Improvement of fuel consumption and maintenance of heating furnaces using a modified heating pattern

This article studies the transient heat conduction in a slab when passing through various sections of the furnace, and focuses on the thickness of the scale layer formed on the slab. The transient heat conduction behavior of a slab in various sections of the heating furnace is analyzed using the Laplace transformation method, including the pre-heating zone, the first heating zone, the second heating zone, and the soaking zone. The heating pattern of the furnace is then modified to reduce fuel consumption. The simulation results show that the scale layer formed on the slab significantly influences the quality of the hot rolled coil formed, and how the furnace parameters affect the efficiency of the furnace and the quality of the coil.

Model of Fractional Heat Conduction in a Thermoelastic Thin Slim Strip under Thermal Shock and Temperature-Dependent Thermal Conductivity

The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of order
is applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.

Analytical design of effective thermal conductivity for fluid-saturated prismatic cellular metal honeycombs

A comparative optimal design of fluid-saturated prismatic cellular metal honeycombs （PCMHs） having different cell shapes is presented for thermal management applications. Based on the periodic topology of each PCMH, a unit cell （UC） for thermal transport analysis was selected to calculate its effective thermal conductivity. Without introducing any empirical coefficient, we modified and extended the analytical model of parallel-series thermal-electric network to a wider porosity range （0.7 ~ 0.98） by considering the effects of two-dimensional local heat conduction in solid ligaments inside each UC. Good agreement was achieved between analytical predictions and numerical simulations based on the method of finite volume. The concept of ligament heat conduction efficiency （LTCE） was proposed to physically explain the mechanisms underlying the effects of ligament configuration on effective thermal conductivity （ETC）. Based upon the proposed theory, a construct strategy was developed for designing the ETC by altering the equivalent interaction angle with the direction of heat flow： relatively small average interaction angle for thermal conduction and relatively large one for thermal insulation.

NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY

In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension.If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only,it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves,while the initial perturbation and the strength of rarefaction waves are suitably small.

Design and Analysis of a Thermally Insulating and Heating Scheme for Piezoelectric Stack Actuators Used in the Cryogenic Environment

In cryogenic wind tunnel tests,piezoelectric stacks are adopted to realize the vibration control of the cantilever sting.However,the free stroke and blocking force of the piezoelectric stack would decrease dramatically as the temperature decreases.This paper proposes a convenient and effective warming structure for the piezoelectric stack,which could keep it working at operating temperatures when the ambient temperature drops.The piezoelectric stack actuator is wrapped with the heating film,and this resulting assembly is then wrapped with the aerogel material for thermal insulation.Both ends of the piezoelectric stack actuator make direct contact with the payload structure.Both one-dimensional and two-dimensional theoretical analyses of the heating conduction problem of the piezoelectric stack actuator are conducted.These analyses results are compared with those of the finite element simulation analysis.The finite element method results show a good consistency with the two-dimensional theoretical results,and a slight deviation of only 0.91 K is observed,indicating its potential for protecting piezoelectric stacks at low temperatures.

The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas

Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.

Interrelationships between leaf heat conductivity and tissue structures of different varieties of Populus tomentosa Carr

Plant heat conductivity largely depends on tissue structure. Different structures lead to different heat conductivity. As well, water transfer also plays a very important role in heat transfer in plants. We have studied leaf heat conductivity and tissue structure of 3- and 30-year-old Populus tomentosa Carr. trees using infrared thermal imaging, steady state heat conductivity surveys and paraffin section and investigated the relationship between leaf heat conductivity, tissue structure and water content of leaves. The results show that the temperature on leaf surfaces among the various varieties of trees was almost the same. Leaf heat conductivity, temperature and water content of leaves are positively correlated. The thicker the leaf tissue structures, the larger the heat resistance. That is, the tighter the cells and the smaller the interspaces, the smaller the heat conductivity, which is not conducive for heat transfer.

Finite Difference Approach for Estimating the Thermal Conductivity by 6-point Crank-Nicolson Scheme

Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured experimentally. The method is a direct approach of second-order and the key advantage of the present method is that it is not required a priori knowledge of the functional form of the unknown thermal conductivity in the calculation and the thermal parameters are estimated only according to the known temperature distribution. Two cases were numerically calculated and the influence of experimental deviation on the precision of this method was discussed. The comparison of numerical and analytical results showed good agreement.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Dynamic response of a thermal transistor to time-varying signals

Thermal transistor,the thermal analog of an electronic transistor,is one of the most important thermal devices for microscopic-scale heat manipulating.It is a three-terminal device,and the heat current flowing through two terminals can be largely controlled by the temperature of the third one.Dynamic response plays an important role in the application of electric devices and also thermal devices,which represents the devices’ability to treat fast varying inputs.In this paper,we systematically study two typical dynamic responses of a thermal transistor,i.e.,the response to a step-function input(a switching process)and the response to a square-wave input.The role of the length L of the control segment is carefully studied.It is revealed that when L is increased,the performance of the thermal transistor worsens badly.Both the relaxation time for the former process and the cutoff frequency for the latter one follow the power-law dependence on L quite well,which agrees with our analytical expectation.However,the detailed power exponents deviate from the expected values noticeably.This implies the violation of the conventional assumptions that we adopt.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

Experiments and Analyses on Heat Transfer Characteristics from a Solid Wall to a Strip-ShapedWick Structure

Centered or striped wick structures have been used to develop ultrathin heat pipes.Differing from traditional heat pipes,the centered or striped wick structures leave noncontact container surfaces with the wick structure.In this study,experiments andnumerical analyseswere conductedtoinvestigate the influenceof thesenoncontact surfaces.In the experiments,a strip-shaped wick structure was placed vertically,the top was sandwiched between wider rods and the bottom was immersed in a working fluid.The rod width was greater than the wick width;thus,noncontact surfaces were left between the rod and the wick structure.The heat was applied from the rod to the wick structure,and the evaporation heat transfer characteristics of the working fluid from the wick structure were evaluated.Water was used as the working fluid.The experiments were conducted by varying the rod and wick widths.The experimental results were obtained when the wick structures were placed separately.In the numerical analyses,the temperature and heat flux distributions in the rod were obtained.From the experimental and numerical results,it was confirmed that the noncontact surfaces caused the heat flux in the rod near both surfaces of the wick structure to concentrate,which increased the evaporation thermal resistance of the wick structure.A reduction in the noncontact surface area by increasing the wick width was found to be effective in decreasing the evaporation thermal resistance and increasing themaximumheat transfer rate of the wick structure.The separation of the wick structure increased the evaporation surface area.However,its effectiveness was limited when the heat transfer rate was small.

Variational Approach to 2D and 3D Heat Conduction Modeling

The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.

Variational Approach to Heat Conduction Modeling

It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte proved that such process can be described by Heaviside’s telegraph equation. This paper shows that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that the equation of heat conduction with finite velocity propagation of the thermal disturbance can be obtained as a solution to one variational problem.

Sterilization Effect of Cooking Process for Guilin Rice Noodles Based on Heat Conduction Model

Guilin rice noodles, a unique cuisine from Guilin, Guangxi, is renowned both domestically and internationally as one of the top ten “Guilin Classics”. Utilizing a heat conduction model, this study explores the effectiveness of the cooking process in sterilizing Guilin rice noodles before consumption. The model assumes that a large pot is filled with boiling water which is maintained at a constant high temperature heat resource through continuous gentle heating. And the room temperature is set as the initial temperature for the preheating process and the final temperature for the cooling process. The objective is to assess whether the cooking process achieves satisfactory sterilization results. The temperature distribution function of rice noodle with time is analytically obtained using the separation of variables method in the three-dimensional cylindrical coordinate system. Meanwhile, the thermal diffusion coefficient of Guilin rice noodles is obtained in terms of Riedel’ theory. By analyzing the elimination characteristics of Pseudomonas cocovenenans subsp. farinofermentans, this study obtains the optimal time required for effective sterilization at the core of Guilin rice noodles. The results show that the potential Pseudomonas cocovenenans subsp. farinofermentans will be completely eliminated through continuously preheating more than 31 seconds during the cooking process before consumption. This study provides a valuable reference of food safety standards in the cooking process of Guilin rice noodles, particularly in ensuring the complete inactivation of potentially harmful strains such as Pseudomonas cocovenenans subsp. farinofermentans.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

Decay rates and time lags of heat conduction in building construction under field conditions

The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.

SEEBECK EFFECT IN OXYGEN PROBE USED FOROXYGEN DETERMINATION IN LIQUID STEEL

Heat conduction in oxygen probe was analyzed by means of non-steady state method and measured using 'double probe' arrangement. The results showed that during the response process the thermal emf was decreased exponentially with the time and in case of low oxygen level the Seebeck coefficient and thermal conductivity of solid electrolyte agreed well with those in literatures.

Dynamic Calibration of the Cutting Temperature Sensor of NiCr/NiSi Thin-film Thermocouple

In high-speed cutting, natural thermocouple, artificial thermocouple and infrared radiation temperature measurement are usually adopted for measuring cutting temperature, but these methods have difficulty in measuring transient temperature accurately of cutting area on account of low response speed and limited cutting condition. In this paper, NiCr/NiSi thin-film thermocouples（TFTCs） are fabricated according to temperature characteristic of cutting area in high-speed cutting by means of advanced twinned microwave electro cyclotron resonance（MW-ECR） plasma source enhanced radio frequency（RF） reaction non-balance magnetron sputtering technique, and can be used for transient cutting temperature measurement. The time constants of the TFTCs with different thermo-junction film width are measured at four kinds of sampling frequency by using Ultra-CFR short pulsed laser system that established. One-dimensional unsteady heat conduction model is constructed and the dynamic performance is analyzed theoretically. It can be seen from the analysis results that the NiCr/NiSi TFTCs are suitable for measuring transient temperature which varies quickly, the response speed of TFTCs can be obviously improved by reducing the thickness of thin-film, and the area of thermo-junction has little influence on dynamic response time. The dynamic calibration experiments are made on the constructed dynamic calibration system, and the experimental results confirm that sampling frequency should be larger than 50 kHz in dynamic measurement for stable response time, and the shortest response time is 0.042 ms. Measurement methods and devices of cutting heat and cutting temperature measurement are developed and improved by this research, which provide practical methods and instruments in monitoring cutting heat and cutting temperature for research and production in high-speed machining.