Thermal Heat Source Research Articles

Nodal predictive error model and Bayesian approach for thermal diffusivity and heat source mapping

This article aims at solving a two-dimensional inverse heat conduction problem in order to retrieve both the thermal diffusivity and heat source field in a thin plate. A spatial random heat pulse is applied to the plate and the thermal response is analysed. The inverse approach is based on the minimisation of a nodal predictive error model, which yields a linear estimation problem. As a result of this approach, the sensitivity matrix is directly filled with experimental data, and thus is partially noisy. Bayesian estimators, such as the Maximum A Posteriori and a Markov Chain Monte Carlo approach (Metropolis–Hastings), are implemented and compared with the Ordinary Least Squares solution. Simulated temperature measurements are used in the inverse analysis. The nodal strategy relies on the availability of temperature measurements with fine spatial resolution and high frequency, typical of nowadays infrared cameras. The effects of both the measurement errors and of the model errors on the inverse problem solution are also analysed.

The Effect of Moisture and Temperature on Thermophysical Properties of Iranian Pistachios

Thermal conductivity, Thermal diffusivity and bulk density of pistachios were measured at temperature ranging from 50 to 93°C and moisture content ranging from 3 to 52% (db). The line heat source method was employed to determine thermal conductivity and diffusivity. Specific heats were calculated from measured thermal conductivity, diffusivity and bulk density. Decreases in moisture content to 11.5% (db) produce reduction in thermal conductivity and specific heat, but decreases in moisture content to 3.3% (db), cause proportional increases in thermal conductivity and specific heat. Average values of thermal conductivity and specific heat were changed from 0.231 to 0.466 W/m°C and from 1894 to 3820 J/Kg°C in different moisture content, respectively. Key word: Bulk thermal conductivitybulk thermal diffusivitybulk densityspecific heatline heat source methodIran pistachio

Transient magneto-micropolar free convection heat and mass transfer through a non-Darcy porous medium channel with variable thermal conductivity and heat source effects

The laminar, fully developed, transient magnetohydrodynamic (MHD) free convection heat and mass transfer of an electrically conducting micropolar fluid between two vertical plates containing a non-Darcy porous medium with heat generation/absorption and asymmetric wall temperature and concentration has been discussed in this article. A similarity transformation is used to render the problem into a system of coupled, partial, differential equations, which are solved using the finite-element method (FEM). The solutions are validated with a robust finite difference method (FDM) solver. The present work examines the effect of Darcian parameter, Forchheimer parameter, heat absorption/generation parameter, vortex viscosity parameter, buoyancy ratio parameter, magnetic parameter, and variable thermal conductivity parameter on velocity, angular velocity, temperature and concentration profiles. Space—time graphs of velocity and microrotation are also plotted to provide a better perspective of the flowfield evolution with respect to time. Applications of the study may arise in, for example, packed-bed chemical reactors, materials processing, magnetic field control of chemical engineering transport processes in filter media, purification of hydrocarbons with electromagnetic fields, etc.

Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source

In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters.

Effects of Variable Thermal Conductivity and Heat Source / Sink on MHD Flow Near a Stagnation Point on a Linearly Stretching Sheet

Aim of the paper is to investigate effects of variable thermal conductivity and heat source/sink on flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a non-conducting stretching sheet. The equations of continuity, momentum and energy are transformed into ordinary differential equations and solved numerically using shooting method. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically and their numerical values for various values of physical parameter are presented through Tables.

Studies on a heat-recirculating microemitter for a micro thermophotovoltaic system

A new microemitter (microcombustor) configuration for a micro thermophotovoltaic system in which thermal energy is directly converted into electrical energy through thermal radiation was investigated experimentally and computationally. The microemitter as a thermal heat source was designed for a 1–10 W power-generating micro thermophotovoltaic system. To satisfy the primary requirements for designing the microemitter (stable burning in the small confinement, maximum heat transfer through the emitting walls, but uniform distribution of temperature along the walls), the present microemitter is cylindrical with an annular-type shield to apply for the heat-recirculation concept. Results show that the heat recirculation substantially improves the performance of the microemitter: the observed and predicted thermal radiation from the microemitter walls indicated that heat generated in the microemitter is uniformly emitted. Thus, the present microemitter configuration can be applied to the practical micro thermophotovoltaic systems without any moving parts (hence frictional losses and clearance problems are avoided). Ratios of the inner radius of the shield to the gap between the shield and microemitter walls and the microemitter wall thickness substantially affect thermal characteristics.

Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.

Mechanical vapour compression desalination plant at Trombay

Desalination plants based on Mechanical Vapour Compression (MVC) technology are inherently the most thermodynamically efficient. The thermodynamic efficiency of the MVC process is derived from the application of the heat pump principle. A single unit of a two-effect MVC desalination pilot plant of 50 m 3 /day capacity has recently been commissioned at Trombay, Mumbai. The desalination unit is very compact and unique in the seawater desalination technologies and is being operated by using electricity only. Horizontal tube thin-film spray desalination evaporators are used for efficient heat transfer. It is suitable for a site where feed water is highly saline and condenser cooling water is absent, and where a thermal heat source is not available. The unit produces high-quality water, nearly demineralised (DM) quality directly from seawater. There is no need for a polishing unit and product water can be used directly as make-up of boiler feed and for other high-quality process water requirements in industry. This paper includes the design and highlights the technical features of this unit.

Natural convection heat transfer from a thermal heat source located in a vertical plate fin

A steady state conjugate conduction–convection investigation is performed on vertical plate fin in which a small heat source is located. Heat from the fin surface is transferred to the surroundings by laminar natural convection. The governing equations for the problem are the heat conduction equation for the fin and the boundary layer equations, which are continuity, momentum and energy equations, for the fluid. A computer program is written by using the finite difference method in order to solve the governing equations which are nonlinear and coupled. The best location of the heat source in the fin for maximum heat transfer rate depends on two parameters which are the conduction–convection parameter and the Prandtl number. The obtained results have shown that for the fin with large conduction–convection parameter, a heat source location for maximum heat transfer rate exists.

Practical approach to gradient direction sensor method in very large scale integration thermomechanical stress analysis

Silicon integrated sensors for thermomechanical stress measurement in very large scale integration (VLSI) has been studied extensively in recent years due to the increasing complexity of modern semiconductor devices. As the chip size has increased continuously to accommodate more functions in modern integrated circuits (IC) technology, the stress induced in it from packaging combined with self-heating becomes serious and may result in the device degradation, circuit malfunction, and even chip cracking. Therefore, for large VLSI devices safe operation, it is necessary to construct in situ thermomechanical stress sensors to control the spatial induced peak stress. In this article, a practical approach to the application of a gradient direction sensor (GDS) for thermomechanical stress prediction in microelectronic packaging is presented. The GDS method has been studied and analyzed for its applicability as inverse engineering problem that is capable to detect the thermomechanical stress. This study uses a thermal heat sources emplacement approach to estimate and predict stress of wafer scale integration (WSI) chip junction. Hence, the geometrical coordinates of the investigated source can be obtained by applying the gradient direction sensors. Then finite element method will be used to build models to validate thermal peaks prediction by GDS method. This way, the possibilities to minimize the thermal peaks in the critical surface areas for ball grid array packaged WSI devices will be explored. Furthermore, in microelectronic, one of the primary roles of IC packaging is to provide structural stability for the VLSI chip. Hence, several considerations have guided our study for a judicious placement of different sensors. That will enable us to establish the most homogeneous thermomechanical cartography. Subsequently, other alternatives for heat sources placement or distribution that are capable in reducing the level of thermomechanical stress will be developed.

A study of magneto-thermoelastic problems with thermal relaxation and heat sources in a three-dimensional infinite rotating elastic medium

This paper is concerned with a study of magneto-thermoelastic problems with thermal relaxation and heat sources in a three-dimensional infinite rotating elastic medium. The medium under consideration is assumed to be homogeneous, orthotropic, electrically as well as thermally conducting. The fundamental equations of the three-dimensional problem of generalized thermoelasticity with one relaxation parameter including heat source in an infinite rotating elastic medium under the influence of magnetic field are obtained as a vector-matrix differential equation form in the Laplace–Fourier transform domain which is then solved by the eigenvalue approach. A closed form solution of the problem is derived in the Laplace–Fourier domain. Finally, the inversion of the transform solution is obtained numerically in the space–time domain. Results of this paper presented graphically and then compared with previous results available in the literature. Two short appendices are included in this paper in order to make the work self-contained.

Eigenfunction expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in three dimensions

The paper deals with the study of the disturbances in an electrically conducting infinite elastic solid permeated by a primary magnetic field containing instantaneous point heat source. The electromagnetic equations of Maxwell and the coupled equations of thermoelasticity have been used. It is assumed that the elastic field under consideration is a homogeneous, orthotropic, electrically as well as thermally conducting one. The fundamental equations of the general three-dimensional problem of magneto-thermoelasticity have been written in the form of an inhomogeneous vector matrix differential equation and solved in the Laplace-Fourier transform-domain by eigenfunction method. Finally, the solution for space-time domain has been made by numerical methods and the graphs for stresses, etc., are drawn.

Non-invasive measurement of in situ thermal diffusivity and local heat source using backscattered ultrasound for thermal therapy planning and monitoring

Bioheat transfer equation (BHTE) estimates of applied dose during HIFU therapy typically use prior knowledge or assume standard values for tissue properties that determine thermal diffusivity (K) and heat source (Q). We have developed a novel signal-processing based technique to noninvasively estimate these parameters in situ based on analysis of raw backscattered RF data from two localized HIFU exposures, one at sub-ablative intensities to determine K, and another at therapeutic intensities to obtain Q. Both exposures are performed prior to therapy. To estimate K, a short HIFU exposure is applied resulting in a temperature rise of less than 15° C. The Gaussian radius of the temperature induced apparent strain profile during cool down is estimated and fit to an approximate analytical heat diffusion expression to obtain K. Independent estimates of K derived using the transient hotwire technique validated the ultrasonic measurements. To estimate Q, an audio range hydrophone was acoustically coupled to the sample to detect the onset of boiling. The time required to bring the sample to boiling was used to estimate Q by iteration of a numerical BHTE model. These results are validated against in situ measured values using thermocouples and linear acoustic calculations.

Eigenfunction expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in two dimensions

In this paper, the linear theory of magneto-thermoelasticity with thermal relaxation is employed to study the disturbances in an infinite elastic solid containing instantaneous heat source and permeated by a primary uniform magnetic field. It is assumed that the elastic field under consideration is a homogeneous, orthotropic, electrically as well as thermally conducting one. The fundamental equations of the general two-dimensional problem of magneto-thermoelasticity have been written in the form of an inhomogeneous vector matrix differential equation and solved in the Laplace-Fourier transform domain by eigenfunction expansion method. Finally, the solution for space-time domain has been made by numerical methods and the graphs for stresses, etc., are drawn.

Low K dielectrics in sintered Al–Zr oxide composites processed by thermal plasma heating

A simple and low cost heating technique based on extended arc thermal plasma heating (EATPH) source has been developed to sinter high temperature Al x –Zr 100− x ( x=0, 10, 20, …, 100) oxides. Structure and morphology of sintered Al–Zr oxide samples were studied by X-ray diffraction (XRD) and scanning electron microscope (SEM). Interesting result pertaining to the reduction of dielectric constant ( K) and dielectric loss (tan δ) were noted in thermal plasma sintered specimen as compared to the conventional sintered sample using resistive heating. It is observed that values of K are reduced up to 40% (maximum) w.r.t. conventional sintering. This low K behavior observed in thermal plasma sintered sample may be attributed to the incorporation of dynamic inclusion in different defect form during thermal plasma heating within a short sintering time. It is also further observed from the frequency and temperature variation of K and tan δ that surface charge polarization along with dipole screening play an important role at high frequencies and temperatures which can be explained by dipole pinning and depinning mechanisms.

Studies on dielectric properties of Al–Zr oxide composites sintered by thermal plasma

High-density sintered product of Al x –Zr 100− x ( x=0, 10, 20,…100) composites were produced using low-cost extended arc thermal Plasma heating (EATPH) source. Dielectric properties of these samples were studied as a function of different frequencies and at different temperatures. Particle sizes and density of the plasma-sintered products were controlled by controlling the plasma power, sintering time and plasmagen gas flow rate during sintering. Morphology and structure of sintered Al–Zr samples were examined by SEM and X-ray diffraction (XRD) to understand the plasma-sintered induced dielectric properties. It is noted that frequency- and temperature-dependent dielectric constant and loss factors are the consequence of polarization of dipole moment, which varied with the variation of plasma-sintered particle size. It is also observed that surface charge polarization along with dipole screening play crucial role at higher frequencies and at higher temperature. Dipole pinning and depinning mechanism are proposed to explain this complicated dielectric behavior.

Effect of thermal plasma heating on the dielectric properties of Al-Zr composites

A low-cost extended arc thermal plasma heating (EATPH) source has been used for the sintering of Al-Zr high-temperature ceramic oxides, and their dielectric properties have been studied. Pellets of Al-Zr composites were sintered using optimum sintering parameters such as sintering time, plasma power and plasmagen gas flow rate in an EATPH reactor. Samples of similar composites were also sintered using a conventional resistive heating furnace at 1500°C for 20 h, and their dielectric properties were studied and compared with the plasma sintered sample. Sintered pellets were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and dielectric measurement, carried out as a function of frequency and temperature. Highly dense sintered products were obtained by the plasma heating route within a very short sintering time compared with the conventional sintering schedule. Dielectric measurements (both dielectric constant and loss factor) showed a significant reduction in the dielectric constant, K, at room temperature under different test frequencies and also as a function of temperature. However, the change in dielectric loss factor, tan Δ, was not as pronounced as the change in K. The behaviour of the K and tan Δ curves changes drastically compared with the conventional sintered material. The reduction in K and the crossover behaviour of tan Δ in the plasma sintered specimen may be due to the action of non-reactive Ar plasmagen gas during plasma sintering, which favours mobile oxygen for the polarization network under the influence of frequency and temperature.

Conversion of natural gas to liquids via acetylene as an intermediate

This paper describes an experimental investigation of the conversion of natural gas to liquid transportation fuels through acetylene as an intermediate. The first step is the direct thermal conversion of methane to acetylene utilizing a thermal plasma heat source to dissociate the methane. The dissociation products react to form a mixture of acetylene and hydrogen. Significant improvements over the prior art were observed; these improvements may be attributed to an improved methane injection configuration and minimization of radial temperature gradients. Conversion efficiencies (percent methane converted) approached 100% and acetylene yields in the 90–95% range with 2–4% solid carbon production were obtained. A variety of methods were examined for the second step, the conversion of acetylene to liquid products. The most promising technology was the reaction of acetylene with hydrogen over a shape-selective zeolite to form C 3–C 5+ aliphatics.

Thermal Stresses and Fracture of Thin Plates during Cutting and Welding Operations

In many technological processes involving cutting or welding of thin plates there is local thermal heating or cooling at the tip of the cut by a thermal source. In this paper we analytically investigate the stress distribution induced by the point thermal source moving with a constant velocity across an infinite elastic plate. Stress intensity factor for the cut formed by the moving thermal source is calculated. It is shown that for welding the value of the stress intensity factor due to thermal stresses induced by the thermal source is equal to zero. For cutting in the case of positive values of the power of thermal source the stress intensity factors will be negative. This means that the thermal field induced by the point thermal heat source will tend to close the cut in the vicinity of the tip. The opposite situation occurs when the cut tip is cooled by the thermal source. As an example, the theory under development is shown when applied to some strength issues of thermal beam cutting of brittle materials.

Elementary mathematical theory of thermal stresses and fracture during welding and cutting

Abstract In many technological processes involving the cutting or welding of thin plates there is local thermal heating or cooling at the tip of the cut. Under particular conditions the cut may be considered as a semi-infinite crack and the thermal source as a point heat source. For cutting processes the cut is behind the moving thermal source and for welding the cut is ahead of the moving thermal source. For most processes the value of the thermal source is positive (e.g. lasers, electron beam cutting, welding and others). In this paper the authors investigate analytically the stress distribution induced by a point thermal source moving with a constant velocity in an infinite plate. The stress intensity factor due to the point thermal source at the tip of the cut is calculated. It is shown that for both welding and cutting in the case of a thermal heat source the stress intensity factors will be negative, which means that the thermal field induced by the point thermal heat source will tend to close the surfaces of the cut in the vicinity of the tip. The opposite situation occurs when the cut tip is cooled by the thermal source. In this case there are positive values for the stress intensity factors and the thermal stresses may lead to brittle fracture ahead of the cut. As an example, the application of the theory under development to the uncontrolled fracture phenomenon during the thermal beam cutting of brittle materials is considered in detail. A fracture criterion for this process is obtained, which enables choosing the manufacturing parameters of the process in order to avoid the possibility of uncontrolled fracture.