Theory Of Heat Conduction Research Articles

Modelling lead-rubber seismic isolation bearings using the unified mechanics theory

Lead-rubber seismic isolation bearings (LRB) have been installed in a number of essential and critical structures, like hospitals, universities and bridges, in order to provide them with period lengthening and the capacity of dissipating a considerable amount of energy to mitigate the effects of strong ground motions. Therefore, studying the damage mechanics of this kind of devices is fundamental to understand and accurately describe their thermo-mechanical behavior, so that seismically isolated structures can be designed more safely. Hitherto, the hysteretic behavior of LRB has been modeled using 1) Newtonian mechanics and empirical curve fitting degradation functions, or 2) heat conduction theories and idealized bilinear curves which include degradation effects. The reason for using models that are essentially phenomenological or that contain some adjusted parameters is the fact that Newton’s universal laws of motion lack the term to account for degradation and energy loss of a system. In this paper, the Unified Mechanics Theory – which integrates laws of Thermodynamics and Newtonian mechanics – is used to model the force-displacement response of LRB. Indeed, there is no need for curve fitting techniques to describe their damage behavior because degradation is calculated at every point using entropy generation along the Thermodynamics State Index (TSI) axis. A finite element model of a lead-rubber bearing was constructed in ABAQUS, where a user material subroutine UMAT was implemented to define the Unified Mechanics Theory equations and the viscoplastic constitutive model for lead. Finite element analysis results were compared with experimental test data.

Non-fourier thermal fracture analysis of a griffith interface crack in orthotropic functionally graded coating/substrate structure

Serving as thermal barrier coatings in the harsh environment, functionally graded materials are usually subject to the extremely high temperature gradient, under which circumstance the classical Fourier's law breaks down and the non-Fourier effect becomes pronounced. The configuration of an orthotropic functionally graded coating bonded to the homogenous substrate containing a Griffith interface crack is considered in this work. The dual-phase-lag heat conduction theory is adopted to analyze the transient heat conduction and the resulting thermal stress intensity factors of the coating/substrate structure. The governing partial differential equations subjected to the complex thermal/mechanical boundary conditions are solved by the integral transform coupled with singular integral equations. A good agreement is achieved between the transient thermal stress intensity factors in the present work and steady-state values from previous literature. The influence of the thermal lags, nonhomogeneous parameters, and the thicknesses of two layers on the thermomechanical responses are investigated.

Theoretical and Experimental Investigation on Temperature Rise of CFRP with Long Pulse Laser Irradiation

Carbon fiber reinforced polymers (CFRP) are a widely used composite material applied in both commercial and industrial utilization. Based on the heat conduction theory, a theoretical model for the temperature rise of braided CFRP irradiated by long pulse laser is established in this work, and the time required for the maximum temperature rise of CFRP (with different thicknesses) to be acted by long pulse laser with different energy densities and pulse widths is simulated. At the same time, the temperature rise experiment and damage morphology of a long pulse laser with braided CFRP were carried out. The theoretical simulation results are in good agreement with the experimental results, which verifies the correctness of the theoretical model. The results of this paper will provide a theoretical basis for laser processing of CFRP.

A theoretical thermal conductivity model for soils treated with microbially induced calcite precipitation (MICP)

Soil thermal conductivity is a predominant factor affecting the efficiency of exploitation of geothermal energy. Microbially induced calcite precipitation (MICP) technology has been proved to be effective in improving soil thermal conductivity. However, there is still a lack of a thermal conductivity prediction model for MICP treated soils. In this study, a theoretical thermal conductivity prediction model was developed based on the heat conduction theory and a simplified 2D geometric soil unit. The performance of this model was evaluated using the measured thermal conductivity in published literature. The results show that the predicted soil thermal conductivity agrees with the measured values well, especially, when the soil saturation (water content of the soil) is greater than 0.1. We analyze the influencing factors of soil thermal conductivity after MICP treatment on micro-scale. The results show that the soil thermal conductivity increases nonlinearly with the ratio of cement radius to soil particle radius, β. For example, the thermal conductivity can be increased by more than 16 times from 0.25 W/(m K) to 4.14 W/(m K) when β increases from 0 is 0.8, if the ratio of soil particle spacing to soil particle radius ξ is zero. ξ is also found to have a significant influence on soil thermal conductivity. For example, the soil thermal conductivity increases by 0.19 W/(m K) and 1.08 W/(m K) in dry and saturated states, respectively, when ξ increases from 0 to 0.33. This theoretical thermal conductivity model will provide a great calculation method for the soil thermal conductivity after MICP treatment.

Nonlocal thermoelasticity: Transient heat conduction effects on the linear and nonlinear vibration of single-walled carbon nanotubes

This novel study presents a framework to investigate the effects of transient heat conduction on the nonlinear deflection and vibration of single-walled carbon nanotubes (SWCNTs) based on Eringen’s nonlocal elasticity and nonlocal heat conduction theories. The first phase of this research involves modifying the hyperbolic heat conduction theory by including a nonlocality term, in which the scale of energy transport is taken into account. The next phase includes a thermoelasticity solution for carbon nanotubes (CNTs), which is developed by Eringen’s nonlocal theory and implementing the obtained temperature. The differential quadrature method (DQM) is used to solve the transversely induced nonlocal heat conduction. We have shown the effect of thermal waves on the mode shapes and nonlinear vibration of a SWCNT by considering phase lag parameters. All boundaries are considered under a temperature-jump at the nanometer scale to consider the boundary phonon scattering. The effects of several parameters, including time-dependent boundary conditions, time lag, nonlocal parameter, length and radius, and end supports on the frequency response of SWCNTs are investigated.

Modelling and evaluation of thermoelastic damping of FGM micro plates based on the Levinson plate theory

Thermoelastic damping (TED) in a simply supported functionally graded material (FGM) micro rectangular plate is investigated analytically based on the higher-order shear deformation plate theory. The equations of motion for the thermo-elastic coupled transverse free vibration and the heat conduction equation coupled are derived based on the Levinson plate theory and the one-way coupled heat conduction theory. A semi-analytical solution of the heat conduction equation with variable coefficients is obtained by using a layer-wise homogenization approach. The complex frequency of the micro plate including TED is determined in terms of the frequency of the corresponding isothermal homogenous Kirchhoff plate by using the mathematical similarity between the eigenvalue problems for the two types of plates. The effects of the shear deformation, the material gradient and the geometry on the TED are examined in detail for the FGM micro plate made of ceramic–metal constituents with the power-law gradient profile. The numerical results show that the TED evaluated by the Levinson plate theory is smaller than that by the Kirchhoff plate theory. Therefore, for a thick or moderately thick micro plate the Levinson plate theory can provide a more accurate prediction of the TED than the Kirchhoff plate theory.

A Case Study of Non-Fourier Heat Conduction Using Internal Variables and GENERIC

Abstract Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

Research of Low-Power MEMS-Based Micro Hotplates Gas Sensor: A Review

In this paper, the research status of low power micro hot plate gas sensor is reviewed. This type of sensor is characterized by the combination of MEMS technology and related insulation measures. Compared with the traditional ceramic tubular sensor, the power consumption of the sensor is greatly reduced, which provides the possibility of remote sensor arrangement and long term stable operation. This paper firstly collects the current sensor-related heat conduction, heat convection and heat radiation theories, and summarizes the calculation model of heat loss in different regions of the micro hot plate gas sensor. Then, the application examples of the finite element method in the analysis of thermal characteristics of the sensor and the common preparation process of the substrate and gas sensitive layer of the micro hot plate are listed. Finally, the main test methods of the stability and gas sensitivity of the micro hot plate gas sensor are summarized.

Size-dependent generalized thermoelasticity model for thermoelastic damping in circular nanoplates

This paper assesses thermoelastic damping (TED) in circular nanoplates by incorporation of the small-scale effect into structural and thermal domains. The nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model are exploited for achieving the size-dependent coupled thermoelastic equations. By choosing time-harmonic and asymmetric form for deflection and temperature change, and solving the size-dependent thermoelastic eigenvalue problem, the damped natural frequency of circular nanoplate is extracted. On the basis of the complex frequency approach, an analytical relation, for the description of TED in circular nanoplates, is derived. For different boundary conditions and vibration modes, a comparison study is performed between the size-dependent results and those provided by classical continuum mechanics and heat conduction theories. Outcomes show a discrepancy between results acquired by the size effect on the structure and heat conduction. It is elucidated that how nonlocal and DPL characteristic parameters can represent the size-dependent phenomenon and can affect the magnitude of TED. A comprehensive parametric study is conducted to specify the influence of boundary constraints, vibration mode and the type of material on the amount of energy loss from TED.

Analytical Solutions of Heat Conduction Problems for Anisotropic Solid Body

Exact analytical solutions of heat conduction problems in anisotropic twodimensional solid bodies are presented in this study. Timedependent and steadystate problems are considered. A linear coordinate transformation is introduced which reduces the anisotropic heat conduction problem to an equivalent isotropic one. The solution of the anisotropic heat conduction problem is expressed in terms of solutions of the corresponding isotropic heat conduction problem. The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed. All result of the paper is based on the Fourier’s theory of heat conduction in solid bodies. Examples illustrate the applications of the developed method

Study of Boiling Heat Transfer Model of Confined Bubble Flow and Annular Flow in a Heating Rectangular Mini-Channel

the Based on the typical characteristics of the restricted bubble, the geometric structure of confined bubble flow is investigated. Based on the time weighted average method, the weights of the confined bubble and the liquid plug area in the confined bubble flow are determined. Based on one-dimensional heat conduction theory and integral method, a method for calculating the evaporation heat transfer coefficient of liquid film was established and applied to the annular flow area.The model works with Re range of 2300 to 5373, Pr range of 2.75 to 19.8, and Ca range of 0.000835 to 0.002767.

Theoretical analysis of magnetorheological finishing of HVOF sprayed WC-Co coating

WC-Co coating with nano-level surface finish is required for some special components in aircraft, automobile and forming industries. In the present study, magnetorheological finishing (MRF) of WC-Co coating is performed. Theoretical models of finishing forces (both normal and tangential force), material removal rate (MRR), surface roughness and surface temperature are proposed for better understanding of the finishing mechanism. During the MRF process, MR fluid gets compressed as it passes through the converging gap. The theory of rolling process is utilized to model the squeezing effect of the MR fluid. The side spreading of the MR fluid ribbon is confirmed by the finite element analysis (FEA) of the magnetic flux distribution in the working gap. The effect of the side spreading is also considered in the force model. It is observed that the squeezing force, magnetic force, and shear force have major contribution in producing overall finishing forces. In the proposed MRR model, the effects of the mechanical properties, shear stress, and hydrodynamic pressure are incorporated. A surface roughness model is proposed by considering the progressive interactions of the active abrasive particles with the surface asperities. The micro-cutting actions and the interfacial friction between the ribbon and work piece surface result in, an increase in surface temperature. The temperature rise of the finishing zone is modelled based on the one-dimensional heat conduction theory. All the proposed models are experimentally verified and good correlations are observed with the experimental values. By performing MRF with diamond abrasives, areal surface roughness (Sa) of the coating is reduced to 130 nm.

Thermal design and simulation of monitoring payload on manned spacecraft

Discharge monitor is a kind of primary payload monitor loaded on the manned spacecraft in the Low Earth Orbit, which is designed for monitoring the secondary discharge problem on the solar array. The issue of integrated electronic device heat dissipation is the key for normal operation supporting. In this study, the integral payload is simulated by finite element method, through structure modeling, based on the theory of heat conduction and heat radiation. In the result, under the measures of adjusting the layout of the electronic devices, coating the circuit board with copper, and black anodization for the case, the payload could definitely meet the needs of the heat dissipation in the extreme conditions, survive safely and functionalize perfectly in the orbit, at least from the angle of thermal design.

Numerical evaluation of transient solar radiation effect on concrete-faced rockfill dam with dual mortar contact method

Extrusion damage in the concrete face was widely observed in high concrete-faced rockfill dams in the last two decades. However, the accurate estimation of the concrete stress remains a great challenge. In this paper, a thermo-mechanical coupling method is presented to numerically evaluate the solar radiation effect on the concrete stress within the dual mortar finite element framework. The heat conduction is modelled as a transient time-dependent equation and hence the heat flow can be determined by meteorological data. The thermo-mechanical coupling is conducted in a weak way such that the linear system can be split into two subsystems friendly to the linear solver. The present method based on using nonconforming meshes is validated by the comparisons with node-to-segment method, conforming mesh and analytical solution. The application to a concrete-faced rockfill dam indicates that the phase lag and amplitude damping effects are apparent in the thermal analysis, confirming the importance of using transient heat conduction theory. The observed slab-slab separations emphasis the importance of using dual mortar contact method. The thermal stress is found to be larger than 10 MPa and therefore needs to be considered in the design and safety assessment.

Revisiting Manne et al. (2000): A reformulation and alternative interpretation under the modified internal energy theory of second-sound

Returning to Manne et al. (2000), wherein a class of hyperbolic reaction-diffusion-acoustic models is considered, we show that the inexact transport equation derived by these authors becomes the exact equation for the propagation of second-sound (i.e., thermal waves) in a rigid solid when reformulated under the modified internal energy model, one of several formulations of what has come to be known as hyperbolic heat conduction theory. We then compare/contrast this PDE with/to its exact version, which is based on Cattaneo’s equation for the thermal flux, in the context of a signaling problem involving weak discontinuities of second-sound propagating in a solid rod. Our analysis also reveals a connection between the modified internal energy model and what has been termed “inertial theory”, a competing theory of second-sound in solids, and suggests a generalization of the quantity known as the “thermasy”. We conclude with a discussion on the application of the present findings to a well known, widely applicable, class of nonlinear wave equations.

On the reflection of thermoelastic waves under an exact heat conduction model with a delay and temperature-dependent elastic parameters

The present work aims at describing the reflection of thermoelastic waves under a recently proposed thermoelasticity theory by Quintanilla [Some solutions for a family of exact phase-lag heat conduction problems. Mech Res Commun. 2011;38:355–360.]. Here the author has highlighted the condition for well-posedness by treating the three-phase-lag heat conduction theory differently and extended the results to obtain an alternative thermoelasticity theory with a single-delay term. In the present work, we formulate a mathematical model under this new theory to investigate the reflection of thermoelastic waves at the boundary of an elastic medium. The work is discussed for an isotropic medium with temperature-dependent elastic parameters. Unified field equations for Quintanilla's theory along with three other theories, namely, classical thermoelasticity theory, Lord-Shulman theory and Green-Naghdi theory, are considered for the analysis. The three waves, i.e. elastic-mode longitudinal wave, thermal-mode wave and transverse wave are found, among which only the first two are observed to be coupled. The amplitude ratio and phase velocity for various waves are obtained for incident longitudinal and incident transverse wave cases. The results are presented graphically for various angles of incidence and temperature dependence index parameter. Some important observations are highlighted and comparison between the considered theories is presented.

An embedded discontinuity peridynamic model for nonlocal heat conduction with interfacial thermal resistance

Thermal resistance induced by imperfectly bonded interfaces is closely related to failure at small scales. In this work, a nonlocal Kapitza thermal resistance model is constructed based on peridynamics. An embedded discontinuity model is formulated to capture the temperature jump condition induced by the interfacial thermal resistance. The model inherits the nonlocality of peridynamics but also captures the key physics of the interfacial heat barrier. To overcome the efficiency bottleneck of peridynamics, an implicit numerical procedure is formulated for both steady-state and transient-state solutions. The model is verified with various numerical examples quantitatively and shows a good agreement with analytical solutions by the classical heat conduction theory. Overall speaking, the proposed model extends the application of peridynamics in modeling general interface behaviors and establishes a foundation for predicting thermal-induced interfacial failure problems.

Thermoelastic Bresse system with dual-phase-lag model

In this work, we study a thermoelastic Bresse system from both mathematical and numerical points of view. The dual-phase-lag heat conduction theory is used to model the heat transfer. An existence and uniqueness result is obtained by using the theory of linear semigroups. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are shown, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behavior of the solution with respect to a constitutive parameter.

Failure analysis on rubber sealing structure of mandrel hanger and improvement in extreme environments

In view of the failure of the sealing structure of mandrel hanger under high pressure and extreme temperature environment, according to the sealing structure characteristics and application requirements of conventional mandrel hanger, based on the principle of the minimum sealing pressure ratio of metal sealing surface and the constitutive model of rubber material, the advantages and disadvantages of three conventional sealing structures are analyzed and compared. Based on the heat conduction theory and the energy conservation equation of thermal coupling, the transient temperature field model of the hanger seal structure is established. The heat transfer analysis and thermo-mechanical coupling calculation of the new metal seal structure are carried out at extreme temperature. The results show that the contact pressure on the double U and single U sealing rings is greater than 140 MPa at extreme temperature, which meets the principle of minimum sealing pressure ratio. The temperature distribution law of the conventional rubber structure under the temperature and pressure load is analyzed, and the reason of early failure of rubber is found. The mandrel hanger of full metal sealing structure is used in the field. The mandrel hanger of full metal have been tested for more than 20 times of gas pressure. The pressure is stable and the sealing effect is good. The test results show that this new structure has the advantages of good seal performance.

Generalized Boltzmann transport theory for relaxational heat conduction

Relaxational heat conduction lacks a modified transport theory at the mesoscopic level. We establish a modified Boltzmann transport theory with the generalized collision term, which can give rise to the convolution relationship between the heat flux and temperature gradient as well as fractional Fourier law. The macroscopic relaxational behaviors are thereafter connected to mesoscopic memory effects in the generalized collision term. The modified Boltzmann transport theory not only provides an underlying explanation for macroscopic relaxational heat conduction but also possesses engineering applications to situations far from equilibrium. The generalized collision term is not unique framework for relaxational heat conduction, and generalizing the drift term in the Boltzmann transport equation (BTE) can also cover macroscopic models. However, this framework will be paired with anomalies in energy continuity and entropy balance, and as a consequence, it is not suggested for relaxational heat conduction.