Steady-state Heat Research Articles

Two-dimensional numerical manifold method for heat conduction problems

The numerical manifold method (NMM) is a calculation method based on Galerkin's variation and contains a dual covering system. Therefore, the NMM can easily deal with the construction of high-order manifold elements and is convenient for adaptive analysis. This study employed the NMM to simulate steady-state and transient heat conduction problems. The system equations were derived and a penalty function method was applied to deal with the boundary conditions. By simulating calculation examples for a one-dimensional bar, cuboid rock specimens, and thick-walled cylinders, the process of solving steady-state and transient heat-conduction problems and the influence law of the temperature pattern are demonstrated. Moreover, the convergence and effectiveness of the NMM in handling two-dimensional (2D) steady-state and 2D transient heat conduction problems was verified.

Ionic heat dissipation in solid-state pores.

Energy dissipation in solid-state nanopores is an important issue for their use as a sensor for detecting and analyzing individual objects in electrolyte solution by ionic current measurements. Here, we report on evaluations of heating via diffusive ion transport in the nanoscale conduits using thermocouple-embedded SiNx pores. We found a linear rise in the nanopore temperature with the input electrical power suggestive of steady-state ionic heat dissipation in the confined nanospace. Meanwhile, the heating efficiency was elucidated to become higher in a smaller pore due to a rapid decrease in the through-water thermal conduction for cooling the fluidic channel. The scaling law suggested nonnegligible influence of the heating to raise the temperature of single-nanometer two-dimensional nanopores by a few kelvins under the standard cross-membrane voltage and ionic strength conditions. The present findings may be useful in advancing our understanding of ion and mass transport phenomena in nanopores.

Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines.

We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities do not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in nonequilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.

Analytical solution for temperature equation of a fin problem with variable temperature-dependent thermal properties: Application of LSM and DTM-Pade approximant

Temperature variation through a longitudinal fin with linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient, subject to radiative heat flux and convective heat transport is explained in the present examination. For the radiative heat flux, the Rosseland approximation is incorporated and convection mode of energy transmission is accounted on the fin's surface. The associated physical problem is developed in such a manner that the steady-state heat transmission problem is governed with the help of dimensionless variables signified by a second order differential equation (ODE). To solve this equation, an analytical approach, DTM-Pade, and the LSM are implemented. Moreover, the consequence of a few non-dimensional factors on the temperature field are depicted graphically. The investigation's main findings illustrate that a significant decline in the thermal field is caused by an increment in the convection and the radiation mechanism. The internal development of heat affects the thermal distribution in the fin.

The application of FEM-BEM coupling method for steady 2D heat transfer problems with multi-scale structure

This paper presents a finite element method and boundary element method (FEM-BEM) coupling scheme to study the steady-state 2D heat transfer problem for structures with multi-scale features. Based on the geometric information or material properties, the considered model is divided into FE sub-domain and BE sub-domain. The closed BE sub-domain in the mixed FEM-BEM model is defined as a finite super-element for which the effective stiffness matrix and effective fluxes are obtained by the self written BE code and hence can be assembled to the FE systems by the user subroutine (UEL) provided in ABAQUS. This method offers a number of key improvements compared with current analysis methods available for multi-scale structures. These improvements are: (i) the flexibility and convenience by using the powerful pre/post-processing in ABAQUS; (ii) the higher accuracy of the solution over the classical FEM; and (iii) the computational cost and time can be highly reduced by using the coupling method. Numerical results are compared with reference solutions and demonstrate the accuracy and effectiveness of the proposed approach.

Characteristic of weld bead using flat wire electrode in GMAW inline during the process: An experimental and numerical analysis

This paper focusses on effect of flat wire electrode on gas metal arc welding (FW-GMAW) inline during the process to improve quality of weld bead. Since the flat wire electrode perimeter has enlarged, the turbulence of the molten droplet characteristics is altered due to the effect of electromagnetic force. To bring out, butt joint welding are proven with use of the flat wire electrode. The experimental results indicated that, the flat wire electrode and their orientations are significantly factors to improve the weld bead dimensions, due to the increased in steady state temperature and heat density. The end result also evident that the depth-to-width (D/W) ratio was improved on an average by 7.7% than regular wire electrode used in GMAW. To validate, a comprehensive numerical model was developed, the result confirmed that the initial arc and steady state temperature are high for FW-GMAW. In addition, improvements in metallurgical and mechanical properties are discussed in this paper.

Steady-State Heat Flux Prediction to Slabs in a Walking Beam Furnace

After casting steel slabs are reheated in a reheat furnace to temperatures in the range 1200-1250 °C in order to be suitable for rolling. The high energy requirements and the importance of reheating for quality control are the motivation behind numerically modeling the furnace. Computational fluid dynamics allows us to understand the fundamental physics with great detail. It is however unclear how assumptions of such models influence the results of the simulations. In this work a steady-state model was analyzed, and it was found that the chosen slab temperature profile can underestimate the average heat flux on the slab surface by 30%. A slab model was employed to simulate the transient slab temperatures which results in an underestimation of the average slab temperatures by about 500 °C for the case with reduced fluxes. The uniform slab temperature assumption also results in the overestimation of heat fluxes on its front and side face.

Numerical Study of Heat Transfer by Natural Convection in Concentric Hexagonal Cylinders Charged with a Nanofluid

In this document, a numerical study of the natural convection of steady-state laminar heat transfer in a horizontal ring between a heated hexagonal inner cylinder and a cold hexagonal outer cylinder. A Cu - water nanofluid traverses this annular space. The system of equations governing the problem was solved numerically by the fluent calculation code based on the finite volume method. Based on the Boussinesq approximation. The interior and exterior sides from the two cylinders are maintained at a fixed temperature. We investigated the impacts of various thermal Rayleigh numbers (103≤ Rat ≤2.5x105), and the volume fraction from the nanoparticles (0≤ Ø ≤0.12) on fluid flow and heat transfer performance. It is found that in high thermal Rayleigh numbers, a thin thermal boundary layer is illustrated at the flow that heavily strikes the ceiling and lower from the outer cylinder. In addition, the local and mean Nusselt number from a nanofluid are enhanced by enhancing the volume fraction of the nanoparticles.The results are shown within the figure of isocurrents, isotherms, and mean and local Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.

Mechanistic Understanding of DNA Denaturation in Nanoscale Thermal Gradients Created by Femtosecond Excitation of Gold Nanoparticles

There is significant interest in developing photothermal systems that can precisely control the structure and function of biomolecules through local temperature modulation. One specific application is the denaturation of double-stranded (ds) DNA through femtosecond (fs) laser pulse optical heating of gold nanoparticles (AuNPs); however, the mechanism of DNA melting in these systems is not fully understood. Here, we utilize 55 nm AuNPs with surface-tethered dsDNA, which are locally heated using fs laser pulses to induce DNA melting. By varying the dsDNA distance from the AuNP surface and the laser pulse energy fluence, this system is used to study how the nanosecond duration temperature increase and the steep temperature gradient around the AuNP affect dsDNA dehybridization. Through modifying the distance between the dsDNA and AuNP surface by 3.8 nm in total and the pulse energy fluence from 7.1 to 14.1 J/m2, the dehybridization rates ranged from 0.002 to 0.05 DNA per pulse, and the total amount of DNA released into solution was controlled over a range of 26-93% in only 100 s of irradiation. By shifting the dsDNA position as little as ∼1.1 nm, the average dsDNA dehybridization rate is altered up to 30 ± 2%, providing a high level of control over DNA melting and release. By comparing the theoretical temperature around the dsDNA to the experimentally derived temperature, we find that maximum or peak temperatures have a greater influence on the dehybridization rate when the dsDNA is closer to the AuNP surface and when lower laser pulse fluences are used. Furthermore, molecular dynamics simulations mimicking the photothermal heat pulse around a AuNP provide mechanistic insight into the stochastic nature of dehybridization and demonstrate increased base pair separation near the AuNP surface during laser pulse heating when compared to steady-state heating. Understanding how biological materials respond to the short-lived and non-uniform temperature increases innate to fs laser pulse optical heating of AuNPs is critical to improving the functionality and precision of this technique so that it may be implemented into more complex biological systems.

New application of MOL-PACT for simulating buoyancy convection of a copper-water nanofluid in a square enclosure containing an insulated obstacle

<abstract> <p>In this study, we have simulated transient and steady state free convection flow and heat transfer inside a square enclosure filled with a copper-water nanofluid of spherical shape nanoparticles following Tiwari-Das model. The cavity containing an insulated rectangular obstacle of height ranging from 0% to 50% of the cavity side-length. The vertical sides of the enclosure are kept at different temperatures, while the flat sides are assumed to be adiabatic as the obstacle. The combined method of lines/penalty-artificial compressibility technique (MOL-PACT) has been applied to solve the dimensional time dependent mathematical model after converting it into a non-dimensional structure. The combined method of lines/penalty-artificial compressibility technique is recently successfully applied to simulate free convection of MHD fluid in square enclosure with a localized heating. The extension of this promising technique for studying heat transfer of nanofluids is one of the objectives of this paper. Another objective of the study is to inspect the impact of several model parameters such as, the obstacle height, nanoparticles volume-fraction, nanoparticles radius and Rayleigh number on streamlines, temperature distribution and Nusselt number as an expression of heat transfer inside the enclosure. The results have been discussed and shown graphically. Comparisons with former results for related cases in the literature are made and reasonably good agreements are observed.</p> </abstract>

Study on influence of forced vibration of cooling channel on flow and heat transfer of hydrocarbon fuel at supercritical pressure

The cooling channel of a scramjet is the fundamental structure of the active thermal protection for an engine. Till now, studies have focused mainly on the steady-state flow and heat transfer process in the cooling channel. However, the vibration intensity of an engine increases sharply as the flight speed increases, because of which, the flow and heat exchange mechanisms based on the cooling channel under stable conditions cannot be applied under vibration. In this study, experimental methods are used to study the characteristics of the forced vibration of a cooling channel on the flow and heat transfer of hydrocarbon fuel at supercritical pressure. In addition, the influences of different vibration frequencies and vibration amplitudes on the flow and heat transfer are analyzed. The research results show that at supercritical pressure, when the fuel temperature is below the critical temperature and the inner wall temperature is above the critical temperature, external vibrations would enhance the heat transfer characteristics of the cooling channel. However, when the pressure and temperature are unstable, the forced vibration of the cooling channel would suppress the instability of temperature and pressure while strengthening the heat exchange.

Predicting subdifferential switching surface in a steady-state complex heat transfer problem using deep learning

Predicting subdifferential switching surface in a steady-state complex heat transfer problem using deep learning

Study of the heat transfer performance of a loop heat pipe with aluminum wick

This study used aluminum powder as a raw material to fabricate a wick for loop heat pipes by the powder metallurgy method and took advantage of the excellent corrosion resistance, low density and low cost of aluminum. The average pore diameter, porosity and permeability of the aluminum wicks were 9 ?m, 47.65%, and 2.1 ? 10?13 m?2, respectively. Then, to verify the feasibility of the aluminum wick, it was installed into a loop heat pipe to test the heat transfer performance. The experimental results showed that the loop heat pipe could transport a heating load of 130 W with a thermal resistance of 0.04 K/W under horizontal condition. A steady-state loop heat pipe mathematical model was developed, and the numerical results were compared with the experimental data. The results show that the model data are consistent with the experimental data, which means that Al wicks are suitable for use in the case of a high heating load and light weight.

Numerical and experimental investigationg of a turbine guide vane with conjugate heat transfer method

Three-dimensional steady-state conjugate heat transfer numerical method was utilized to study the flow and heat transfer characteristics of a turbine guide vane. In experiment, a real-sized turbine vane model and corresponding test section were designed. We verified the simulation accuracy of different turbulence models, coupling with transition model and limiter factor in conjugate heat transfer method. Compared with the experimental results, the results indicated that the SST model shows better accuracy and economy than other models studied in this paper.

Isogeometric Boundary Element Method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

Isogeometric Boundary Element Method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

A Steady-State Inverse Heat Conduction-Convection Conjugated Problem in Determining Unknown Spatially Dependent Surface Heat Flux

A Steady-State Inverse Heat Conduction-Convection Conjugated Problem in Determining Unknown Spatially Dependent Surface Heat Flux

Neural Networks to Solve Partial Differential Equations: A Comparison With Finite Elements

We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM ($0.015$ for a solution on the order of unity) is easily achieved with NN too without much tuning of the hyperparameters. Accuracies below $0.01$ instead require refinement with an alternative optimizer to reach a similar performance with NN. A rough comparison between the Floating Point Operations values, as a machine-independent quantification of the computational performance, suggests a significant difference between FEM and NN in favour of the former. This also strongly holds for computation time: for an accuracy on the order of $10^{-5}$, FEM and NN require $54$ and $1100$ seconds, respectively. A detailed analysis of the effect of varying different hyperparameters shows that accuracy and computational time only weakly depend on the major part of them. Accuracies below $0.01$ cannot be achieved with the "adam'' optimizers and it looks as though accuracies below $10^{-5}$ cannot be achieved at all. In conclusion, the present work shows that for the concrete case of solving a steady-state 2D heat equation, the performance of a FEM algorithm is significantly better than the solution via networks.

Influence of contact pressure on the thermal contact conductance of layered metallic sheets

For the optimisation of the annealing process of aluminium coils, simulation of the process is often performed. To simulate the process with higher accuracy, reliable input parameters are required, and thermal conductivity (thermal contact conductance) is one of them. In the present study, a method to measure the thermal conductivity and thermal contact conductance of metallic sheets were developed based on the steady-state comparative longitudinal heat flow. The apparatus was built with a compression test machine, and thus it allows to control the pressure to the sample and carry out the measurements at different contact pressure. An equipped heater allows to heat the sample to 573 K. To evaluate the thermal conductance at the interface, a thermal resistance network model was applied. The measurements were carried out with an aluminium alloy (AA3003 sheets). In addition to the thermal contact conductance measurements, the surface roughness of the sheets was also investigated. The semi-empirical equation for the relationship between thermal contact conductance and contact pressure was obtained based on the measurement results.

Numerical calculations of heat transfer during FC-72 flow in minichannels performed with ANSYS software

The main aim of the paper was to apply numerical calculations in ANSYS software to solve problems related to steady-state convective heat transfer during FC-72 flow in a minichannel heat sink. A mathematical model of fluid flow in a minichannel heat sink was proposed. Data from research conducted on the experimental stand with asymmetrically heated test section were selected. The element cooled by fluid flowing in minichannels was a thin foil. The distribution of temperature on the outer heated foil surface was measured using infrared thermography. Thermocouples and pressure meters were installed at the inlet and outlet of the minichannels. A CAD model was prepared with respect to the geometry of the test section. The mesh was created in ANSYS Mesher. A suitable model of turbulences was selected and materials temperature dependencies were considered. The iterative process of creating the model and comparing the results obtained by the CFD calculation was used to capture the fluid behavior. The velocity magnitudes and temperature distributions were presented as the main results of numerical calculations.

Development of a two-dimensional mathematical model of flow boiling heat transfer in micro- and minichannels

The paper concerns flow boiling heat transfer in micro- and minichannels. In the mathematical model, the steady state heat transfer process in a single asymmetrically heated minichannel was considered. Calculations with the use of Trefftz functions were based on the data from own experiments. The temperature of the heater and the refrigerant were assumed to satisfy the Laplace equations and the energy equation respectively. The problem was solved by the Trefftz method using two sets of Trefftz functions. The known heater and refrigerant temperature distributions were used to determine the heat transfer coefficient at the heater – refrigerant contact. To verify the proposed mathematical model, data from experiments were applied to calculations. The essential part of the experimental stand was the test section which comprises a minichannel heat sink. The heated element for Fluorinert FC-72 flowing along minichannels was a thin foil. The temperature of its outer side was measured using infrared thermography. Thermocouples and pressure transducers installed at the inlet and outlet of the test section monitored fluid temperature and pressure. Mass flow rate, the current supplied to the heater and the voltage drop were also recorded. The resulting graphs presented thermograms of measured temperature on outer surface of the heater, temperature distributions of fluid temperature and local values of the heat transfer coefficient.