One-dimensional Heat Research Articles

Heat-Transfer Stability of Porous Fibrous Composition under Different Condition

In this paper, the influences of different conditions on heat-transfer stability of porous fibrous composition were analyzed by the one-dimensional unsteady heat transfer model. It was resulted that the surface condition of composition was key parameter for heat performance during different thermal process. Great humidity and thermal difference caused the heat transfer fluctuating of material covering, and then changed the thermal conductivity. For the insulation materials under low temperature, the heat performance was sharply fluctuated nearby 0°C.

Transient Thermoelastic Analysis of a Solid Cylinder Containing a Circumferential Crack Using the C–V Heat Conduction Model

This article presents the transient thermoelastic analysis in a long solid cylinder with a circumferential crack using the C–V heat conduction theory. The outer surface of the cylinder is subjected to a sudden temperature change. The Laplace transform technique is adopted to solve the one-dimensional hyperbolic heat conduction equation, and the axial thermal stress is obtained for the un-cracked cylinder in the Laplace domain. Then this axial thermal stress with a minus sign is applied to the crack surface to form a mixed boundary value problem in the cylindrical coordinate system. A singular integral equation is derived by applying the Fourier and Hankel transforms to solve the mode I crack problem. The transient thermal stress intensity factors are obtained by solving the singular integral equation numerically. The influences of thermal relaxation time, crack geometry, and Biot's number upon transient temperature distributions, axial stress fields, and stress intensity factors are analyzed.

A new inverse problem for the determination of textile fabrics thickness

This paper deals with a new inverse problem of estimating textile fabrics thickness based on a one-dimensional steady-state heat and moisture transfer model. First, we give an existence and uniqueness theorem for the solution to the heat and moisture transfer problem in the Banach space. Then we present an inverse problem for the determination of textile fabrics thickness and formulate the inverse problem as an optimization problem with maximum probability, according to the requirement of heat-moisture comfort of clothing. Moreover, considering that the objective function of the proposed optimization problem may not be continuous and the points achieving maximum value may not be unique, we proceed to recast this inverse problem as a minimum norm with a maximum probability constraint problem. Finally, we use a static penalty method to convert the constrained problem into an equivalent unconstrained minimization problem and obtain the solution for the optimization problem by a stochastic search method known as particle swarm optimization algorithm. Numerical experiments show that our new model and its equivalent transformation is quite acceptable, and the proposed numerical method is valid and robust.

Estimation of slip parameters associated with frictional heating during the 1999 Taiwan Chi-Chi earthquake by vitrinite reflectance geothermometry

Abstract To estimate the slip parameters and understand the fault lubrication mechanism during the 1999 Taiwan Chi-Chi earthquake, we applied vitrinite reflectance geothermometry to samples retrieved from the Chelungpu fault. We found a marked reflectance anomaly of 1.30% ± 0.21% in the primary slip zone of the earthquake, whereas the reflectances in the surrounding deformed and host rocks were 0.45% to 0.77%. By applying a kinetic model of vitrinite thermal maturation together with a one-dimensional heat and thermal diffusion equation, we determined the shear stress and peak temperature in the slip zone during the earthquake to be 1.00 ± 0.04 MPa and 626°C ± 25°C, respectively. Taking into account the probable overestimation of the temperature owing to a mechanochemically enhanced reaction or flash heating at grain contacts, this temperature should be considered an upper limit. The lower limit was previously constrained to 400°C by studies of fluid-mobile trace-element concentrations and magnetic minerals. Therefore, we inferred that the peak temperature during the Chi-Chi earthquake was 400°C to 626°C, corresponding to an apparent friction coefficient of 0.01 to 0.06. Such low friction and the previous evidence of a high-temperature fluid suggest that thermal pressurization likely contributed to dynamic weakening during the Chi-Chi earthquake.

Well-posedness and spectral properties of heat and wave equations with non-local conditions

We consider the one-dimensional heat and wave equations but – instead of boundary conditions – we impose on the solution certain non-local, integral constraints. An appropriate Hilbert setting leads to an integration-by-parts formula in Sobolev spaces of negative order and eventually allows us to use semigroup theory leading to analytic well-posedness, hence sharpening regularity results previously obtained by other authors. In doing so we introduce a parametrization of such integral conditions that includes known cases but also shows the connection with more usual boundary conditions, like periodic ones. In the self-adjoint case, we even obtain eigenvalue asymptotics of so-called Weylʼs type.

Frost and Ice Transport on Superhydrophobic Copper Surfaces with Patterned Micro- and Nano-Structures

Texture and wettability have an important influence on fogging, frosting, and icing on a metal surface. We fabricated micro- and nano-structure patterns on a copper surface by wire electrical discharge machining and subsequent chemical oxidation. By controlling the manufacturing process, three types of microstructure were machined: gratings, pillars, and pyramids. We then studied the wetting performance of the superhydrophobic surfaces with one-tier texture or two-tier texture and the corresponding transport of water in different phase states including fog, frost and icing and their melting processes. Two-tier roughness on the copper effectively improved the superhydrophobicity and retarded the formation and growth of frost. More importantly, these surfaces showed a long delayed icing time, even after several heating and cooling cycles, displaying good resistance to frost and icing. This can be well explained by an understanding of classical nucleation theory, Brown coalescence, and one-dimensional heat and mass transport.

Thermal performance of mechanical face seal with built-in heat pipe

Performance of a prototype mechanical face seal with built-in heat pipe is experimentally evaluated. The results demonstrate the feasibility of using phase change to remove frictional heating and thus reduce interfacial temperature. In this design, the heat pipe is integrated into the seal mating ring and there is no need to modify the gland design or the flush arrangement. The experimental results show that by means of phase change, this design is capable of significantly reducing the temperature at the seal rings’ interface. To gain insight into the heat transfer enhancement of the heat pipe mating ring, a one-dimensional steady-state heat transfer analysis is applied to predict the ring wall temperature distribution and to estimate the saturated vapor temperature. The effective thermal conductivity of heat pipe mating ring is estimated. These results of prediction are in good agreement with experimental measurements.

Thermal properties of permeable friction asphalt mixture and estimation of temperature profiles

The compaction of asphalt mixture at a proper temperature range is a very important factor to get the desired density of the asphalt mixture. The aim of this study was to determine the time at which the desired temperature is achieved and to investigate the effect of the permeable friction course (PFC) asphalt mixture properties on thermal conductivity. The thermal conductivity was measured using a surface probe type, and the values of thermal conductivity of PFC mixtures were smaller compared to dense-graded mixture. The relationships between thermal conductivity and asphalt mixture properties were investigated. Compaction temperature profiles were predicted using a simulation program that is developed based on one-dimensional (1D) heat conduction equation, finite difference method and environmental conditions. The results of the predicted temperature profiles were evaluated by comparing the measured in situ temperature profiles during compaction. From the results, it was found that the predicted time at a specified temperature could be used to determine the compaction time.

Research on Model of Plastic Flow Heat Transfer during Linear Friction Welding for Low Melting Point Metal

With the self-developed physical simulation equipment of linear friction welding, the plastic flow heat transfer simulation experiment of low melting point Lead metal was implemented. A physical model of plastic flow heat transfer of linear friction welding low melting point metal was established based on the process of the Lead metal plastic flow recorded by high speed digital camera and the Lead metal temperature variation recorded by infrared thermal imager. Introducing the plastic flow element into one-dimensional unsteady heat transfer differential equation, heat transfer mathematical model of plastic zone, perpendicular to the direction of vibration, was proposed. Using finite difference method to solve this mathematical model, calculated value of this model and measured temperature was compared. The results show that the two values correspond basically, which indicates that the proposed model could be used to characterize the process of heat transfer of plastic zone during linear friction welding low melting point metal.

Analytical modelling of hysteresis heating in rolling contact of rubber covered rollers

In a previous paper, an approximate model for the contact between a rubber covered roller and a rigid roller was developed as analytical functional relationships connecting geometric parameters and material properties of the rubber to nip properties such as maximum contact pressure, etc. in a two-dimensional relationship. The results from that development are used in this work, with the objective to provide a means of estimating the temperature rise due to hysteresis heating. In the heat conduction modelling, one-dimensional steady state heat conduction is assumed. The heat source is a power input coming from internal friction developed during the rolling contact. The power input is expressed by the hysteresis in the rubber represented by a loss angle of the material together with the peripheral speed and some parameters taken from the previously developed contact model. The temperature distribution is calculated in accordance with temperature and heat flow boundary conditions.

Numerical Simulation of Thermal Sensitivity for Explosives

In order to compare the thermal sensitivity of several typical explosives, this article solved numerically one-dimensional transient heat conduction equation including thermal decomposition for explosives with finite difference method. The explicit difference equations under different boundary conditions were established, and the corresponding stability criterion was derived. The ignition times for typical explosives were calculated, which was used to evaluate thermal sensitivity of explosives.

Analysis of Electric Performance and Optimization of Trough Concentrating Solar Thermoelectric Cogeneration System

This study introduced the basic situation of the parabolic trough concentrating solar cogeneration system, and set a one-dimensional steady-state mathematical heat transfer model based on the experimental devices, at the same time clarified influencing factors of the major heat transfer process and thermal performance of the system. The article did perspectives theoretical analysis and simulation for the system in different aspects, through using of solar trough concentrator reflecting device, established thermal performance experiments that water as the working fluid flow, provided theoretical and experimental basis for the thermal performance optimization of the system.

Compensation Heating Technique for Experimental Investigation of Thermal Contact Conductance across GH4169/K417 Interface

Abstract An experimental apparatus to measure the thermal contact conductance (TCC) between interfaces of two contact solid materials was introduced, and a new compensating heater was proposed to better achieve the one-dimensional axial heat transfer. A practical engineering example was used with pressed pairs of GH4169/K417 contacts in the range 160∼280 °C and 60∼180 MPa to demonstrate the applicability of the experimental apparatus. The measured values of TCC with and without compensation heater were studied and compared. The results show that the measured TCC with compensation heater is larger than that without compensation heater under the same condition and the compensation heater works better at high temperature.

Heat transfer in vertical casks engulfed in open pool fires

Characterization of the heat transfer to a cask engulfed in pool fire is extremely important. Experiments are carried out on diesel pool fires of diameters 0.5, 0.7, and 1.0 m with stainless steel 304L thermal casks of different sizes. Net surface heat flux on the cask is estimated using one-dimensional inverse heat conduction problem code. Velocities of the pool fires are measured using bidirectional probe to estimate the convective heat transfer coefficient ( h). The concept of adiabatic surface temperature, using plate thermometer, is applied to the pool fires and the thermal casks. By employing a mixed boundary condition (adiabatic surface temperature and h) in computational fluid dynamics package, transient temperature and heat flux of the cask are estimated. These predicted data are within 10% of the experimental results. This study demonstrates that the transient adiabatic surface temperature of the pool fire can be used to predict the behavior of the thermal cask engulfed in an open pool fire.

Measurement of Thermal Conductivity of Liquid Based on Transient Double-Hot Wire Technique

A new experimental apparatus has been developed for measuring the thermal conductivity of liquid by the two transient hot-wire method, which is based on the theory of one-dimensional unsteady heat conduction in infinite medium. The glass tubes, the heating line source and temperature measurement devices are designed in this experiment. As the temperature controller, low-temperature bath provides a constant water bath environment and current calibrator is the power source. Wheatstone bridge is used to test the relation between the temperature changes and resistance. Data acquisition and control unit is data acquisition devices of the Wheatstone bridge. As the temperature coefficient of platinum wire resistance is calibrated. It can be used to measure 32 groups of data from 10°C to 40°C at the every 10°C according to the experimental steps.

Energy Dissipation Effect in the One-Dimensional Limit of the Energy Equation in Turbulent Compressible Flow

The transportation of natural gas through high pressure transmission pipelines has been modeled by numerically solving the conservation equations for mass, momentum, and energy for one-dimensional compressible viscous heat conducting flow. Since the one-dimensional version is a result of averages over the pipe cross-section and the flow is normally turbulent, the order of averaging in space and time is an issue; in particular, for the dissipation term. The Reynolds decomposition and time averaging should be performed first, followed by the contraction to the one-dimensional version by the cross-sectional averaging. The result is a correction factor, which is close to unity, on the usual expression of the dissipation term in the energy equation. This factor will, to some extent, affect the temperature distribution along the pipeline. For low Reynolds numbers (Re≃104) it reduces the dissipation by as much as 7%, irrespective of roughness. For high Reynolds numbers (Re ≥ 107) and roughness in the high range of the micron decade, the dissipation is increased by 10%. If the pipeline is also thermally isolated such that the flow can be considered adiabatic, the effect of turbulent dissipation gains further importance.

Analytical solution of nonstationary heat conduction problem for a half-space with a multilayer coating

Based on the use of generalized boundary conditions, an analytical solution of the one-dimensional nonstationary heat conduction problem has been obtained by the method of integral Laplace transform for a half-space with a multilayer coating. Investigation was carried out and the laws governing the progress of the thermal process in the solid body and coating heated convectively by the external medium have been derived.

A Revised Approach for One-Dimensional Time-Dependent Heat Conduction in a Slab

Classical Green’s and Duhamel’s integral formulas are enforced for the solution of one dimensional heat conduction in a slab, under general boundary conditions of the first kind. Two alternative numerical approximations are proposed, both characterized by fast convergent behavior. We first consider caloric functions with arbitrary piecewise continuous boundary conditions, and show that standard solutions based on Fourier series do not converge uniformly on the domain. Here, uniform convergence is achieved by integrations by parts. An alternative approach based on the Laplace transform is also presented, and this is shown to have an excellent convergence rate also when discontinuities are present at the boundaries. In both cases, numerical experiments illustrate the improvement of the convergence rate with respect to standard methods.

Numerical simulations of 1D inverse heat conduction problems using overdetermined RBF-MLPG method

This paper proposes a numerical method to deal with the one-dimensional inverse heat conduction problem (IHCP). The initial temperature, a condition on an accessible part of the boundary and an additional temperature measurements in time at an arbitrary location in the domain are known, and it is required to determine the temperature and the heat flux on the remaining part of the boundary. Due to the missing boundary condition, the solution of this problem does not depend continuously on the data and therefore its numerical solution requires special care especially when noise is present in the measured data. In the proposed method, the time variable is eliminated by using finite differences approximation. The method uses a weak formulation of the problem to enjoy the stability condition. To avoid the numerical integration on the whole domain, the weak form equations are constructed on local subdomains. The approximate solution is assumed to be a linear combination of Multi Quadric (MQ) radial basis function (RBF) constructed on nodal points in the domain and on the boundary. Since the problem is known to be ill-posed, Thikhonov regularization strategy is employed to solve effectively the discrete ill-posed resultant linear system.

Geotemperature Evolution of the Ordovician Strata in the Tarim Basin and its Petroleum Geology Significance

The Tarim basin is an important petroleum basin in China, which produces a large amount of oil and gas resources. This paper calculates the geotemperature of the middle-upper Ordovician basal boundary during the main geological periods using the one-dimensional steady-state heat conduction equation. The simulation result reveals that from the late Ordovician to the present, the Manjiaer sag in the Tabei depression retains the highest temperature in the Tarim basin, and its highest temperature reaches 400°C in the present, while other areas in the Tarim basin have undergone relatively low temperature. Only in the Manjiaer sag of the Tabei depression and the Yecheng and Tanggubasi sags in the Southwest depression, the temperature exceeds 250°C, reaching the condition of liquid oil cracking into gas. Geotemperature of the middle-upper Ordovician basal boundary in the Tahe oilfield of the Central uplift is lower than 250 °C. It is thus inferred that there are abundant oil resources in the Ordovician strata of the Tahe oilfield. This study may provide effective geotemperature data for the next petroleum exploration in the Tarim basin.