Boundary Conditions Of Heat Exchange Research Articles

The use of Thermography to Determine the Boundary Conditions of Heat Exchange on The Inner Surfaces of Translucent Enclosing Structures

The paper presents an approach to determining the boundary conditions of heat transfer (heat transfer coefficients) on the inner surfaces of translucent enclosing structures using thermal imaging data. To implement this approach, it is necessary to use additional equipment in the form of sheets of paper. A sheet of paper is installed close to and perpendicular to the investigated surface of the structure. At the same time, the profile of the sheet of paper exactly repeats the geometry of the surface under study. Based on the results of thermal imaging, thermograms and temperature graphs are constructed on characteristic areas of the inner surface of the translucent enclosing structure. They are used to determine the thickness of the boundary layer of air adjacent to the inner surface of the translucent enclosing structure. These data are used later to calculate the heat transfer coefficient at the inner surface of these structures. The presented approach was implemented in the course of field studies of heat transfer conditions at the internal surfaces of four PVC windows.

Performance analysis of CO2 thermal management system for electric vehicles in winter

CO2 is well-suited for thermal management systems (TMSs) in electric vehicles, particularly in winter when both the cabin air and the battery require heating. However, due to the distinct heat exchange boundary conditions of these two heated components, traditional theories of optimal operation of CO2 cycle are not applicable. In this paper, the system characteristics of a CO2 TMS in the cabin-and-battery mixed heating mode are comprehensively investigated. The results show that there is a pseudo-optimal discharge pressure that maximizes the COPTMS, regardless of whether the system is operating in a transcritical or subcritical mode. In addition, besides the global optimal COPTMS, there may still be other local maximum points, which are determined by the CO2 flow distribution in both gas coolers and the COP rise rate of the battery cycle. Furthermore, this work offers a thorough investigation of the impact of essential factors on the pseudo-optimal discharge pressure and proposes an accurate prediction approach for the best control of the CO2 TMS. The CO2 TMS can still ensure a COPTMS above 2.0 to meet the thermal demands of both the cabin and the battery even under the challenging operating circumstances of −20 °C, proving the technology's great competitiveness.

Dissociation and combustion of mixed methane-ethane hydrate

Non-isothermal decomposition of mixed methane-ethane hydrate in a furnace is studied experimentally and theoretically with varying temperature. Over the combustion duration, the dissociation rates of the gas hydrate powder and tablet are approximately estimated under five different combustion schemes: at decomposition in a high-temperature muffle furnace and during induction heating under different boundary conditions of heat exchange. With an increase in the temperature in the furnace from 890 K to 1350 K, the dissociation rate of methane-ethane hydrate increases by 25–50%. The maximum dissociation rate corresponds to a thin layer of powder in the furnace at a temperature of 1350 K. Gas release is measured at combustion using a gas analyzer: H2, CH4, CO, CO2 and NOx. The emissions of nitrogen and carbon oxides from the combustion of methane-ethane hydrate are shown to be much lower than from the combustion of high-potential and conventional fuels. It is established that the high concentration of water vapors from the combustion of methane-ethane hydrate can reduce anthropogenic gas emissions. The concentration of unreacted methane gases drops significantly with increased temperature in the furnace. A mathematical model was developed to describe the dissociation and combustion of a porous methane-ethane hydrate layer, accounting for ice melting, water evaporation, as well as convective flows in the gas mixing layer. The simulation results correspond to the experimental data. The obtained results may be used to improve the combustion efficiency of double hydrates, as well as to reduce emissions of both combustible H2 and CH4 gases and harmful emissions of CO2 and NOx.

Generalization of the Fourier Problem on Fluctuations in the Temperature of the Earth’s Crust

The problem of asymptotic fluctuations of temperature and moisture content in a half-space is solved by the method of complex amplitudes. The material filling the half-space consists of a solid base (capillary-porous body) and water. The well-known Fourier solution for temperature fluctuations in half-space in the absence of moisture and under the boundary conditions of heat exchange of the first kind is generalized to the case of a wet material under the boundary conditions of Newton for temperature and Dalton for moisture content. The results of the work can be used in geocryology to model seasonal fluctuations in the thermophysical characteristics of frozen rocks and soils.

Time fractional thermoelastic problem of a thick cylinder with non homogeneous material properties

In this article, we assume a two dimensional thermoelastic problem of nonhomogeneous thick hollow cylinder within the context of fractional order derivative of order 0 < α ≤ 2. Convective heat exchange boundary conditions are applied at the curved surface, whereas the lower surface and the upper surface of the cylinder are considered at zero temperature. Furthermore cylinder is subjected to a sectional heating at the outer curved surface of cylinder. Let the material properties of the cylinder except Poisson’s ratio and density are considered to be expresses by a simple power law in axial direction. The solution of the thermoelastic problem is obtained in terms of trigonometric and Bessel’s functions. Both the thermal and mechanical behavior is analyzed by the influence of inhomogeneity. Numerical computations are carried out for a mixture of copper and tin metals for both homogeneous and nonhomogeneous cases. Results of numerical solutions are illustrated graphically for temperature distribution and thermal stresses for all the different values of the fractional-order parameter α with the help of Mathematica software.

Analysis of Time-Fractional Heat Transfer and its Thermal Deflection in a Circular Plate by a Moving Heat Source

Mathematical modeling of a thin circular plate has been made by considering a nonlocal Caputo type time fractional heat conduction equation of order &lt;i&gt;0 &lt;&lt;/i&gt; α ≤ &lt;i&gt;2&lt;/i&gt;, by the action of a moving heat source. Physically convective heat exchange boundary conditions are applied at lower, upper and outer curved surface of the plate. Temperature distribution and thermal deflection has been investigated by a quasi-static approach in the context of fractional order heat conduction. The integral transformation technique is used to analyze the analytical solution to the problem. Numerical computation including the effect of the fractional order parameter has been done for temperature and deflection and illustrated graphically for an aluminum material.

Parametric identification of differential-difference models of heat transfers in the systems of bodies

The combined inverse heat conduction problem (IHCP) was solved to restore the boundary conditions of heat exchange, in particular, unsteady heat flux, while simultaneously refining the thermophysical properties of the object material by parametric identification of the differential - difference models (DDM) of heat transfer in the object of study. The differential-difference model is a system of first order ordinary differential equations with respect to the state vector. The type of feedback, control, and measurement matrices included in the DDM is established. A priori parametrization and parametric identification of the heat transfer model was performed. The parametrization involves approximation of the desired heat flux by B-splines of the first order for each piecewise-linear segment. With parametric identification, the discrepancy between the model and experimental values of the parameters is minimized using a recurrent linear Kalman filter. Taking into account the parametrization and parametric identification, the time-varying heat flux at the body boundary was restored and its thermal and physical properties, in particular, thermal conductivity, were simultaneously refined. The uncertainty of restoration of parameters based on the Gram matrix is estimated. The boundaries of confidence areas for determining the desired parameters based on the sensitivity functions, which are obtained by solving the heat transfer equations, are established. The results of model experiments, in which initial estimates of the desired parameters were set twice less than the true ones, are given.

A dynamic thermo-mechanical actuator system with contact and Barber's heat exchange boundary conditions

AbstractThis work, motivated by the rapid developments in Micro-Electro-Mechanical Systems (MEMS) structures, especially actuators and grippers, analyses the dynamics of a thermo-mechanical system consisting of a horizontal beam joined at one end to a vertical rod. As a result of thermal expansion or vibration of the rod, the other end may come into contact with another part of the MEMS device and that closes an electrical circuit, which is the actuating or switching function of such a beam–rod system. The interaction between the rod's contacting end and the supporting device is described by a normal compliance contact law for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is a multi-function taking into account the air resistance in the gap when there is no contact and the contact pressure when contact occurs. The model consists of a nonlinear variational inclusion for the temperature coupled with a nonlinear variational equation for the displacements. The existence of a weak solution to the problem is proved by using the Galerkin method, a regularization of Barber's condition with the Yosida approximation of a maximal monotone operator, and a priori estimates.

Diagnosis of Temperature Conditions in Metals When Heated in Continuous Furnaces

We have developed an algorithm for diagnosing temperature conditions in metals during heating in a continuous furnace. This algorithm is based on a mathematical model of the process which uses a single differential equation to describe the non-steady-state thermal conductivity and heat exchange boundary conditions based on current measurements of the parameters describing the external heat exchange. We have also developed an approach for real-time monitoring of the quality of the results obtained using the proposed diagnosis algorithm, based on comparison of different determinations of the thermal flux absorbed by the metal.

Experimental Method for Determination of Boundary Conditions of Heat Exchange in Parts of External Combustion Engines

Представлено обоснование экспериментального метода определения граничных условий теплообмена в камере сгорания двигателей внутреннего сгорания. Показано, что, несмотря на большие возможности современных численных методов определения теплового состояния деталей двигателей и имеющихся на их основе современных интегрированных пакетов, точность получаемых результатов определения теплового состояния деталей двигателя, образующих камеру сгорания, зависит от точности экспериментального определения граничных условий теплообмена. Граничными условиями теплообмена для дифференциального уравнения, описывающего процесс нестационарной теплоотдачи от рабочего тела к стенкам деталей, образующих камеру сгорания двигателя, являются значения мгновенного коэффициента теплоотдачи от газа к стенкам деталей камеры сгорания, температура газа в камере сгорания, мгновенная температура поверхности деталей камеры сгорания и температурный градиент по нормали к поверхности деталей. Для определения коэффициента теплоотдачи от газа к стенкам деталей, образующих камеру сгорания двигателя, разработан метод измерения температуры пламени в камере сгорания на основе пирометрии спектрального отношения со специальной оптической системой с интерференционными светофильтрами. Для измерения мгновенной температуры поверхности деталей камеры сгорания и температурного градиента по нормали к поверхности деталей разработана пленочная термопара и проведено исследование ее динамических характеристик. Для проведения экспериментальных исследований разработана усилительно-регистрирующая аппаратура и проведено экспериментальное измерение основных параметров теплообмена в камере сгорания двигателя. Полученные результаты подтверждают эффективность предложенных методов для экспериментального определения граничных условий теплообмена в двигателях внутреннего сгорания.

Modeling of Gas Turbine Cooled Blades

In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasi-stationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received [6]. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.Copyright © 2006 by ASME

Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading

ABSTRACTThe transient thermal stress crack problem for a half-space with a multilayer coating under thermal surface loading containing an undercoat crack, perpendicular to the interface, is considered. The problem is solved using the principle of superposition and uncoupled quasi-static thermoelasticity. Transient temperature distribution and corresponding thermal stresses for the uncracked multilayer assembly are obtained in a closed analytical form using the model with generalized thermal boundary conditions of heat exchange of a half-space with ambient media via the coating. The crack problem is formulated as a perturbation mixed boundary value problem, in which the crack surface loading should be equal and opposite to the thermal stresses obtained for the uncracked medium, and is reduced to a singular integral equation and solved numerically. Numerical computations are performed for the analysis of influence of the coating upon thermal stresses and thermal stress intensity factor.

Energy-based variational modeling of fully formed adiabatic shear bands

Abstract An energy-based variational modeling approach of adiabatic shear bands (ASB) for thermo-viscoplastic materials is proposed. In the process of derivation of this thermo-mechanical coupled problem, the variational methodology is first applied to classical problems, such as Couette flow, thermal conduction in a fluid layer and thermal Couette flow. The solutions are compared to the corresponding analytical solutions. In a second part, a slab under stationary simple shear is analyzed by a Ritz–Galerkin method combined with an energy-based variational approach of thermo-mechanical problems. The velocity and temperature profiles within an ASB are parameterized by two quantities: the shear band width and central temperature. It is shown that this variational formulation works for various material constitutive models, as illustrated by adopting two popular constitutive models (power law and Johnson–Cook law) and the results are checked by using a variational Finite Element Method. In a last part, mixed heat exchange boundary conditions are introduced to limit the effect of slab width on the solution. The profiles of velocity and temperature in the slab, as well as the influence of material properties on the formation of shear band are evaluated and in good agreement with results from the literature.

Variational analysis of a thermomechanically coupled quasi-steady rolling problem

In this work, a thermomechanically coupled rolling problem with nonlocal contact, Coulomb’s friction and heat exchange boundary conditions, for incompressible rigid-plastic, temperature-, equivalent strain- and strain-rate-dependent materials, is considered. A coupled variational formulation, consisting of a nonlinear variational inequality for the velocity, a nonlinear variational equation for the temperature and an evolution equation for the equivalent strain, is derived. A variable stiffness parameters method is proposed, its convergence is proved and existence and uniqueness results are obtained.

Mathematical Modeling of Gas Turbine Blade Cooling

In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade. Keywords—Mathematical Modeling, Gas Turbine Blade Cooling, Neural Networks, BIEM and FDM.

Thermal fatigue crack propagation in massive cylinders during their cyclic heating

Processes that reduce the level of maximum unsteady stresses during thermal fatigue crack propagation in massive bodies during their convective cyclic heating are considered. It is shown that during crack propagation, the stress intensity factor K1 increases initially to a certain limit K1max and then decreases. The factor K1max depends on the initial and boundary conditions of heat exchange as well as on the rates of decrease in the maximum stresses during thermal fatigue crack propagation. It is shown that the asymmetry of boundary and initial conditions of heat exchange can contribute to either acceleration or retardation of crack propagation depending on the material properties and heating conditions.

Energy recovery from municipal solid waste incineration—A review

Heat recovery from the incineration of municipal solid waste (MSW) can make a useful contribution to the nation's energy needs. This paper reviews the literature on the field of energy recovery from MSW incineration. This review includes (1) An historical background on the MSW methods of disposal and the recent trends. (2) The potential role of waste as a fuel from the knowledge of its analysis, heating value and quantity. (3) The alternative methods of waste disposal including the thermal (mass incineration, refuse-derived fuel and pyrolysis), the mechanical and the biochemical processes. (4) Some economic considerations regarding MSW disposal costs. (5) The combustion characteristics of MSW and waste combustion plants. (6) Heat recovery from waste burning including the main types of waste heat boilers; the heat recovery rates; heat exchange boundary conditions; fouling, erosion and corrosion of waste heat boilers; control of waste incineration particulate emissions and finally the control of nitrogen oxides emissions. The intensive data given here is essential to the proper design and operation of any MSW-to-energy plant. The design needs to be undertaken with careful consideration of the experience that already exists in order to achieve success.