Numerical Simulation of Dual-Phase-Lag Model and Inverse Fractional Single-Phase-Lag Problem for the Non-Fourier Heat Conduction in a Straight Fin

In recent years, many studies have been done on heat transfer in the fin under unsteady boundary conditions using Fourier and non-Fourier models. In this paper, unsteady non-Fourier heat transfer in a straight fin having an internal heat source under periodic temperature at the base was investigated by solving numerically Dual-Phase-Lag and Fractional Single-Phase-Lag models. In this way, the governing equations of these models were presented for heat conduction analysis in the fin, and their re...     

Thermal Behavior of a Thin Layer Carrying Pulsating Signals in the Dual-Phase-Lag Model

The thermal behavior of a thin layer carrying pulsating signals under the effect of the dual-phase-lag heat conduction model is investigated. Two types of pulsating signals are considered, a pulsating heat source and a pulsating imposed temperature at the boundary. The deviation between the predictions of the classical diffusion and the dual-phase-lag models is investigated.     

双室热保护法测VIP导热系数的测试装置及实验研究

传统的测试真空绝热板(VIP)导热系数的平板热保护法,受VIP尺寸限制及热桥效应影响,存在弊端。通过分析双室热保护法测定VIP导热系数的原理,设计了测试装置。外室作为热保护装置,内室作为测试加热装置,基于稳态下测试VIP平板的导热系数,该装置不受VIP尺寸限制,减少了热桥效应。找出了影响测试结果的因素做了理论误差分析,与标定值对比,测试结果较精确。该装置可以用于VIP出厂前导热系数的测试及用过的VIP老化程度检验。     

Thermoelastic Damping in the Axisymmetric Vibration of Circular Microplate Resonators with Two-Dimensional Heat Conduction

Predicting thermoelastic damping (TED) is crucial in the design of high Q micromechanical resonators. Circular plates are common elements in the microresonators. In the past, some analytical models have been developed for TED in circular microplate resonators. However, to obtain a simple analytical expression, the previous models neglected the temperature gradient along the radial and circumferential directions, only the heat conduction through the thickness of the circular plate was considered. Thus the previous models cannot be used for general purpose design and optimization of microplate resonators. This paper presents a new analytical model for the TED in the circular microplates vibrating in the axisymmetric mode. Compared with the previous models, the present model considers two-dimensional heat conduction over thermoelastic temperature gradients along the thickness direction and the radial direction. The temperature field is represented by the product of the Bessel series along the radial direction and an unknown function along the thickness direction, which is determined in the solution procedure. The present model is validated by comparison with the previous model and the finite element method (FEM) model.     

高性能钢—混组合板激励响应动力特性试验

基于楼板振动性能研究现状,通过研发的空气调频激励装置及其测试方法,以压力传感检测系统为核心控制参数,提出装配式高性能钢-混组合板模型,进行激励响应动力特性试验。结果表明,该种动力特性时程分布特征由瞬态阶段、稳态阶段和衰减阶段三种状态组成,不同位置处激励响应传播特性一致,加速度、位移、应变等动力响应幅值均不同。该方法可应用于大型水工建筑物板结构及组合楼板结构基频测试与识别等实际工程中。     

Development of a Theoretical Process Map for Laser Cladding Using a Three-Dimensional Conduction Heat Transfer Model

In this article, a three-dimensional conduction heat transfer model is developed to predict the clad geometry (e.g., height, width, and dilution) and microstructure (scale and morphology) of the solidified layer for a laser cladding process. The effect of controllable input process parameters like absorbed laser power, powder deposition rate, and processing speed on the clad characteristics is critically assessed with the help of dimensionless parameters. A process map is developed which enables operators to pick up the proper process parameters for a feasible laser cladding process with desirable characteristics. The present conduction model is solved using the finite-volume method in a multiblock, nonorthogonal grid system. The effect of melt pool convection is taken care of by introducing an enhanced thermal conductivity factor for the molten pool.     

Estimation of a Location- and Time-Dependent High-Magnitude Heat Flux in a Heat Conduction Problem Using the Kalman Filter and the Approximation Error Model

This paper aims to estimate a location- and time-dependent high-magnitude heat flux in a heat conduction problem. The heat flux is applied on a small region of a surface of a flat plate, while transient temperature measurements are taken on the opposite surface. This inverse problem is solved using the Kalman filter and a reduced forward model, obtained by simplifications of a three-dimensional and nonlinear heat conduction problem. To deal with the modeling errors of this reduced model, the Approximation Error Model is used. The results show that excellent estimates can be obtained at feasible computational times.     

A Four-Variable Plate Theory for Thermoelastic Bending Analysis of Laminated Composite Plates

In this article, the thermoelastic bending analysis of laminated composite plates subjected to thermal load linear across the thickness using the four variable refined plate theory is presented. The theory involves four unknown variables, as against five in case of other higher-order theories and first-order shear deformation theory. The theory gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free conditions at top and bottom surfaces of the plate. The theory does not require problem-dependent shear correction factors that are associated with the first-order shear deformation theory. The principle of virtual work is used to obtain variationally consistent governing equations and boundary conditions. The simply supported laminated composite plates are considered for the detail numerical study. A closed-form solution is obtained using the double trigonometric series technique suggested by Navier. The numerical results for thermal displacements and stresses of laminated composite plates are obtained and compared with those of other refined theories and exact solutions wherever applicable to assess the efficiency of the present theory. From the numerical results it is observed that since plate is subjected to pure thermal load and not subjected to transverse mechanical load, the present theory has strong similarity with classical plate theory in many aspects.     

Thermoelastic Analysis of an Annulus Using the Green-Naghdi Model

ABSTRACT

The linear theory of thermoelasticity of Green-Naghdi (GN) types II and III for homogeneous and isotropic materials are employed to study the thermal and mechanical waves in an annulus domain. The disturbances are generated by sudden application of temperature to the boundary. The nondimensional form of the governing equations are solved utilizing the Laplace transform method. Locally transversal linearization (LTL) technique, and a numerical inverse Laplace transform method are used to obtain the temperature, displacement, and stress fields in the physical time domain. The thermomechanical wave propagation and reflection from the boundary are investigated and the influence of the damping parameter on temperature, displacement, and stress fields in the Green-Naghdi type III is discussed.     

Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Radiative heat transfer with and without conduction in a differentially heated 2‐D square enclosure is analyzed. The enclosure with diffuse gray boundaries contains radiating and/or conducting gray homogeneous medium. Radiatively, the medium is absorbing, emitting and scattering. On the south boundary, four types of discrete heated regions, viz., the full boundary, the left one‐third, left two third and middle one third, are considered. In the absence of conduction, distributions of heat flux along the south boundary are studied for the effect of extinction coefficient. In the presence of conduction, distributions of radiation, conduction and total heat fluxes along the south boundary are analyzed for the effects of extinction coefficient, scattering albedo, conduction–radiation parameter, and south boundary emissivity. Effects of these parameters on centerline temperature distribution are also studied. To assess the performance of three commonly used radiative transfer methods, in all cases, the radiative transfer equation is solved using the discrete ordinate method (DOM), the conventional discrete ordinate method (CDOM) and the finite volume method (FVM). In the combined mode problem, with volumetric radiative information known from one of the three methods, viz., DOM, CDOM, and FVM, the energy equation is solved using the finite difference method (FDM). In all cases, the results from FDM‐DOM, FDM‐CDOM, and FDM‐FVM are in good agreement. Computationally, all three sets of methods are equally efficient.     

Two-Dimensional Heat Conduction Problem in a Functionally Graded Plate with a Slanting Boundary to the Functional Gradation

This article presents analytical results for temperature in a functionally graded material plate (FGMP) with a slanting boundary to the functional gradation subjected to a partial heating. The heat conductivity is expressed in terms of a exponential function of the position. The general solution of the heat conduction equation for FGMP with a slanting boundary to the functional gradation is derived by use of the variable separation method and the analytical solution, which satisfies the boundary condition is obtained. Numerical calculations are carried out for ZrO₂/Ti-6Al-4V and ZrO₂/stainless (SUS304) functionally graded plates, when the ceramic surface is partially heated. Temperature and heat flux are graphically displayed for these two cases.     

Optimal Boundary Control of Thermal Stresses in a Plate Based on Time-Fractional Heat Conduction Equation

This article presents an optimal control problem for a fractional heat conduction equation that describes a temperature field. The main purpose of the research was to find the boundary temperature that takes the thermal stress under control. The fractional derivative is defined in terms of the Caputo operator. The Laplace and finite Fourier sine transforms were applied to obtain the exact solution. Linear approximation is used to get the numerical results. The dependence of the solution on the order of fractional derivative and on the nondimensional time is analyzed.     

Nonhomogeneous Heat Conduction Problem and Its Thermal Deflection Due to Internal Heat Generation in a Thin Hollow Circular Disk

This article is concerned with the determination of temperature and thermal deflection in a thin hollow circular disk under an unsteady-state temperature field due to internal heat generation within it. Initially, the disk is kept at an arbitrary temperature F(r, z). For times t > 0 heat is generated within the thin hollow circular disk at a rate of g(r, z, t) Btu/hr ft³, while the boundary surfaces at (r = a), (r = b), (z = 0) and (z = h) are kept at temperatures f ₁(z, t) and f ₂(z, t), f ₃(r, t) and f ₄(r, t), respectively. The governing heat conduction equation has been solved by using a finite Hankel transform and the generalized finite Fourier transform. The results are obtained in series form in terms of Bessel's functions. As a special case, different metallic disks have been considered. The results for temperature change and the thermal deflection have been computed numerically and illustrated graphically.     

Numerical Technique for Resolving the Dual Phase Lag Heat Conduction in Thin Film Metal

Abstract

In this article, a three-time level finite difference scheme is used to resolve the dual phase lag’s (DPL) heat conduction in a micro scale gold film subjected to spontaneous temperature boundary conditions without knowing the heat flux. Finite difference analog of DPL equation on applying to the intermediate grid points of the computational domain results into a system of linear, algebraic equations which can be solved using Thomas’ algorithm to finally obtain the transient temperature solution distributions in the film. The solution predicted by the DPL model is compared with that obtained by the single-phase Cattaneo–Vernotte’s model. Further, the way in which non-Fourier’s temperature distributions affected by the diffusion due to the increase in Heat Conduction Model numbers agree with the predecessor’s published results. The results by both the models revealed a finite thermal wave speed in the film contrasting the infinite speed of heat propagation as stated by the classical Fourier’s thermal model. Low spatial step and higher order finite difference schemes are recommended for better accurate numerical results of the non-Fourier’s temperature distributions occurring in the very short transient period between the instants of the suddenly applied spatial temperature gradient and the reaching of the steady state conditions.     

Resolution of Unknown Heat Source Inverse Heat Conduction Problems Using Particle Swarm Optimization

The main objective of this article is to solve inverse heat conduction problems with the particle swarm optimization method. An enhanced particle swarm optimization (EPSO) algorithm is proposed to overcome the shortcoming of earlier convergence of standard PSO algorithms. The EPSO is used to estimate the unknown time-dependent heat source in complex regions. Numerical experiments indicate the validity and stability of the EPSO method.     

Measurement of a Heated Surface Temperature Using a High-Speed Infrared Camera During Critical Heat Flux Enhancement by a Honeycomb Porous Plate in a Saturated Pool Boiling of a Nanofluid

Abstract

This article presents an experimental study to investigate the critical heat flux (CHF) enhancement mechanism using honeycomb porous plate (HPP). The CHF enhanced significantly with combination of the HPP and nanofluid, up to 3.2?MW/m² at maximum compared to a plain surface, 1.0?MW/m². The mechanism by which the CHF is improved in this system was elucidated by measuring the temperature of the heated surface using an indium tin oxide (ITO) heater and a high-speed infrared camera. The pool boiling experiment of water and nanofluid is performed under saturated temperature and atmospheric pressure conditions. The CHF values obtained using ITO heater is in good agreement with a conventional CHF pool boiling experiment with HPP attachment. High-speed infrared camera is analyzed to understand the behavior of local temperature at various locations over time. It is observed at the burnout condition, the highest average temperature is occurred at the intersection of HPP wall. Moreover, the reversible dry spots were initiated in the cell part of the HPP, and small dry spots coalesced into a growth of large irreversible dryout that leads to burnout. Further CHF enhancement could be realized if the initiation of the dryout region could be suppressed.     

Thermoviscoelastic Response for a Thin Narrow Composite Strip with Transverse Matrix Cracking

Based on von Kármán non-linear strain-displacement relationships and classical thin plate theory, a list of non-linear dynamic equilibrium equations for a thin narrow composite strip with transverse matrix cracking under thermal and mechanic loads are established and solved by the finite difference method, Newmark method, Newton-Cotes method and iterative method synthetically. Numerical examples show effect of the mechanical parameters, thermal environment, damage evolution and geometric parameters for thermoviscoelastic dynamic behavior of the thin narrow composite strip.     

Closed-Form Thermoelastic Moduli of a Periodic Three-Phase Fiber-Reinforced Composite

ABSTRACT

In previous works, using the asymptotic homogenization method (AHM), analytical formulae have been obtained for all global elastic constants of a binary fiber composite with perfect interfaces. In many cases of interest the perfect interphase is not an adequate model and it is necessary to include in the analytical models one or more interphases separating the reinforcement inclusion phase from the host matrix phase. In this article, an extension of AHM to thermoelastic heterogeneous problems is given. A simple closed form of effective properties for a three-phase unidirectional transversely isotropic composite is presented. By using homogenization schemes for periodic media, the local problems are solved and effective thermoelastic properties moduli are determined. The method is based on the assumption that the scale ratio between the periodic cell and the whole composite tends to zero. New universal relations for the three-phase thermoelastic composite are found from the AHM. In order to analyze the interphase effect, the effective thermoelastic moduli are compared with some theoretical approaches and experimental results reported in the literature.     

Conjugate Forced Convection Heat Transfer From a Heated Flat Plate of Finite Thickness and Temperature- Dependent Thermal Conductivity

In this paper, a conjugate forced convection heat transfer from a good conducting plate with temperature-dependent thermal conductivity is studied. The semi-analytical solution for the nonlinear integro-differential equation occurring in the problem is handled easily and accurately by implementing the differential transform method (DTM). The horizontal plate is heated with uniform heat flux at the lower surface while being cooled at the upper surface under laminar forced convection flow. A numerical approach is also performed via a finite-volume method to examine the validity of the results obtained by DTM. The results of DTM show closer agreement with the results of the numerical method than the results obtained by the perturbation method existing in the literature. It is concluded that for a good conducting plate with a finite thickness the distribution of the conjugate heat flux at the upper surface is significantly affected by the plate thickness. Moreover, we conclude that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the nonconjugate case.