip at walls of the channel. The Reynolds number was kept at 10, Knudson Number 0.002, and aspect ratio (length/height) of 2. The fluid shows a slip of 8% of free stream velocity which is in the reported range. The resulting local Nusselt number was calculated which is responsible to quantify convective heat transfer. The simulation results were ahown to coraborate well with the analytical solution and empirical relations. Hence thermal lattice Boltzmann method satisfactorily predicted heat transfer and momentum transfer phenomena in microchannel.

Thermo-Bioconvection Performance of Nanofluid Containing Oxytactic Microorganisms Inside a Square Porous Cavity Under Constant and Periodic Temperature Boundary Conditions

Thermo-Bioconvection Performance of Nanofluid Containing Oxytactic Microorganisms Inside a Square Porous Cavity Under Constant and Periodic Temperature Boundary Conditions

Heat transfer in BCC lattice materials: Conduction, convection, and radiation

Research studies have recently been conducted on heat transfer in architected materials. As a type of rationally-designed lightweight material, lattices have received much attention in the past few years due to their multifunctional properties, mainly realized by the application of 3D printing techniques. In the present research, fluid flow and conduction, convection, and radiation heat transfer in three-dimensional periodic BCC lattices, as a topologically cubic example among a myriad of cellular architectures, are studied for a wide range of porosity (0.7–0.99) and Reynolds numbers (1–150) via a CFD analysis. The steady and incompressible flow of cool fluid with constant thermophysical properties inside a unit cell or an assembly of unit cells is simulated using the Fluent software. First, the hydrodynamic behavior of the fluid flow in the unit cell without a thermal gradient is studied. In the absence of radiation, conduction and convection heat transfer are explored under two different thermal conditions, namely Constant temperature at solid struts and Constant heat release from solid struts. The numerical results show that cell temperature increases for the constant temperature boundary condition and decreases for the constant heat release when the cell porosity decreases at the same Reynolds number. By considering radiation mechanism via the Discrete Ordinates Method, it is observed that radiative thermal conductivity increases by increasing the porosity. The increase, linearly correlated with the cell size, slightly enhances by increasing the solid radiative emission coefficient and the applied temperature difference. At lower porosities, the heat conduction, and at higher porosities, the radiation heat transfer plays a significant role in the effective thermal conductivity. At the average cell temperature of 1800 K, the ratio of radiative thermal conductivity to the effective thermal conductivity is 95% for the porosity of 0.99 and is 12% for the porosity of 0.7. After examining all three modes of heat transfer at the constant heat release thermal condition, it is found that the temperature of solid struts increases by decreasing the Reynolds number, leading to an increase of the ratio of radiation heat transfer to the total heat transfer (the ratio rises six times as the Reynolds number decreases from 150 to 1.5625 for the porosity of 0.99). For the constant heat release thermal condition, radiation heat transfer in BCC lattices can not be ignored when the porosity is high or the thermal conductivity of constitutive solid and the flow Reynolds number are low.

The influence of thermal boundary conditions of wellbore on the heat extraction performance of deep borehole heat exchangers

The previous studies on the heat transfer characteristics of deep borehole heat exchangers (DBHE) were mainly numerical simulations due to the high cost of in-situ experiments. The thermal boundary conditions of the wellbore used in these numerical simulations can be divided into the following three categories: (a) Robin or mixed boundary condition where a stable fluid with constant inlet water temperature flows through a coaxial tube. (b) Neumann boundary condition of constant heat flux locally or averaged as a whole through the wellbore, and (c) Dirichlet boundary condition of constant wellbore temperature. In this paper, a numerical study on the heat extraction performance of the deep borehole heat exchanger is carried out, the model is verified by comparing the obtained results with the experimental or numerical simulation results reported in the literature, and the influences of three thermal boundary conditions on heat output that varies with time were analyzed. The results indicate that the Neumann boundary condition commonly used in the analysis of shallow borehole heat exchangers are not suitable for actual DBHE. Under Dirichlet boundary conditions, the thermal disturbance radius after 120 days of continuous heat extraction is the largest. In addition, stable heat outputs under different operating parameters was obtained.

Sensitivity analysis of nanofluid flow over different flat tubes confined between two parallel plates using Taguchi method and statistical analysis of variance

In this research, the effect of simultaneous use of nanofluids and flat tubes to evaluate the efficiency of heat exchangers in the fluid flow over tandem tubes between two parallel plates is investigated and analyzed. The use of effective methods to reduce the number of numerical experiments and achieve accurate and reliable analysis with statistical techniques as well as the use of passive methods to improve the performance of tube heat exchangers are investigated in this study. The focus of the research is to achieve the optimal values of controlling factors, determine the effectiveness of each variable and evaluate the hydraulic and thermal behaviors of the flow structure. For this purpose, nanofluid containing aluminum oxide nanoparticles with volume fractions of 0–8%, flat tubes with 1.5, 2, 2.5 axial ratios, and square sections in comparison with circular tubes are used. Constant temperature boundary conditions are applied on the confining plates and the surface of the tubes. To perform sensitivity analysis, the Taguchi method with L25 orthogonal array and statistical analysis of variance (ANOVA) are utilized. The obtained results show that by changing the cross-section and further flattening, heat transfer and pressure drop decrease concurrently. Moreover, with increasing the volume fraction of nanoparticles, both parameters related to heat transfer rate and flow pressure drop increase. Examining the combination of the two output parameters of the flow and obtaining the efficiency evaluation criterion, it is determined that flattening the tubes, in contrast to increasing the volume fraction of nanoparticles, increases the efficiency of the heat exchanging modules. One of the important results obtained in utilizing the Taguchi method with ANOVA analysis, in addition to reducing the numerical calculations by 80%, is accurate and reliable findings that are confirmed by comparison with the full factorial method.

Numerical analysis of hydromagnetic transport of Casson nanofluid over permeable linearly stretched cylinder with Arrhenius activation energy

The current study is modelled to evaluate numerous flow applications in applied sciences espeically in nuclear reacting cooling, geothermal reservoirs, chemical engineering and thermal oil recovery. The present research investigates the magnetohydrodynamic transport of non-Newtonian Casson Nano fluid past due to stretching permeable cylinder by employing Buongiorno's mathematical model. Unlike the frequently used constant temperature and concentration boundary conditions, the present study employed convective boundary conditions. The influences of important sundary parameters like an inclination of magnetic field, joule heating, viscous dissipation, thermophoresis, Brownian motion, Arrhenius activation energy, and chemical reaction are taken into account. The physical flow phenomenon is modelled and after that transformed into a non-dimensional form by incorporating suitable similarity transforms. For solution purpose, Runge-Kutta-Fehlberg fourth-fifth order (RKF45) numerical integrating procedure along with shooting algorithm is adopted. Impacts of several emerging parameters on the velocity distribution, temperature distribution, and concentration distribution, coefficient of skin friction, Sherwood number, and Nusselt number are clarified via graphical and tabular results. It seems to establish that with the rise of chemical reaction parameter chemical reaction parameter the nanoparticles concentration distributions decline while the contrasting trend is perceived for activation energy parameter.

Three-dimensional condensation in a vertical channel filled with metal foam using a pseudo-potential lattice Boltzmann model

In this study, three-dimensional condensation in a domain filled with metal foam is investigated using the lattice Boltzmann method for the first time. A recently proposed two-phase pseudo-potential lattice Boltzmann model is extended to 3D phase-change problems by adding the energy equation with the Peng–Robinson equation of state. The phase-change model is validated using the thermodynamic consistency test, Laplace law, contact angle test, and D2-law. To provide accurate pore-scale analysis, both the flow and energy equations are discretized with the D3Q27 model. Moreover, the metal foam cell structure is reconstructed by implementing the Lord Kelvin model on the mesh nodes. The results are reported in terms of condensation modes, droplet nucleation, growth and removal, heat flux on the walls and mass flow rate of the discharged condensate. Furthermore, the effects of the Jakob number (in range of Ja=0.06 to 0.24) and cell size (S=16,32, and 64) are investigated regarding the condensation process, average heat flux, and mass flow rate. The condensation curve under constant temperature boundary condition is presented for different configurations. It is shown that the model is capable of simulating convection heat transfer along with different condensation modes, including dropwise and filmwise modes. Our results revealed that the onset of nucleation and mode transition occurs at lower Jakob values as the metal foam cell size is increased. Also, it is shown that at a fixed configuration, increasing the Jakob number affects the condensate mass flow rate more than heat flux. The results of this study could be useful in the design of phase-change heat exchangers with metal foam construction.