Imperfect Thermal Contact Research Articles

Homogenization and simulation of heat transfer through a thin grain layer

<abstract><p>We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled through either perfect or imperfect thermal contact. The size and the period of the grains are of order $\varepsilon$, therefore forming a thin layer. The equation parameters inside the grains also depend on $\varepsilon$. We considered two distinct scenarios: Case (a), where the grains are disconnected, and Case (b), where the grains form a connected geometry but in a way such that the fluid and solid are still in contact. In both cases, we determined the effective differential equations for the limit $\varepsilon \to 0$ via the concept of two-scale convergence for thin layers. We also presented and studied a numerical algorithm to solve the homogenized problem.</p></abstract>

The Mutual Influence of Thermal Contact Conductivity and Convective Cooling on the Temperature Field in a Tribosystem with a Functionally Graded Strip.

An analytical model to find the temperature field that has been developed for friction systems consists of a strip and semi-space. The strip is made of a two-component functionally graded material (FGM) with an exponentially changing coefficient of thermal conductivity. In contrast, the material of the semi-space is homogeneous. An appropriate boundary-value problem of heat conduction with constant specific friction power was formulated and solved using the Laplace integral transform method. The model takes into consideration the imperfect thermal friction contact between the strip and the semi-space, and also the convective cooling on the exposed surface of the strip. The appropriate asymptotic solutions to this problem for low and high values of Fourier number were obtained. It is shown how the determined exact solution can be generalized using Duhamel's formula for the case of a linearly reduction in time-specific friction power (a braking process with constant deceleration). Numerical analysis for selected materials of the friction pair was carried out in terms of examining the mutual impact on the temperature of the two Biot numbers, characterizing the intensity of the thermal contact conductivity and convective heat exchange on the exposed surface of the strip. The obtained results can be used to predict the temperature of friction systems containing elements made of FGM. In particular, such systems include modern disc braking systems.

Approximate semi-analytical technique based on eigenfunction expansion for phase change heat transfer in a cylindrical body contained within a thick multilayered annular wall

Phase change heat transfer occurs commonly in thermal management and energy storage problems. Most literature in this direction assumes direct contact between the phase change material (PCM) and the heat source/sink. However, in practical problems, the PCM is often enclosed within a non-melting wall. This work presents an approximate eigenfunction expansion-based analysis of inwards phase change propagation in a cylindrical PCM encapsulated in a multilayer annular wall. The model accounts for imperfect thermal contact between layers. The transient temperature distribution is determined by solving a transient multilayer thermal conduction problem. Evolution of the phase change front is determined by inserting the temperature distribution into the interfacial energy conservation equation. Results are shown to agree with past work for special cases of the general problem considered here. Good agreement with both experimental and numerical data from past work, and with finite-element numerical simulations is demonstrated. The role of key non-dimensional parameters on phase change characteristics, including total time to melt/freeze is quantified. Ranges of non-dimensional numbers in which the approximate method offers good accuracy are determined. This work extends the state-of-the-art of phase change modeling, with potential applications in energy storage, nuclear engineering, oil/gas transport, and in mass transport problems.

Axisymmetric Thermoelastic Deformation of a Multilayer Foundation with Imperfect Thermal Contact of the Layers

An axisymmetric stationary problem of thermoelasticity for a multilayer foundation with imperfect thermal contact between the layers is solved by the method of compliance functions along with the Hankel transform. The recurrence relations are constructed for the auxiliary functions and the compliance functions of neighboring layers of the foundation. We analyze the influence of the coefficient of thermal resistance on the distribution of normal and tangential stresses and temperature at the points of the bottom boundary of the top layer for a two-layer foundation subjected to the action of thermal loads.

An efficient parametrized optical infrared thermography 3D finite element framework for computer vision applications

Matching infrared thermography (IRT) with deep learning-based computer vision has recently gained a lot of interest for automated defect assessment in materials. One of the remaining bottlenecks concerns the necessity of a large and diverse experimental and/or virtual training dataset in order to achieve a sufficiently generalizable computer vision algorithm. This paper presents a parametrized 3D finite element (FE) framework, implemented in Fortran90, for efficiently simulating optical infrared thermographic inspection of multi-layer anisotropic media and establishing large-scale virtual dataset with sufficient diversity. The interface element is introduced for the modelling of an imperfect thermal contact, allowing to simulate a variety of defect types. The flexibility of the interface element makes it possible to simulate delaminations with different thickness using the same discretized model. Validation is done for two benchmark cases which are representative for a fiber reinforced polymer laminate with delamination-like defects. In order to achieve true-to-nature thermographic simulation data, non-uniform heating conditions are adopted from experiment, and a stochastic morphology generator is introduced for modelling realistic irregular defect geometries. To demonstrate the added value of a large, diverse and true-to-nature virtual database for computer vision applications, a Faster-RCNN model was trained on a generated virtual dataset for the detection of delamination-like defects in fiber reinforced polymer laminates. Application of the trained Faster-RCNN on experimental thermographic data yields excellent inference results, illustrating the high generalization ability of the virtually trained object detector.

An imperfect thermal contact problem for consolidation of bilayered saturated soil subjected to ramp-type heating

This study proposes a generalized imperfect thermal contact model to simulate the thermal contact resistance existing at the interface between the two adjacent soil layers. Based on the generalized imperfect thermal contact model, a thermo-hydro-mechanical (THM) coupled consolidation model for bilayered saturated soil under ramp-type heating load is established. By means of the Laplace transform, the semi-analytical solutions of temperature increment, excess pore water pressure and displacement of the bilayered saturated soil are obtained. Based on the present solutions, the THM coupled consolidation behaviors are investigated through comparative and parametric analysis. The results show that the generalized imperfect thermal contact model can realistically describe the imperfect thermal contact problem and can be degenerated into other commonly-used thermal contact models. Due to the existence of interfacial thermal contact resistance, only a portion of heat flux passes through the interface, weakening the influence of the thermal load on the consolidation behaviors of non-heated layer. With the decrease of contact transfer coefficient and the increase of partition coefficient, the interfacial thermal contact resistance increases, and the influence of the thermal conductivity of soil grains reduces.

The influence of phonon boundary scattering on the thermal conductivity of a two-dimensional noninteractive phonon system of nanosized structures

One of the problems that arise when studying the thermal conductivity of low-dimensional phonon systems at low temperatures is the appearance of differences in expressions for the thermal conductivity as a function of sample size, as well as the appearance of unusual dependences of heat fluxes on temperature gradients. For example, in the generally accepted Casimir – Zaiman model, it is assumed that a linear temperature gradient is created on the lateral surface by external sources. Moreover, the Casimir model requires two conditions at the border. This is a diffuse reflection in which the phonon is reflected with an isotropic angular distribution function. The second condition is the presence of redistribution of phonons by energy, so that the distribution of reflected phonons corresponds to the radiation of an absolutely black body - that is, the reflection of phonons must be inelastic. And if the first condition can be achieved, for example, by boundaries with a certain degree of roughness, the second condition can be achieved only in the presence of thermal contact between the side edges of the sample and the thermal medium at a certain temperature distribution. In the case of thermally insulated sample boundaries (for example, when the sample is in vacuum) or at least with imperfect thermal contact, the fulfillment of the second condition is practically impossible.In this paper, we consider the problem of thermal conductivity of two-dimensional nanostructures - nanobands - in the temperature range, when the interaction between phonons can be neglected. In this ballistic mode, heat fluxes can be limited only by the interaction of phonons with the sample boundaries. A number of types of interaction of phonons with the boundaries of two-dimensional samples are considered: absorption at the boundary, finite number of reflections, absorption inside the sample on defects, impurities, etc. Explicit expressions of thermal conductivity in these cases are derived. Interpolation relations are obtained, which generalize the existing expressions of thermal conductivity in the case of mirror reflection and reflection with losses.

Heat transfer model of fire protection fiberglass thermal barrier coated with thin aluminium layer

Fiberglass thin blankets with an aluminium coating are often used for fire protection due to their capacity to withstand extreme incident radiant and convective heat fluxes. This article develops a one-dimensional heat transfer model for predicting the temperature distribution for this coated thermal barrier considering the radiant heat flux from the flame front [O(101)kW/m2] and convective heat fluxes from the heated combustion gases on the front side, and a convective heat transfer on the opposite side. The mathematical model developed uses a Padé Approximant to convert the analytical solution from the Laplace to the Fourier domain. And this approximation is validated numerically through finite differences, and experimentally with an appropriate laboratory experimental setup. The accuracy of the results obtained show a good agreement in both validation schemes. Namely, concerning the laboratory experiments, the heat transfer model captured the barrier’s thermal behaviour with maximum absolute deviations of 14% on the heat source side of the thermal barrier and 8.7% on the opposite side. The imperfect thermal contact in the experimental setup was discussed as a possible source of error.

Axisymmetric thermoelastic deformation of a multilayer plate with imperfect thermal contact of its layers

An axisymmetric stationary problem of thermoelasticity for a multilayer plate with imperfect thermal contact between its layers is solved by using the method of compliance functions along with the Hankel transform. It is assumed that the conditions of perfect mechanical contact are satisfied on their common boundaries. The Hankel transforms of displacements, stresses, and temperature at the points of the layer can be represented in the form of the linear combinations of the six auxiliary functions. The auxiliary functions are connected with the Hankel transforms of displacements, stresses, temperature and flow at the points of the upper boundary of the corresponding layer. For the problem considered six auxiliary functions can be found from the boundary conditions. Using the conditions on the common boundaries of the layers and entering a dummy layer the recurrent formulas for finding other auxiliary functions are constructed. The auxiliary functions of each layer are dependence. This dependence is represented in the matrix form using so-called compliance functions. The recurrence relations for the compliance functions of the thermoelastic multilayer plate are constructed. The algorithm for solving the сonsidered problem is formulated. The numerical calculations are made for a two-layer plate subjected to the action of the thermal loads. The influence of the coefficient of thermal resistance on the distribution of temperature at the points of the lower boundary of the upper layer and at the points of the upper boundary of the lower layer is analyzed. Also the influence of this coefficient on the distribution of normal stresses at the common boundary of layers is analyzed.

Direct method of studying heat exchange in multilayered bodies of basic geometric forms with imperfect heat contact

Purpose. Characteristics of heat transfer processes in multilayer bodies of basic geometric shapes simultaneously under conditions of convective heat transfer on its surfaces and taking into account imperfect thermal contact between the layers. Methodology. A direct method was applied to solve a one-parameter family of boundary value problems in the theory of heat conduction. This method is based on the reduction method, the concept of quasiderivatives, a system of differential equations with impulse action, the method of separation of variables, and the modified method of eigenfunctions of Fourier. It is worth noting that the application of the concept of quasiderivatives allows you to circumvent the well-known problem of multiplication of generalized functions, which arises when using the differentiation procedure of the coefficients of a differential equation. Such a procedure, in our opinion, casts doubt on the equivalence of the transition to the differential equation obtained in this way with generalized coefficients. Findings. The solution to the problem is obtained in a closed form. The proposed algorithm does not contain a solution to volume conjugation problems. It includes only: a) finding the roots of the corresponding characteristic equations; b) the multiplication of a finite number of known (2 2) matrices; c) the calculation of certain integrals; d) summing the required number of members of the series to obtain the specified accuracy. As an illustration, we consider model examples of heating eight-layer structures in a fire. Originality. For the first time, the direct method has been applied to solving the problem of the distribution of an unsteady temperature field over the thickness of multilayer structures of basic geometric shapes simultaneously, in the presence of imperfect thermal contact between the layers. Practical value. The implementation of the research results allows us to effectively study the heat transfer processes in multilayer structures, which are found in a number of applied problems.

INFLUENCE OF IMPERFECT THERMAL CONTACT ON HEAT EXCHANGE IN THE SYSTEM OF MULTILAYER CYLINDRICAL BODIES

Introduction. Solving the problem of heat transfer in multilayer structures devoted a large number of works. The vast majority of them are limited to the case of perfect thermal contact between the layers. However, according to the authors, the problems of thermal conductivity in multilayer structures using into account the imperfect thermal contact are insufficiently studied. The number of such studies is quite limited. Also, known studies are usually limited to two layers. That is because the increase in the number of layers (given the choice of methods of practical implementation) leads to several computational difficulties. Therefore, the problem of constructing an effective analytical scheme for the study of heat transfer processes in multilayer structures in the presence of imperfect thermal contact between the layers remains an urgent task.Purpose. Application of the direct method to the study of heat transfer processes in the system "continuous cylinder inside a multilayer cylindrical shell" with imperfect thermal contact.Methods. An auxiliary problem set for the distribution of the temperature field in a multilayer solid cylindrical hollow body (a cylinder of the sufficiently small radius is "removed") taking into account the imperfect thermal contact between the individual layers. According to the already known scheme of the direct method solve this problem.Results. Boundary transition obtained the solution of the original problem. Boundary transition: the radius of the"removed" cylinder, with the centre at the origin, goes to zero. This approach established that the solution to the problemis limited in the whole structure. In this case, the solution obtained explicit formulas.Conclusions. Effective analytical scheme constructed for application of the direct method to the study of heattransfer processes in multilayer hard cylindrical solids taking into account the non-ideal thermal contact between thelayers. The number of layers, their size and arrangement are considered arbitrary.

Multi-Layer Transient Heat Conduction Involving Perfectly-Conducting Solids

Boundary conditions of high kinds (fourth and sixth kind) as defined by Carslaw and Jaeger are used in this work to model the thermal behavior of perfect conductors when involved in multi-layer transient heat conduction problems. In detail, two- and three-layer configurations are analyzed. In the former, a thin layer modeled as a lumped body is subject to a surface heat flux on the front side while it is in perfect (fourth kind) or in imperfect (sixth kind) thermal contact with a semi-infinite or finite body on the back side. When dealing with a semi-infinite body in imperfect contact, the temperature solution is derived by means of the Laplace transform method. Green’s function approach is also used but for solving the companion case of a finite body in perfect contact with the thin film. In the latter, a thin layer with internal heat generation is located between two semi-infinite or finite bodies in perfect/imperfect contact. For the sake of thermal symmetry, such a three-layer structure reduces to a two-layer configuration. Results are given in both tabular and graphical forms and show the effect of heat capacity and thermal resistance on the temperature distribution of conductive layers.

Axisymmetric thermoelastic deformation of a multilayer foundation with imperfect thermal contact of its layers

Axisymmetric thermoelastic deformation of a multilayer foundation with imperfect thermal contact of its layers

SIMULATION OF HEAT EXCHANGE IN A MULTILAYER FLAT STRUCTURE UNDER PERFECT THERMAL CONTACT IN FIRE CONDITIONS

The proposed work is devoted to the application of the direct method to the study of heat transfer processes in a multilayer flat structure. It is assumed that each layer is made of isotropic material of different thickness. There is an imperfect thermal contact between them, and the layers have internal heat sources. In this case, the isothermal surfaces are parallel planes, i.e the temperature changes in only one direction. On the outer surfaces of the structure there is a convective heat exchange with the environment, i.e the boundary conditions of the third kind are fulfilled. The coefficients of the thermal conductivity equation are considered to be piecewise constant with respect to the spatial coordinate. This is the first time the problem has been solved in this setting. The solution of the problem is realized by applying the method of reduction using the concept of quasi-derivatives and applying the theory of systems of differential equations with impulse action. The following is the procedure for separating Fourier variables using a modified method of eigenfunctions.Based on the physical content of the problem, the differential equation of thermal conductivity was written in the Cartesian coordinate system, but the solution scheme presented here without any fundamental difficulties extends to similar problems for multilayer bodies of basic geometric shapes by switching to appropriate coordinate systems. To illustrate the proposed method, a model example of finding the distribution of a nonstationary temperature field in a seven-layer flat structure under the influence of the hydrocarbon temperature of the fire is solved. The condition of ideal or non-ideal thermal contact is fulfilled between two adjacent layers. In addition, some layers have internal heat sources. The results of the calculations are presented in the form of a graph of temperature changes depending on timeand spatial coordinates.

Contact resistance analysis applied to simultaneous estimation of thermal properties of metals

This work aims to present a method for simultaneously estimating the thermal conductivity, k, and specific heat, cp, in samples of stainless steel 304 and cemented carbide by accounting the imperfect thermal contact at the heater–sample interface. A transient one-dimensional heat conduction model with constant thermal properties is used. The metallic sample is placed in the middle of a polyimide heater and a thermal insulator. A constant heat flux is applied on the specimen upside surface and a thermal insulation condition is maintained on the opposing surface, where a type T thermocouple measures the temperature response. Contact resistance is determined and accounted for as a reducing factor on heat flux. Instead of considering a lumped model, a microscopic approach of the contacting regions is used to describe both the surface roughness and the fluid gap. With the intention of guaranteeing simultaneous and reliable estimates for both thermal properties, sensitivity analysis is used to establish heat flux intensity, experiment duration, time step for data acquisition, and other characteristics of the experiments. To simultaneously achieve both thermal properties, the optimization method BFGS (Broyden–Fletcher–Goldfarb–Shanno) is employed to minimize a least-squares objective function comparing experientially measured and numerically calculated temperatures. The numerical solution for the transient conduction problem is determined with COMSOL, which solves the transient heat diffusion problem by discretizing it applying the finite element method (FEM). The linear system of equations is solved using the PARDISO solver and backward differentiation formula (BDF) method. Heat flux is estimated employing the sequential function specification method (SFSM) as a means of verifying the robustness of parameter estimation and experimental procedure. Moreover, uncertainty analysis is performed to confirm the quality of the results obtained. Finally, the uncertainty analysis outcomes and thermal properties estimated are compared with literature.

Numerical algorithm of multipole expansion method for conductivity of ellipsoidal particle composite

The paper addresses the numerical implementation of the multipole expansion method in application to the conductivity problem for the ellipsoidal particle composite with isotropic constituents and imperfect interfaces. The main steps of the numerical algorithm are considered in detail including generation of the geometry model, evaluating the re-expansion coefficients, fulfilling the periodicity and interface conditions and determination of the series expansion coefficients by iterative solving a set of linear equations. For each step, the numerical tests are performed which illustrate an accuracy and efficiency of the method. The rational computational strategies and the ways of boosting the computer code performance are discussed. The algorithm-based code provides a fast and accurate analysis of the local potential fields and the effective conductivity of composite with an adequate account for the arrangement and orientation of inhomogeneities. The imperfect thermal contact between the matrix and inhomogeneities is taken into account accurately. The application area covers the polydisperse and multiphase composites of matrix type. Its extension to the ellipsoidal particle composites with anisotropic constituents is straightforward. Incorporation of this feature yields possibly the most general model of composite that may be considered in the framework of analytical approach, and the proposed numerical algorithm is by far the most efficient method for studying these models.

Effect of Heat Source and Imperfect Contact on Simultaneous Estimation of Thermal Properties of High-Conductivity Materials

In the current paper a novel methodology accounting for both the heater heat capacity and the imperfect thermal contact between a thin heater and a specimen is proposed. In particular, the volumetric heat capacity of the heater is considered by modelling it as a lumped capacitance body, while the imperfect thermal contact is considered by means of a contact resistance. Thus, the experimental apparatus consisting of three layers (specimen-heater-specimen) is reduced to a single finite layer (sample) subject to a “nonclassical” boundary condition at the heated surface, known as sixth kind. Once the temperature solution is derived analytically using the Laplace transform method, the scaled sensitivity coefficients are computed analytically at the interface between the heater and the sample (heater side and sample side) and at the sample backside. By applying the proposed methodology to a lab-controlled experiment available in the specialized literature, a reduction of the thermal properties values of about 1.4% is observed for a high-conductivity material (Armco iron).

Fire ember pyrometry using a color camera

Firebrands can dramatically increase the hazards of wildland fires. While embers have been extensively studied, little is known about their temperatures. To address this an imaging ember pyrometer is developed here using an inexpensive digital color camera. The camera response was calibrated with a blackbody furnace at 600–1200 °C. The embers were smoldering cylindrical maple rods, 6.4 mm in diameter and 2 cm long. Temperatures were obtained from ratios of green/red pixel values and from grayscale pixel values. Ratio pyrometry is more accurate when ember emissivity times ash transmittance is below unity, but grayscale pyrometry has signal-to-noise ratios 18 times as high. Thus a hybrid pyrometer was developed that has the advantages of both, providing a spatial resolution of 17 μm, a signal-to-noise ratio of 530, and an estimated uncertainty of ±20 °C. The measured ember temperatures were between 750 and 1070 °C with a mean of 930 °C. Comparing the ratio and grayscale temperatures indicates the ember's mean emissivity times ash transmittance in the visible was 0.73. Temperatures were also measured with fine bare-wire thermocouples, which were found to underpredict the ember's mean temperature by 230 °C owing to ember quenching and imperfect thermal contact.

Hot stamp pressure on elastic half-space taking into account imperfect thermal contact through thin intermediate layer

Hot stamp pressure on elastic half-space taking into account imperfect thermal contact through thin intermediate layer

Domain decomposition algorithms for problems of thermomechanical contact between several elastic bodies

We consider a thermoelastic multibody contact problem for finite bodies with unilateral mechanical and imperfect thermal contact conditions. Using a penalty method, we obtain a weak formulation of this problem in the form of a system of linear and nonlinear variational equations in Hilbert space. To solve this variational system, we propose a class of iterative Robin type domain decomposition algorithms. In each iterative step of these algorithms one have to solve two linear variational equations for each of the bodies, which correspond to heat conduction problem with Newton boundary conditions on the possible contact areas and linear elasticity problem with additional volume forces and Robin boundary conditions respectively. The program implementation of proposed algorithms is made for plane thermoelastic contact problems with the use of linear and quadratic finite element approximations on triangles. The numerical analysis is performed for one-body and two-body thermoelastic contact problems.