Method to derive thermoelastic Green’s functions for cylindrical domains

This article presents a new method to derive Green’s functions for boundary value problems (BVPs) of steady-state thermoelasticity for domains described in cylindrical system of coordinate. The proposed method is based on new integral representations for main thermoelastic Green’s functions (MTGFs) in terms of Green’s functions for incompressible Lamé equations written in a cylindrical system of coordinates. The method is demonstrated on a BVP for cylindrical half-wedge for which MTGFs and Green-type integral formula are derived. The obtained MTGFs for half-wedge are validated by MTGFs for respective BVP for thermoelastic wedge that are obtained earlier using ΘG convolution method (ΘGCM). New MTGFs for octant, quarter-space, and half-space as particular cases of the cylindrical half-wedge also can be easily written. The advantages of the proposed method, called method of incompressible cylindrical integral representations (MICIR), in comparison with ΘGCM, are: (a) it is not necessary to construct influence functions for elastic volume dilatation Θ^(q), caused by unit point body force; and (b) it is not necessary to compute complicated convolution (volume integral of product between Θ^(q) and Green’s function G_T) in heat conduction equation.     

Green’s function for a line heat source acting on the surface of a coated isotropic thermoelastic material

Two-dimensional Green’s function, for a line heat source acting on the surface of a coated isotropic thermoelastic material, is investigated in this paper to improve the understanding of interface mechanisms of coating/substrate system. The coating and substrate are modeled as infinite layer and semi-infinite substrate respectively. They are perfectly bonded or are in smooth contact at the interface. Based on the two-dimensional general solution of isotropic thermoelastic materials expressed by harmonic functions, the corresponding harmonic functions with undetermined constants for coating and semi-infinite substrate are constructed, respectively. The thermoelastic field can be obtained by substituting the harmonic function into the general solution. The constants can be determined by the free surface boundary conditions and interface continuous conditions between the coating and the semi-infinite substrate. Numerical results are exhibited in the form of contours and some valuable conclusions for interface effect, interface shear debonding and coating tensile failure are presented.     

Memory response for thermal distributions moving over a magneto-thermoelastic rod under Eringen’s nonlocal theory

Abstract

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of Lord–Shulman (LS) theory of thermoelasticity based on Eringen’s nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effects of moving heat source speed, time instance, memory-dependent derivative, magnetic field and nonlocality on temperature, stress, and temperature are studied.     

Roadmap for developing heat pipes for ALCATEL SPACE’s satellites

Heat pipe has become a common thermal control component on satellites since the beginning of its industrial development in 1970s. ALCATEL SPACE develops and manufactures its own axially grooved heat pipes made of aluminium and with ammonia as working fluid.After a quick overview of heat pipe development for space applications worldwide, the present paper will give an outlook of ALCATEL SPACE’s heat pipes and their thermal performances.The Research & Development activities are strongly concerned with new heat pipe developments. Indeed there is a need for an upgraded technology to meet the future thermal control requirements on telecommunication and scientific satellites. A roadmap gives the objectives to reach and the technical challenges to overcome. The main technical characteristics that need to be addressed are:

• •an increase in heat transport capability,
• •a higher heat flux density,
• •an extension of the operational temperature range,
• •a characterisation of the reflux mode for ground testing.

To develop such an upgraded heat pipe, it is necessary to gain understanding on the physical processes which rule heat pipes. A three year Ph.D. research work is on going with experiments on a heat pipe testing apparatus at the University laboratory LET (Laboratoire d’Etudes Thermiques), Poitiers. Modelling studies are also being developed. The outcome of these studies will be useful to design optimised heat pipe profiles.     

Green and cool roofs’ urban heat island mitigation potential in European climates for office buildings under free floating conditions

Heat island which is the most documented phenomenon of climatic change is related to the increase of urban temperatures compared to the suburban. Among the various urban heat island mitigation techniques, green and cool roofs are the most promising since they simultaneously contribute to buildings’ energy efficiency. The aim of the present paper is to study the mitigation potential of green and cool roofs by performing a comparative analysis under diverse boundary conditions defining their climatic, optical, thermal and hydrological conditions. The impact of cool roof’s thermal mass, insulation level and solar reflectance as well as the effect of green roofs’ irrigation rate and vegetation are examined. The parametric study is based on detailed simulation techniques coupled with a comparative presentation of the released integrated sensible heat for both technologies versus a conventional roof under various climatic conditions.     

Assessment of Bejan’s heat exchanger allocation model under the influence of generalized thermal resistance,relaxation effect,bypass heat leak and internal irreversibility

This article reports an analytical investigation of the optimal heat exchanger allocation and the corresponding efficiency for maximum power output of a Carnot-like heat engine. To mimic a real engine, the generalized power law for the resistance in heat transfer external to the engine, relaxation effect in heat transfer, bypass heat leak and finally internal irreversibility of the power producing compartment of the engine is taken into consideration. From the engineering perspective the temperature ratio of the heat source and sink as well as to that of hot end and cold side of the working fluid is considered not to be the controllable parameters. A parametric study is presented for the other possible controllable variables. Selection of a power law over a linear model has a significant effect on the optimal heat exchanger allocation for maximum power output and the corresponding efficiency. For a higher degree of relaxation effect the drop in the maximum power efficiency is prominent along with the shift of equipartitioned allocation of heat exchanger inventory. Bypass heat leak and internal irreversibility exhibits relatively less pronounced effects on the maximum power efficiency and on the optimal heat exchanger allocation. Thus the endoreversible formulation of thermodynamic model is physically realistic. Strikingly when the optimal allocation of the heat exchanger inventory obeys the principle of equipartition in macroscopic organization for the linear law of the external heat resistance, the thermal efficiency appears to assume the representative documented value. Hence the linear model due to Bejan is also capable of capturing the essential features of a real power plant.     

Role of ‘Bejan’s heatlines’ in heat flow visualization and optimal thermal mixing for differentially heated square enclosures

Heat flow patterns in the presence of natural convection have been analyzed with Bejan’s heatlines concept. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. The physical significance of heatlines have been demonstrated for a comprehensive understanding of energy distribution and optimal thermal management via analyzing three cases. Case 1 involves the uniform and non-uniform heating of bottom wall with cooled side walls. The studies illustrate that the heat flow primarily occurs from the central regime of the bottom wall to a very small regime of the top portion of side walls. A large portion of central regime of cold side walls do not receive significant amount of heat. In order to maximize the thermal energy distribution, the distributed heating at the middle portions of the bottom and side walls have been considered in case 2 and heatlines clearly depict the distributions of heat from the hot walls to the large regimes of the cold wall. Further case 3 illustrates the enhanced heat flows in presence of heated bottom and left side walls. Heatline is found as an effective numerical tool to visualize energy distribution in order to establish a suitable heating strategy.     

Hyperbolic model of thermal interactions in a system biological tissue—protective clothing subjected to an external heat source

Abstract

The numerical modeling of thermal processes in domain of biological tissue (the male thigh) secured by multilayered protective clothing being in the thermal contact with the environment is discussed. The thigh is treated as the nonhomogeneous domain in which the sub-domains of skin tissue, fat, muscle, bone and blood vessels are distinguished. Between the protective clothing and skin tissue the air gap is taken into account. The heat transfer is described by the system of hyperbolic Cattaneo–Vernotte equations (for the tissue sub-domains) and parabolic Fourier equations (for the remaining sub-domains). The process of external heating is determined by the appropriate boundary condition and the internal heat source (in the fabric sub-domain) related to the absorption of incident thermal radiation. The mathematical model is solved numerically using the control volume method, while the considered sub-domains (the 2?D problem) are covered by the Voronoi meshes. In the final part of the article, the example of computations is presented.     

Analysis of Bejan’s heatlines on visualization of heat flow and thermal mixing in tilted square cavities

This article analyzes the detailed heat transfer phenomena during natural convection within tilted square cavities with isothermally cooled walls (BC and DA) and hot wall AB is parallel to the insulated wall CD. A penalty finite element analysis with bi-quadratic elements has been used to investigate the results in terms of streamlines, isotherms and heatlines. The present numerical procedure is performed over a wide range of parameters (10³ ? Ra ? 10⁵,0.015 ? Pr ? 1000,0° ? φ ? 90°). Secondary circulations cells are observed near corner regions of cavity for all φ’s at Pr = 0.015 with Ra = 10⁵. Two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 15° at Pr = 0.7 and Pr = 1000 with Ra = 10⁵. Heatlines indicate that the cavity with inclination angle φ = 15° corresponds to large convective heat transfer from the wall AB to wall DA whereas the heat transfer to wall BC is maximum for φ = 75°. Heat transfer rates along the walls are obtained in terms of local and average Nusselt numbers and they are explained based on gradients of heatfunctions. Average Nusselt number distributions show that heat transfer rate along wall DA is larger for lower inclination angle (φ = 15°) whereas maximum heat transfer rate along wall BC occur for higher inclination angle (φ = 75°).     

Numerical solution of hyperbolic heat conduction problems in the cylindrical coordinate system by the hybrid Green’s function method

In the present study, we have analyzed the hyperbolic heat conduction problems in the cylindrical coordinate system using a hybrid Green’s function method. The major difficulty encountered in the numerical solutions of hyperbolic heat conduction problems is the suppression of the numerical oscillations in vicinity of sharp discontinuities (Chen and Lin (1993) [11]). The proposed method combines the Laplace transform for the time domain, Green’s function for the space domain and ε-algorithm acceleration method for fast convergence of the series solution. Six different examples included the one-, two- and three-dimensional problems have been analyzed by the present method. It is found from these examples that the present method does not exhibit numerical oscillations at the wave front and the propagation of the two- and three-dimensional thermal wave becomes so complicated because it occur jumping discontinuities, reflections and interactions in these numerical results of the hyperbolic heat conduction problem.     

An atomistic Green’s function method hybrid with a substructure technique for coherent phonon analysis

ABSTRACT

By virtue of substructure technique, the atomistic Green’s function method can be applied to efficiently evaluate the coherent phonon transport in a large device. Comprised of several substructures without inner atoms, the device can be described by a small system of algebraic equations, which can give a small but crucial submatrix of the retarded Green’s function of the open device without loss in accuracy. While avoiding solving the entire device problem, the method can basically give all the information to describe the quantum transport within the ballistic limit, such as the transmission function and local density of states. The validity and efficiency of the proposed method is demonstrated by the one- and three-dimensional cases. The multilevel substructure technique is also feasible.     

Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model

The natural convection heat transfer in a cavity filled with three layers of solid, porous medium, and free fluid is addressed. The porous medium and free fluid layers are filled with a nanofluid. The porous layer is modeled using the local thermal nonequilibrium (LTNE) model, considering the temperature difference between the solid porous matrix and the nanofluid phases. The nanofluid is modeled using the Buongiorno’s model incorporating the thermophoresis and Brownian motion effects. The governing equations are transformed into a set of nondimensional partial differential equations, and then solved using finite element method in a nonuniform grid. The effects of various nondimensional parameters are discussed. The results showed that the Brownian motion and thermophoresis effects result in significant concentration gradients of nanoparticles in the porous and free fluid layers. The increase in Rayleigh (Ra), Darcy (Da), the thermal conductivity ratios for the solid wall and solid porous matrix, i.e., K_r and R_k, enhanced the average Nusselt number. The increase in the convection interaction heat transfer parameter between the solid porous matrix and the nanofluid in the pores (H) increases the average Nusselt number in the solid porous matrix but decreases the average Nusselt number in the nanofluid phase of the porous layer.     

Calculation of jet’s inlet temperature for plate temperature control in an impinging jet cooling problem

In this study, a conjugate gradient method based inverse algorithm is applied to estimate the inlet jet temperature in an impinging jet cooling problem. Given the maximum allowable plate temperature and the extent of the area on plate where temperature needs to be controlled, the jet temperature required to meet the two demands can be determined. The tests in two scenarios show that very accurate inlet jet temperatures were returned, resulting in a maximum temperature less than 1% difference with the specified temperature within the specified area. The technique presented here can be a great assist to engineers to design adequate thermal management systems for devices or processes requiring jet impingement cooling.     

Green’s function method hybrid with the finite element method for ballistic phonon transport at low temperatures in nanostructures of arbitrary shape

An atomistic Green’s function method hybrid with the finite element method (FEM) is presented to analyze the ballistic phonon transport in a device with arbitrary geometries. Discretized by the FEM, the continuous system is transformed into a lattice system. In this analogy, the nodes play the role of atoms, and the stiffness matrix stands for the interaction between atoms. The method can be used to calculate the phonon transmission between the terminals of device, and the local density of states in the device. The validity of the method is demonstrated by the one- and three-dimensional cases and a comparison with the transfer matrix method. The method also can be used to investigate elastic waves in the acoustic metamaterials and phononic crystals.