Heat Propagation Research Articles

Mathematical modeling of temperature fields in antenna reflectors of space vehicles

The main factor that determines the distortion of the shape of the reflectors in outer space is the temperature deformation due to the uneven distribution of heat fluxes in the structural elements. Therefore, it is important to develop models and methods for calculating temperature fields in reflectors with uneven distribution of heat fluxes on the surface. The use of such methods will reduce the number of expensive field experiments. The paper first constructs a mathematical model for calculating temperature fields in a parabolic reflex antenna, in the form of a paraboloid of rotation rotating at a constant angular velocity, taking into account the finite velocity of heat propagation as a boundary value problem of mathematical physics for the hyperbolic equation of thermal conductivity. that the thermophysical properties of the body are constant. At the initial moment of time, the body temperature is constant, and on the outer surface of the body are known values of heat flux which are continuous coordinate functions. To solve the obtained boundary value problem, a new integral transformation for a two-dimensional finite space was constructed. The formula of inverse transformation is given. Eigenvalues and eigenfunctions for the kernel of integral transformation are found using finite element methods and Galorkin. The division of the region into simplex elements was made. Thus the problem of finding eigenvalues and eigenfunctions was reduced to the algebraic problem of finding eigenvalues and eigenfunctions. After applying the constructed new integral transformation to the obtained boundary value problem, we obtained the Cauchy problem, the solution of which was found analytically. The obtained solution of the boundary value problem is twice continuously differentiated by spatial coordinates and once in time. The solution of the boundary value problem found can be used to modulate the temperature fields that occur in a parabolic reflex antenna. The paper first constructs a mathematical model for calculating temperature fields in a paraboloid rotating at a constant angular velocity, taking into account the finite velocity of heat propagation as a boundary value problem of mathematical physics for the hyperbolic equation of thermal conductivity with Neumann boundary conditions. Using the developed integral transformation, the temperature fields in the paraboloid in the form of convergent series by Fourier functions were found. The solution of the generalized boundary value problem of heat exchange of the paraboloid of rotation can be used to modulate the temperature fields that occur in the antenna reflectors of spacecraft.

Determinism, well-posedness, and applications of the ultrahyperbolic wave equation in spacekime.

Spatiotemporal dynamics of many natural processes, such as elasticity, heat propagation, sound waves, and fluid flows are often modeled using partial differential equations (PDEs). Certain types of PDEs have closed-form analytical solutions, some permit only numerical solutions, some require appropriate initial and boundary conditions, and others may not have stable, global, or even well-posed solutions. In this paper, we focus on one-specific type of second-order PDE - the ultrahyperbolic wave equation in multiple time dimensions. We demonstrate the wave equation solutions in complex time (kime) and show examples of the Cauchy initial value problem in space-kime. We extend the classical formulation of the dynamics of the wave equation with respect to positive real longitudinal time. The solutions to the Cauchy boundary value problem in multiple time dimensions are derived in Cartesian, polar, and spherical coordinates. These include both bounded and unbounded spatial domains. Some example solutions are shown in the main text with additional web-based dynamic illustrations of the wave equation solutions in space-kime shown in the appendix. Solving PDEs in complex time has direct connections to data science, where solving under-determined linear modeling problems or specifying the initial conditions on limited spatial dimensions may be insufficient to forecast, classify, or predict a prospective value of a parameter or a statistical model. This approach extends the notion of data observations, anchored at ordered longitudinal events, to complex time, where observables need not follow a strict positive-real structural arrangement, but instead could traverse the entire kime plane.

Use of the Alternating Directions Method in Cylindrical Coordinates, Applied to the Two-Dimension Unsteady Conduction Heat Transfer

Abstract Finding analytical solutions for the unsteady conduction heat transfer equation is generally very difficult due to the intrinsic complexity of the problem. In most cases, the equation has no analytical solutions. A numerical approach that surmounts these difficulties consists of the finite difference technique. The alternate directions finite-difference technique especially suits to the two-dimension heat conduction. The paper considers a hollow cylinder consisting of a conduction heat transfer medium, and the two-direction unsteady heat propagation within this medium is studied by means of the alternate directions method. The approach simulates the heat conduction process during a charge-discharge cycle of a single borehole heat storage.

Modeling of Heat Propagation Processes in Detection Pixel of Thermoelectric Single-Photon Detector with High-Temperature Superconducting Absorber

Modeling of Heat Propagation Processes in Detection Pixel of Thermoelectric Single-Photon Detector with High-Temperature Superconducting Absorber

Discrete and continuum fundamental solutions describing heat conduction in a 1D harmonic crystal: Discrete-to-continuum limit and slow-and-fast motions decoupling

In the recent paper by Sokolov et al. (Int. J. of Heat and Mass Transfer 176 (2021) 121442) ballistic heat propagation in a 1D harmonic crystal is considered and the properties of the exact discrete solution and the continuum solution of the ballistic heat equation are numerically compared. The aim of this note is to demonstrate that the continuum fundamental solution can be formally obtained as the slow time-varying component of the large-time asymptotics for the exact discrete solution on a moving point of observation.

Study on propagation mechanisms of the actuations generated by plasma synthetic jet actuator in a supersonic flow

The plasma synthetic jet actuator (PSJA) has a potential application in the flow control, especially for the supersonic and hypersonic flow. In order to make a deeper understanding on the propagation processes of the actuation generated by the PSJA in a supersonic flow, both the schlieren experiment and the numerical simulation are adopted for the analyses. Based on the analytic geometry method, the propagation of the diffracted wave, the synthetic jet and the dis-charged heat are discussed in detail. The effects of the mainstream Mach number and the discharge strength on the propagation processes are also deeply analyzed. Besides, an analytic model and relevant motion equations are established for the forecast of the actuations. The results suggest that the 1st diffracted wave expands around and propagates along the mainstream direction. The synthetic jet will change the start point of the oblique wave. Further, the propagation of the dis-charged heat is also related to the mainstream.

Three-Phase-Lag Bio-Heat Transfer Model of Cardiac Ablation

Significant research efforts have been devoted in the past decades to accurately modelling the complex heat transfer phenomena within biological tissues. These modeling efforts and analysis have assisted in a better understanding of the intricacies of associated biological phenomena and factors that affect the treatment outcomes of hyperthermic therapeutic procedures. In this contribution, we report a three-dimensional non-Fourier bio-heat transfer model of cardiac ablation that accounts for the three-phase-lags (TPL) in the heat propagation, viz., lags due to heat flux, temperature gradient, and thermal displacement gradient. Finite element-based COMSOL Multiphysics software has been utilized to predict the temperature distributions and ablation volumes. A comparative analysis has been conducted to report the variation in the treatment outcomes of cardiac ablation considering different bio-heat transfer models. The effect of variations in the magnitude of different phase lags has been systematically investigated. The fidelity and integrity of the developed model have been evaluated by comparing the results of the developed model with the analytical results of the recent studies available in the literature. This study demonstrates the importance of considering non-Fourier lags within biological tissue for predicting more accurately the characteristics important for the efficient application of thermal therapies.

The chemical interaction charged particles with target material under surface treatment of metal with particle beam

AbstractThe paper presents a nonlinear coupled nonisothermal model of the process of material implementation into the target surface under conditions of surface treatment by a particle beam in the form of one or few consecutive pulses. The model takes into account the interaction of impurity diffusion, heat propagation, and mechanical disturbances, as well as the chemical reaction between the introduced impurity and the target material. The problem is solved numerically using an implicit symmetric difference scheme of the second‐order approximation in time and spatial coordinates. The results of solution are obtained for different time intervals. It was found that the interaction of different processes leads to the appearance of distortions in the front of waves. The distributions of temperature and impurity concentration have a wave character. The increment of the reaction product in the dynamics for different numbers of pulses is presented. The interaction mechanisms of the studied processes do not change and do not depend on the number of pulses. However, a more complicated picture is observed under treatment by several successive pulses due to the appearance of new extremes and distortions.

Detection of the Lateral Thermal Spread during Bipolar Vessel Sealing in an Ex Vivo Model-Preliminary Results.

Background: As an unwanted side effect, lateral thermal expansion in bipolar tissue sealing may lead to collateral tissue damage. Materials and Methods: Our investigations were carried out on an ex vivo model of porcine carotid arteries. Lateral thermal expansion was measured and a calculated index, based on thermographic recording and histologic examination, was designed to describe the risk of tissue damage. Results: For instrument 1, the mean extent of the critical zone > 50 °C was 2315 ± 509.2 µm above and 1700 ± 331.3 µm below the branches. The width of the necrosis zone was 412.5 ± 79.0 µm above and 426.7 ± 100.7µm below the branches. For instrument 2, the mean extent of the zone > 50 °C was 2032 ± 592.4 µm above and 1182 ± 386.9 µm below the branches. The width of the necrosis zone was 642.6 ± 158.2 µm above and 645.3 ± 111.9 µm below the branches. Our risk index indicated a low risk of damage for instrument 1 and a moderate to high risk for instrument 2. Conclusion: Thermography is a suitable method to estimate lateral heat propagation, and a validated risk index may lead to improved surgical handling.

Deep Heating of a Snowpack by Solar Radiation

The observed gradual change in the Earth’s climate most noticeably affects the snow cover and ice sheets in the polar regions, especially during the long polar summer, when solar radiation leads to considerable increase in temperature and partial melting at some distance from the snow or ice surface. This effect, which in the polar regions is more pronounced in the snow cover, deserves serious attention as an important geophysical problem. In this article, for the first time, a theoretical analysis is made of the conditions under which the absorption of directional radiation penetrating a weakly absorbing scattering medium has a maximum at some distance from the illuminated surface. It is shown that the maximum absorption of radiation inside an optically thick medium exists only at illumination angles less than 60° from the normal. An analytical solution was obtained that gives both the magnitude of this maximum absorption and its depth below the illuminated surface. Calculations of solar radiation transfer and heat propagation in the snow layer are also performed. Various experimental data on the ice absorption index in the visible range are taken into account when determining the optical properties of snow. To calculate the transient temperature profile in the snow layer, the heat conduction equation with volumetric absorption of radiation is solved. The boundary conditions take into account the variation of solar irradiation, convective heat transfer, and radiative cooling of snow in the infrared transparency window of the cloudless atmosphere. The calculations show that the radiative cooling should be taken into account even during the polar summer.

Effects of non-Fourier bioheat transfer on bone drilling temperature in orthopedic surgery: Theoretical and in vitro experimental investigation.

The mechanical drilling process is a typical step in treating bone fractures to fix broken parts with screws and plates. Drilling generates a significant amount of heat and elevates the temperature of the bone, which can cause thermal osteonecrosis and damage to the surrounding bone tissue and nerves. Thermal inertia between heat flux and temperature gradient in nonhomogeneous interior structural medium-like biological tissues is arguable. Therefore, this paper proposes an analytical model of heat propagation in bone drilling for orthopedic surgery based on the hyperbolic Pennes bioheat transfer equation (HPBTE). Drilling experiments in bovine cortical bone samples were also carried out using an infrared thermography approach to confirm the proposed analytical model. Around the drilled hole surface, thermal necrosis is spread out from 1 to 10 mm. Increased feed rate reduces necrosis penetration distance and increases intense bone necrosis. The HPBTE includes thermal relaxation time effect and internal convective function of tissue perfusion rate. As these factors are not considered in the parabolic heat transfer equation (PHTE), the results show that the HPBTE is more accurate in predicting temperature and thermal osteonecrosis than the PHTE. As a result, proposed analytical model is a handy tool for calculating temperature to avoid thermal damage while improving process efficiency. Furthermore, it has the capability of controlling the manual or robotic drilling procedure for minimally invasive operations.

Phenomena of thermo-sloutal time’s relaxation in mixed convection Carreau fluid with heat sink/source

Recently, with the fast growth of new engineering technologies various researchers have presented fantastic dynamism in sightseeing the heat propagation through a wave mechanism instead of essentially by dispersion. Further studies insist that this is not a little temperature phenomenon; however, relatively one which has probable vital physical uses. This topic caught exceptional thought because of its generous uses in industrial and current built-up processes. Thus, here advanced Cattaneo–Christov heat and mass fluxes have been reported for the study of thermo-sloutal time relations. Aspects of MHD, heat sink/soure, variable properties of mass diffusivity and thermal conductivity in mixed convection Carreau fluid have been elaborated. The bvp4c numerical process has been exploited for the solutions of influential factors graphically. The mixed convection factor improves the fluid velocity of Carreau fluid. Our outcomes report the diminishing performance for thermo-relaxation factor on temperature field and sloutal-relaxation factor in concentration field. The escalating performance of mass diffusivity factor has been detected on concentration field. Tables for comparison with former studies with good agreement have been also disclosed.Abbreviations: : ratio of stretching rates parameter: thermal conductivity factor: mass diffusivity factorHAM: homotopy analysis method: magnetic factorODEs: ordinary differential equationsPDEs: partial differential equations: Schmidt number

Heat propagation simulation of thin-walled Ti6Al4V alloy components fabricated by double-wire GTAW additive manufacturing

In this study, a temperature field finite element model of the thin-walled Ti6Al4V alloy component fabricated by double-wire tungsten arc welding-based wire arc additive manufacturing was established. Detailed heat propagation of the molten pool and the deposited layer was analysed systematically. The simulated results illustrate that the heat accumulation of the thin-walled Ti6Al4V alloy component becomes evident step by step as the deposition process proceeds. The height of the specified heat affect zone increases gradually, and then stabilises, and the stable value is ∼14 mm. The molten pool influences two deposition layers when it moves. The heat conduction from the thin-walled to the substrate still plays a major role as the layers are deposited.

Effects of Thermal Gradients in High-Temperature Ultrasonic Non-Destructive Tests.

Ultrasonic inspection techniques and non-destructive tests are widely applied in evaluating products and equipment in the oil, petrochemical, steel, naval, and energy industries. These methods are well established and efficient for inspection procedures at room temperature. However, errors can be observed in the positioning and sizing of the flaws when such techniques are used during inspection procedures under high working temperatures. In such situations, the temperature gradients generate acoustic anisotropy and consequently distortion of the ultrasonic beams. Failure to consider such distortions in ultrasonic signals can result, in extreme situations, in mistaken decision making by inspectors and professionals responsible for guaranteeing product quality or the integrity of the evaluated equipment. In this scenario, this work presents a mathematical tool capable of mitigating positioning errors through the correction of focal laws. For the development of the tool, ray tracing concepts are used, as well as a model of heat propagation in solids and an experimentally defined linear approximation of dependence between sound speed and temperature. Using the focal law correction tool, the relative firing delays of the active elements are calculated considering the temperature gradients along the sonic path, and the results demonstrate a reduction of more than in the error of flaw positioning.

Parameter sensitivity study on startup characteristics of high temperature potassium heat pipe

Due to high power density, compact structure and easy modular assembly, heat pipe cooled reactor (HPR) is considered as an excellent candidate for removable power supply system. The heat transfer characteristic of liquid metal heat pipe, which is the only device to conduct the heat from reactor core, is extremely important for the safe operation of HPR. In this paper, the heat transfer performances of high temperature potassium heat pipes (Φ28 × 800 mm) are tested under different heating power (300–1000 W), wick mesh (600 and 800), filling charge amount (20 g and 50 g) and inclination angle (0°, 45°, 90°). The results show there is a temperature difference of 170 °C in condensation section at heating power of 336 W. With the increase of heating power, the melting and propagation speed of the working fluid in container increases, and the heat pipe performance is improved. Both wick mesh and filling charge amount increasing can promote the heat transfer performance of heat pipes, the filling charge amount is the main influencing factor to prevent from overheating at evaporation section. However, the heat pipes, having 50 g potassium, have a great geyser boiling phenomenon at 45°and 90° which could threaten the safe operation of HPR. This study provides experimental data support and theoretical basis for design and optimization of liquid metal heat pipes.

Analysis of temperature-dependent viscosity effect on wire coating using MHD flow of incompressible third-grade nanofluid filled in cylindrical coating die

The convective heat and mass propagation inside dies are used to determine the characteristics of coated wire products. As a result, comprehending the properties of polymerization mobility, heat mass transport, and wall stress concentration is crucial. The wire coating procedure necessitates an increase in thermal performance. As a result, this research aims to find out how floating nanoparticles affect the mass and heat transport mechanisms of third-grade fluid in the posttreatment for cable coating processes in presence of a magnetic field with time-dependent viscosity. For nanofluids, the Buongiorno model is used. The model equations are developed using continuity, momentum, and energy in the presence of nanoparticle and time-dependent variable viscosity. We propose a few nondimensional transformations that are relevant. The numerical technique Runge-Kutta fourth method is used to generate numerical solutions for nonlinear systems. Pictorial depictions are used to examine the effects of various factors in the nondimensional flow. Furthermore, the numerical results are also verified analytically using Homotopy Analysis Method (HAM). The analytical findings of this investigation reveal that within the Reynolds modeling, the stress on the whole wire surface combined shear forces at the surface predominate the Vogel model. The contribution of nanomaterials on force on the entire surface of wire and shear forces at the surface appears positive. A non-Newtonian feature can increase the capping substance’s velocity. This research could aid in the advancement of wire coating technologies. For the very first instance, the significance of nanotechnology during wire coating evaluation is explored utilizing time-dependent variable viscosity regarding the magnetic field. For time-dependent viscosity, two alternative models are useful. The Lorentzian strength (a resistive form of force) increases in magnetic strength increases. As a result of the increased magnetic field, the motion of the polymerization in a die decreases. It is clear that increasing the intensity of Nb increases the heat transfer. The innovative fragment of the present study is to scrutinize the magnetized third-grade nanofluid for wire coating with variable viscosity inside the pressurized coating die, which still not has been elaborated in the available works to date. Consequently, in the restrictive sense, the existing work is associated with available work and originated in exceptional agreement.

Experimental Investigation of Combustion Characteristics of a Spark Ignition Engine Fueled with Methanol-Gasoline Blends (M15 and M85)

Combustion characteristics of a 2.8 kW, constant speed, spark ignition engine fuelled with methanol-gasoline blends (M15 and M85) were studied. It was observed that the maximum in-cylinder pressure and maximum heat release rate with M85 were almost like gasoline while these values were significantly lower with M15. The flame development duration was 30.5% and 5.5% shorter at lower and higher load respectively with M85 as compared to gasoline. In addition to this, the flame propagation duration was shorter by 37% and 14.28% at lower and higher load with M85. Similar results were obtained with M15 blend. The crank angle for fifty percent mass burnt fraction was near to the top dead centre of engine with both the blends as compared to gasoline. The methanol-gasoline fuelled spark ignition engine’s important combustion characteristics including heat release rate, cumulative heat release, combustion duration, flame development, propagation and laminar flame velocity are analysed in detail.

Mathematical model and method of solving the generalized Dirichle problem of heat exchange of a cut count

The choice of thermal protection of the rocket fairing is approached with special care, because the fairing must protect against aerodynamic heating, radiation, temperature changes. Currents with large Mach numbers are accompanied by gas-dynamic and physicochemical effects. When flowing around the blunt body, a shock wave is formed, which departs from the body, remaining in the vicinity of the frontal point almost equidistant to its surface. Physico-chemical effects are due to rising temperatures caused by the inhibition of gas by the shock wave. At the same time there is a transition of kinetic energy of a stream rushing in thermal, fluctuating degrees of freedoms of gas molecules are excited, its dissociation and even ionization begins. Therefore, among the problems of great theoretical and practical interest is the problem of studying the temperature fields arising in the fairings for missiles in the form of a truncated cone, which rotate around its axis, given the finiteness of the rate of heat propagation. In the article the mathematical model of calculation of temperature fields for a truncated cone is constructed for the first time which approximately models distribution of temperature fields which arise in fairings for rockets, with taking into account the angular velocity and the final speed heat distribution in the form of a boundary value problem of mathematical physics for hyperbolic equation of thermal conduc-tivity with boundary conditions Dirichlet. A new integral transformation for a two-dimensional finite space is constructed, in the application of which the temperature field in the form of a convergent series is found. The solution found can be used to predict the possible value of thermomechanical stresses, to promote the correct choice of technological parameters, objective control, allows to identify ways to improve the thermal protection of fairings for missiles.

MATHEMATICAL MODELING OF THE FOREST FIRE IMPACT ON THE BRANCH OF A CONIFEROUS TREE

It is necessary to develop quantitative methods to assess the formation of thermal burns in the morphological parts of coniferous trees. The purpose of the study is mathematical modeling of heat transfer in the layered structure of a coniferous tree branch under the influence of a forest fire front. The heat propagation in the «branch — needles — flame zone» system is described by a system of non-stationary differential equations of heat conduction with the corresponding initial and boundary conditions. As an object of research, a digital model of a branch of a coniferous tree for various species, namely, pine, larch and fir, was used. Temperature distributions are obtained for different variants of the branch structure and conditions of the impact of the forest fire front. Conclusions are made about the need for further modernization of the mathematical model. The developed model is the basis for creating software tools for specialized geographic information systems.

High performance epoxy resin with efficient electromagnetic wave absorption and heat dissipation properties for electron packaging by modification of 3D MDCF@hBN

Exploiting electronic packaging materials with simultaneously high thermal conductivity and electromagnetic wave absorbing capacity has been considered as a key strategy to resolve the ever-increasing heat flux density and electromagnetic interference of integrated circuits, although it is hard to achieve. Here, we report 3D MDCF@hBN filled epoxy resin (i.e., MDCF@hBN/EP) as a promising candidate. 3D MDCF@hBN was created by self-assembling negative charged hydroxyl-modified hBN on the surface of positive charged melamine foam through electrostatic effect, and subjected to carbonization at 900 ℃. In which, the hBN can enhance the dielectric loss capability and impedance matching of MDCF, resulting in the minimum reflection loss (RL)value of − 52.77 dB at 9.36 GHz and the maximum effective absorption bandwidth of 5.60 GHz (from 12.40 to 18.00 GHz) for 25 wt% MDCF@hBN filled EP. In addition, the 3D MDCF@hBN also acts an effective heat propagation path in EP, leading to a high thermal conductivity of 0.99 W·m−1 K−1 at room temperature, 450% higher than that of pristine EP. The coalesced high thermal conductivity and electromagnetic wave absorption performance in EP indicate that MDCF@hBN/EP has a promising practical application in high-power integrated circuits.