Study on dynamic characteristics of the temperature and stress field in induction and laser heating for the semi-infinite body

This study analyzed the dynamic characteristics of temperature and stress fields during induction and laser heating of a semi-infinite body. The semi-infinite body was subjected to a distribution heat flux (induction heating) at a particular depth range and then to a surface heat flux (laser heating). Using the Green function method and the Laplace transform, the temperature and stress fields solutions were acquired for both heating methods. The analytical results of the temperature and stress fields are shown graphically in the time domain for a selected position. It was found that under the same input power conditions, the temperature field acquired is identical in both induction and laser heating in the range of more than one skin depth. The peak dynamic thermal stress from both heating methods increases rapidly along the depth, and converges to a fixed value. Meanwhile, the peak thermal shock stress is relatively small, and quickly decays at a certain position in a very short duration. Therefore, the thermal shock dynamic characteristics are negligible in the two highly variant transient heating methods—induction and laser.     

Unsteady forced convection heat transfer on a flat plate embedded in the fluid-saturated porous medium with inertia effect and thermal dispersion

For an unsteady forced convection on a flat plate embedded in the fluid-saturated porous medium with inertia effect and thermal dispersion, this paper presents a precise and rigorous method to obtain the entire solutions from one-dimensional transient conduction (ξ=0) to steady forced convection in porous medium (ξ=1) under conditions of uniform wall temperature and uniform heat flux, respectively. It is worth noted that the rate of unsteady heat transfer can be accelerated by the thermal dispersion, which may be regarded as the effect of mixing or agitating, to enhance the heat transfer in porous medium. Additionally, it is found that the time response, from the transient heat conduction to a steady forced convection in Darcy's flow, is τ=1, and is independent of wall heating condition and thermal dispersion strength (φ).     

Investigation of thermal performance of a ground coupled heat pump system with a cylindrical energy storage tank

An analytical and computational model for a solar assisted heat pump heating system with an underground seasonal cylindrical storage tank is developed. The heating system consists of flat plate solar collectors, an underground cylindrical storage tank, a heat pump and a house to be heated during winter season. Analytical solution of transient field problem outside the storage tank is obtained by the application of complex finite Fourier transform and finite integral transform techniques. Three expressions for the heat pump, space heat requirement during the winter season and available solar energy are coupled with the solution of the transient temperature field problem. The analytical solution presented can be utilized to determine the annual variation of water temperature in the cylindrical store, transient earth temperature field surrounding the store and annual periodic performance of the heating system. A computer simulation program is developed to evaluate the annual periodic water and earth temperatures and system performance parameters based on the analytical solution. Copyright © 2003 John Wiley & Sons, Ltd.     

Compound Material Thermal Parameters for a Layered Material Resembling an Automobile Firewall

Heat transmission through a layered compound material consisting of carbon steel backing and insulation (either aluminized silver or fiberglass) was examined to determine thermal properties. The heat flux impinged on the insulation material side of this simulated "firewall." A heat transfer model was developed that could, in principle, be used to predict the heat transfer through layered compound materials using techniques of thermal property parameter estimation. The parameter estimates are based on thermocouple measurements of surface temperatures during heating on both sides of the material. The experiment analyzed in this article involved a vertical plate exposed on the insulation side to a transient step-applied radiant heat flux. The transient temperature measurements were fitted to heat transfer models. Thermal diffusivity and Biot number were estimated using ordinary least-squares nonlinear regression.     

The transient thermo-electro-elastic fields in a piezoelectric plate with a crack

This paper is concerned with a thin plate made by a piezoelectric ceramic material and containing a crack perpendicular to its surfaces. It is assumed that the transient thermal stress is set up by the application of a heat flux as a function of the time and position along the crack edge and the heat flow by convection from the plate surfaces. The plate is also subjected to mechanical and electric loadings. The exact analytical formulae are obtained for transient thermo-electro-elastic fields in the plate. The exact analytical solutions for the stress and electric displacement intensity factors and crack-opening displacement are obtained. Numerical examples show, among others, a dependence of the stress and electric displacement intensity factors on the thermal and elastic, piezoelectric and dielectric constants of the piezoelectric materials.     

A quasi-3D analysis of the thermal performance of a flat heat pipe

The thermal performance of a flat heat pipe thermal spreader has been described by a quasi-3D mathematical model and numerically modeled. An explicit finite volume method with under-relaxation was used for computations in the vapor phase. This was combined with a relatively small time step for the analysis. The physical problem consisted of an evaporator surface that was transiently heated non-uniformly for a short period of time and the heat source then removed. Then the system was cooled by natural convection and radiative heat transfer at the condenser region. The transient temperature distributions at the front and back of the heat spreader were obtained for different times during the transient period. The velocity distribution in the vapor core was also obtained. Due to the effect of phase change at the evaporator and condenser sides, a significant amount of energy is found to be absorbed and partially released during the transient heating and cooling processes. The numerical results indicate that advection and the high thermal diffusivity of the vapor phase accelerate the propagation of the temperature distribution in the vapor core, making it uniform during this process. The condenser temperature distribution was almost uniform at the end of the transient heating process. The transient temperature distribution on a solid aluminum plate was compared with the flat heat pipe results and indicated that the flat heat pipe successfully spread the heat uniformly at the condenser side of the structure.     

Experimental investigation of a flat plate heat pipe performance using IR thermal imaging camera

This paper presents results and analysis of an experimental investigation into determining the thermal performance of a flat plate heat pipe using infra red (IR) thermal imaging camera. Steady state and transient temperature distribution of the evaporator surface of the flat plate heat pipe were measured using a single heat source with varied heat flux inputs. For performance comparison, the experimental measurements were also carried out on an identical flat plate heat pipe with a defect and on a solid copper block of similar dimensions. It was shown that temperature excursion on the surface of the fully functioning flat plate heat pipe is less than 3 °C for operating temperatures up to 90 °C and heat flux inputs ranging from 4 to 40 W/cm². Furthermore, the thermal spreading resistance of the flat plate heat pipe was found to be about 40 times smaller than that of the solid copper block and flat plate heat pipe with a defect.     

Generalized thermoviscoelastic analysis with fractional order strain in a thick viscoelastic plate of infinite extent

Viscoelastic materials (e.g. rubber, resin, concrete skeleton, etc.) serve as one of the most promising candidate for new multifunctional materials due to their excellent rheological properties, as they are widely used in biology, petroleum industry, chemical and civil engineering, and other areas. The interaction of high-heat-flux loads (e.g. ultrafast pulsed lasers) with viscoelastic materials is a hot topic of numerous theoretical and experimental studies. Nevertheless, classical and extended generalized thermoviscoelasticity models available in literatures cannot characterize the strain relaxation behavior for viscoelastic materials. In this work, the time-based fractional thermoviscoelasticity model is further extended with a new consideration of fractional order strain. The governing equations involving strain and thermal relaxation times as well as fractional order parameters of strain and heat flux are formulated and are also applied to investigate thermal shock problem of a transient heated thick viscoelastic plate of infinite extent. With the aids of Laplace transformation methods, the transient solutions are also obtained. Finally, the effects of fractional order parameters of strain and heat flux on the transient thermoviscoelastic responses are studied and discussed.     

Unsteady Natural Convective Boiling in a Narrow Vertical Channel

The purpose of this work is to describe the two-phase flow structure and heat transfer of unsteady natural convective boiling in a narrow vertical channel. The experiments are performed with saturated n-pentane at a pressure of 1 bar. An unheated plate is placed parallel to the heating surface and lateral sides are closed. The distance between the heated surface and the confinement plate is 800 μm. Void fraction measurements are performed using capacitive sensors. The void fraction increases with heat flux and reaches a maximum of 0.80 in the mid-height of the channel when the heat flux is equal to 90% of the critical heat flux. Flow observations using a high-speed video camera show an unsteady thermo-hydraulic behavior. The frequency of the cycles increases with the wall temperature during nucleate and transient boiling. Local velocities of the bubble meniscus developing within the confined space are determined during the boiling cycles. The time-averaged liquid flow rate increases significantly with heat flux and reaches a maximum for heat flux close to the critical heat flux.     

A view of the thermal wave behaviors in thin plates

The objective of this research is to study the temperature variation in thin dielectric materials. The thermal wave model is being used as the classical Fourier law of heat conduction breaks down when a dielectric material of sub-micron geometry is heated rapidly. The first part of the work reviews the temperature distribution due to thermal wave in semi-infinite bodies. The main emphasis of this paper is to accurately determine the temperature profile in a finite plate made up from a dielectric material. The boundary conditions of the first and the second kind are selected for this study. Using the classical Laplace transform technique, analytical solutions are obtained for finite bodies with different boundary conditions the first kind and the second kind. Due to complexity of the problem, a symbolic algebra provided the solution for examining the thermal behavior of dielectric materials during rapid heating.     

Transient hygrothermoelastic response in a porous cylinder subjected to ramp-type heat-moisture loading

Abstract

The classical theory of heat conduction (Fourier theory) predicts an infinite speed for thermal disturbance propagation, which is physically unrealistic. By extending the classical Fourier heat conduction and Fick’s diffusion, this article develops hyperbolic diffusion/heat conduction laws with phase lags of heat/moisture flux to simulate coupled heat-moisture diffusion-propagation behavior with the Defour and Soret effects. A porous cylinder subjected to a ramp-type heating and humidifying at the surface is studied. The Laplace transform is used to obtain a closed-form solution of the temperature, moisture, displacements and stresses in the cylinder. Numerical results are calculated via the inversion of the Laplace transform. Obtained results show that the thermal/moisture relaxation time or phase lag plays a significant role in affecting transient hygrothermoelastic field. For a non-vanishing phase lag, non-Fourier and non-Fickian effects exist and hygrothermal waves have finite propagation speeds. The influences of the phase lag of heat/moisture flux and ramp-type time parameter on the transient response of hygrothermoelastic field are presented graphically. A comparison of the numerical results based on the classical model and the present one is made. The non-Fourier heat conduction and non-Fickian diffusion can effectively avoid the shortcomings induced by the classical Fourier and Fick laws.     

Continuous Monitoring of Whey Protein Fouling Using a Nonintrusive Sensor

Abstract

In this work, a nonintrusive device to monitor fouling of a plate heat exchanger is presented. This device is composed of a flat electrical resistance covering a thermocouple located on the external face of a tubular holding section. The tubular holding section is placed immediately after the investigated plate heat exchanger, constituting the heating zone for which fouling monitoring is required. The principle of detection consisted in following the evolution of the measured temperature with time when a fixed thermal heat flux imposed by the resistance is dissipated through the temperature sensor. The measured temperature is supposed to vary with time since the inner temperature on the inner surface of the holding tubular zone is linked to the fouling growth. It is shown that the device response is highly correlated to the fouling occurring in the plate heat exchanger and could be a promising way for monitoring fouling rate (cheap and easy to implement avoiding cleanability drawbacks).     

Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes

An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface heat fluxes of the forms: (i) Q₁(t) = Q₀(1+a cos ωt); and (ii) Q₂(t) = Q_o(1+bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q₀. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositions C_r and S_r of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. In addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.     

Temperature distribution in a thin composite plate exposed to a concentrated heat source

This study focuses on measuring and predicting the temperature distribution in a composite panel exposed to a concentrated heat source. The two heat sources studied in this work are a radiant heater and a gas burner flame. The parameters that are varied are the material properties and geometry, heat flux and distance. Finite element method based software Wintherm is used to predict the temperature distribution. The predictions are dependent on the choice of how one models the convective heat transfer coefficient along the surface of the plate exposed to the heat source. For the gas burner, the boundary condition will change dramatically from the centerline to the outward edges of the plate due to the plume effect. Empirical expressions are used and modified to determinate the air temperature in the region between the source and the plate. This information is implemented in the boundary condition along the plate surface to predict the thermal history of the plate. The predicted results are compared with the experimental temperature distribution which is measured with an infra-red camera. A parametric study is conducted to identify important dimensionless numbers and their impact on the temperature history.     

Exact thermoelastic analysis of a thick cylindrical functionally graded material shell under unsteady heating using first order shear deformation theory

In this article, a new analytical formulation is presented for an axisymmetric thick‐walled functionally graded material cylinder with power‐law variation in mechanical and thermal properties under transient heating using first order shear deformation theory. Equilibrium equations are derived by virtual work principles and the energy method. The unsteady heat conduction equation is solved using the method of separation of variables, generalized Bessel functions, and an Eigen‐function method. Validation of the analytical solutions is conducted with a finite element method. The effects of time on stress and displacement distribution are studied in detail. The numerical values used in this study are selected based on earlier studies. The influence of effect of transient heat transfer on heterogeneous thick‐walled cylinder elasticity is clearly demonstrated. In particular, the significant influence of time and the heterogenous constant on radial displacement, hoop stress, and temperature distributions is computed. The study is relevant to rocket chamber thermomechanics, propulsion duct thermophysical design, industrial thermal storage systems, and so forth.     

THERMALLY INDUCED VIBRATION IN A THIN PLATE UNDER THE WAVE HEAT CONDUCTION MODEL

Thermally induced vibration in a thin plate under a thermal excitation is investigated. The excitation is in the form of a suddenly applied laser pulse (thermal shock). The resulting transient variations of temperature are predicted using the wave heat conduction model (hyperbolic model), which accounts for the phase lag between the heat flux and the temperature gradient. The resulting heat conduction equation is solved semianalytically using the Laplace transformation and the Riemann sum approximation to calculate the temperature distribution within the plate. The equation of motion of the plate is solved numerically using the finite difference technique to calculate the transient variations in deflections.     

Stress Evolution and Thermal Shock Computation Using the Finite Volume Method

This work presents a novel numerical approach to thermal shock and transient thermal stress distribution based on the Finite Volume method. A unified approach was developed based upon the coupling between a three-dimension thermal solution and a linear thermo-elastic, multi-layered plane stress approximation. Temperature distributions were compared to analytical solutions for a flat plate and to experimental results using a temperature-dependent heat transfer coefficient. The numerical results were assessed against three analytical methods: Timoshenko and Goodier, Lu and Fleck, and Collin and Rowcliffe. This work demonstrates that the FVM provides also accurate results for thermal stress distributions in solids.     

A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace

A mathematical heat transfer model for the prediction of heat flux on the slab surface and temperature distribution in the slab has been developed by considering the thermal radiation in the furnace chamber and transient heat conduction governing equations in the slab, respectively. The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient. The steel slabs are moved on the next fixed beam by the walking beam after being heated up through the non-firing, charging, preheating, heating, and soaking zones in the furnace. Radiative heat flux calculated from the radiative heat exchange within the furnace modeled using the FVM by considering the effect of furnace wall, slab, and combustion gases is introduced as the boundary condition of the transient conduction equation of the slab. Heat transfer characteristics and temperature behavior of the slab is investigated by changing such parameters as absorption coefficient and emissivity of the slab. Comparison with the experimental work show that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace.     

Fundamental solution of steady and transient bio heat transfer equations especially for skin burn and hyperthermia treatments

In the field of bio heat transfer, as of now, the main concern of researchers lies in the proper and accurate thermal damage of the diseased tissues without destroying or damaging the neighboring healthy tissues during the tumor treatment. The present work aims to develop a new approach toward solving the bio heat transfer equations for the skin burn and hyperthermia treatments. Both analytical and numerical solutions are proposed. For the analytical study, a differential transform method is used to solve steady and unsteady state heat equations. The finite volume method is adopted to solve these equations numerically, which provides a better scope to solve the highly nonlinear complex equations. To obtain a complete solution, a code is developed in MATLAB and MATHEMATICA. The variation of different parameters, such as perfusion constant, space heating, surface step heating, and thermal conductivity, with time were observed. Apart from the above analysis of temperature distribution during skin burn through the spilling of hot beverage, its numerical solution was also performed for this problem at different boundary conditions. It was observed that with the help of the temperature distribution, depending on the time and the severity of the burn, different ranges of depths of the burn can be determined.     

Temperature Prediction for Tumor Hyperthermia with the Behavior of Thermal Wave

In magnetic nanoparticle hyperthermia for cancer treatment, controlling the heat distribution and temperature elevations is an immense challenge in clinical applications. It is expected for treatment quality to understand the heat transport occurring in biological tissue. The non-Fourier thermal behavior in biological tissue has been experimentally observed. This work uses the thermal wave model to predict the temperature excess occurring in a two-layer concentric spherical tissue with the heat source of Gaussian distribution. The solutions to the hyperbolic bio-heat equation with the space-dependent source term in the spherical coordinate system are presented. The influences of relaxation time, blood perfusion rate, and heating strength on the thermal response in tumor and normal tissue are discussed.