A fuel droplet vaporization model in a hot air stream

The gasification behavior of a fuel droplet has been studied. The convective heat transfer is focused on in most literature on droplet evaporation. In this paper, a mathematic model of droplet evaporation is improved. Considering the presence of simultaneous mass and heat transfer at the interface between phases, a proper heat transfer equation for droplet evaporation model is established. Based on the model, a computer simulation program was developed, and the predictions of the model are compared with the experimental data. Sample calculations show the capabilities of the model for droplet evaporation.     

Object-oriented modelling and simulation of heat exchangers with finite element methods

The paper describes the derivation of finite-element models of one-dimensional fluid flows with heat transfer in pipes, using the Galerkin/least-squares approach. The models are first derived for one-phase flows, and then extended to homogeneous two-phase flows. The resulting equations have then been embedded in the context of object-oriented system modelling; this allows one to combine the fluid flow model with a model for other phenomena such as heat transfer, as well as with models of other discrete components such as pumps or valves, to obtain complex models of heat exchangers. The models are then validated by simulating a typical heat exchanger plant.     

Heat and mass transfer in liquid desiccant air-conditioning process at low flow conditions

This paper investigates the transient heat and mass transfer in liquid desiccant air-conditioning process at low flow conditions. Using local volumetric average approach, one-dimensional non-equilibrium heat and mass transfer models are developed to describe the humid air and liquid desiccant interaction at counter flow configuration. Using triethylene glycol solution as desiccant, some experimental studies are completed. Experimental results are used to justify the numerical models. Numerical results are then obtained to demonstrate process characteristics. The models include a transient desiccant flow model for initial liquid desiccant building-up process, empirical wetted specific surface ratio for mass transfer, and heat and mass transfer coefficients. The objective of this research is to develop a process analytical tool for liquid desiccant air-conditioner design.     

Modelling of Heat Transfer and Vehicle Dynamics for Thermal Load Reduction by Hypersonic Flight Optimization

Heat input reduction by appropriate, optimal trajectory control is considered for the range cruise and the return-to-base cruise of a hypersonic vehicle propelled by a turbo/ram jet engines combination. A mathematical model is developed for describing the unsteady heat transfer through the thermal protection system. This model is coupled to the model of the dynamics of the vehicle. An efficient optimization technique is applied for constructing a solution for the two cruise problems. The results show that significant heat input reductions can be achieved with only a small penalty in fuel consumption.     

Mathematical modeling of aerosol emission from die sinking electrical discharge machining process

Emission of toxic gases and aerosol is an important hazard associated with the electrical discharge machining (EDM) process, one of the most widely used non-conventional manufacturing processes. These emissions can cause adverse health effects to the operators and has a direct impact on the environment. The emission from this process is directly related to the temperature at the process location. This paper was aimed at developing a model that quantifies the aerosol generated from the die sinking EDM process while machining steel workpiece with copper electrode. The model developed in this paper made use of energy balance and heat transfer equations. The modeling results were then validated using experimentally obtained values of the emission rate of aerosol from this process. The results showed a close correlation of +0.89 with experimental results. The model developed in this paper can predict the level of emissions at different process locations; thereby reducing the direct cost and time associated with experimentation.     

Coefficient inverse extremum problems for stationary heat and mass transfer equations

A technique is developed for analyzing coefficient inverse extremum problems for a stationary model of heat and mass transfer. The model consists of the Navier-Stokes equations and the convection-diffusion equations for temperature and the pollutant concentration that are nonlinearly related via buoyancy in the Boussinesq approximation and via convective heat and mass transfer. The inverse problems are stated as the minimization of certain cost functionals at weak solutions to the original boundary value problem. Their solvability is proved, and optimality systems describing the necessary optimality conditions are derived. An analysis of the latter is used to establish sufficient conditions ensuring the local uniqueness and stability of solutions to the inverse extremum problems for particular cost functionals.     

Modelado numérico del proceso de soldadura FSW incorporando una técnica de estimación de parámetros

Numerical models of heat transfer and fluid flow used in the simulation of the friction-stir welding (FSW) process have contributed to the understanding of the process. However, there are some input model parameters that cannot be easily determined from fundamental principles or the welding conditions. As a result, the model predictions are not always in agreement with experimental results. In this work, the Levenberg-Marquardt (LM) method is used in order to perform a non-linear estimation of the unknown parameters present in the heat transfer and fluid flow models, by adjusting the temperatures results obtained with the models to temperature experimental measurements. These models are implemented in a general-purpose software that uses a numerical formulation developed from the finite element method (FEM). The unknown parameters are: the friction coefficient and the amount of adhesion of material to the surface of the tool, the heat transfer coefficient on the bottom surface and the amount of viscous dissipation converted into heat. The obtained results show an improvement in the numerical model predictions from the incorporation of parameter estimation techniques.     

Frequency-domain regression method for estimating CTF models of building multilayer constructions

The conduction transfer function (CTF) models of heat conduction through building constructions are widely used in building energy analysis and heating, ventilation, and air conditioning (HVAC) system design and simulation. A frequency-domain regression (FDR) method is developed to estimate the CTF model of a building construction from its theoretical response characteristics in this paper. First, the theoretical response characteristics are calculated simply by numerical matrix multiplication. The CTF coefficients are then obtained by simply solving a set of linear equations. The tests and comparisons have shown that CTF models obtained by the FDR method are completely equivalent to those found by the methods currently available. The FDR method can provide a short series of CTF coefficients, and the models by this method have a high accuracy in calculating heat gain/loss through building constructions. The FDR method is very simple and straightforward, has high computational speeds, and needs less computational efforts. Therefore, the FDR method is much easier and convenient to use and implement in building energy analysis and HVAC system simulation programs.     

Modeling,simulation and optimization of general solar updraft towers

A model to describe a solar chimney power plant with a generally sloped collector field and for the general situation of humid air is presented. This is a significant development of existing simple models for solar updraft towers with planar collector fields for the situation of purely dry air. The model describing the gas dynamics in the collector and in the chimney includes a turbine model, friction and heat transfer losses, evaporation and condensation models etc. However, the relevant physics can be modeled in one space dimension. It is the result of a fully compressible gas dynamic model in the small Mach number limit. A numerical algorithm is defined which admits very fast simulations. Therefore optimization procedures can easily be applied. Numerical results on optimization with respect to geometric and physical parameters which may be considered both in the planning and the operational phase are presented. The results are compared qualitatively and – if available – quantitatively to prototype data and to simulations from the literature.     

Mathematical model of muscular contraction with a ccount of excitability

A model of muscular contraetion has been developed which establishes the relationship between normal stresses and longitudinal deformations of the muscle tissue and takes into account its excitability. A transfer function has been proposed for the equation describing the behavior of the muscle as a dynamic system which is controlled by synegisms. The validity of the model has been tested experimentally. The model has been used to develop type-II Lagrange equations for the solution of the basic task of biomechanics for some movements of the human body.Paper presented at the FirstAll-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.P. F. Lesgaft State Institute of Physical Culture, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 608–612, July–August, 1975.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.     

Numerical optimisation for induction heat treatment processes

This paper aims at introducing new approaches for designing and optimising induction heat treatment processes. Although the final objectives of induction heating processes may deal with some specific mechanical or metallurgical properties for manufactured parts, we shall primarily focus here on achieving an accurate control of temperature distribution and evolution in the Heat Affected Zone (HAZ). This objective can be formalised as a classical optimisation problem: we seek to minimise a cost function which measures the difference between computed and goal temperatures – along with some constraints on process parameters. We deal here with both zero-order algorithms – using a method based on Efficient Global Optimization algorithm which is an optimisation procedure assisted by a meta model – as well as first-order algorithms. These algorithms have been coupled with 2-D and 3-D finite element models developed in our laboratory; this model is based on a coupling procedure between Maxwell equations and heat transfer models, and has been extended to mechanical and metallurgical computations.     

Thermal control of Huygens mock up probe in Earth atmosphere: Thermo‐fluid dynamic simulation and mission data

A mock up of Huygens probe with 76 channels acquisition has been developed at University of Padova and successfully flown with a stratospheric space balloon from Italian Space Agency Base in Trapani on May 30th 2002. Temperature sensors have monitored temperature profiles in critical points of electronics, batteries and structure during raise at 40 km altitude, floating and parachuted descent. A thermal model of the probe has been implemented taking into consideration incoming external fluxes (solar direct, albedo and radiative heat fluxes), internal heat fluxes generation and convective heat transfer with atmosphere as a function of probe altitude. For the evaluation of convective fluxes and probe spinning rates an algebraic turbulent model, developed by the present authors, has been employed. This model is suitable to predict effects such as flow curvature and separation and solid boundary rotations. Simulation results have been utilized during project phase to optimize thermal paths in order to keep critical components in the allowable temperature range and for post flight analysis of mission data. These data show that passive thermal control of the probe has performed as expected contributing to a extremely successful scientific flight.     

直接配置法求解连续铸钢过程中的最优控制问题

利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 .     

A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin

A fin is traditionally thought of as an extension of a surface to facilitate the transfer of heat away from a larger body to which it is attached. In this paper, the authors study some mathematical properties of a nonlinear heat transfer model for a fin and its relation to an associated linear model. Specifically, they prove that the solution exists and is unique, and they determine bounds for the temperature. Further, they prove the monotonicity of the temperature distribution, and they obtain an estimate for the maximal difference between the temperatures as determined by the nonlinear and linear models.     

A three-dimensional steady state thermal fluid model of jumbo ingot casting during electron beam re-melting of Ti–6Al–4V

A 3-D coupled thermal-fluid model describing mass, momentum and energy transport within a Ti–6Al–4V rolling ingot cast in an (Electron Beam Cold Hearth Remelting) EBCHR process has been developed to describe steady state casting conditions. The model incorporates a number of the physical phenomena inherent to the industrial process, including a metal inlet in the center of one of the narrow faces, complex boundary conditions based on industrial practice, buoyancy driven flow within the liquid and flow attenuation using a Darcy momentum source term within the mushy zone. The model ignores turbulence in the liquid pool and Marangoni (surface tension) driven surface flows. The model has been validated against liquid pool depth and profile measurements made on an experimental casting seeded with insoluble dense markers and doped with dense alloy additions. Comparisons have also been made to video images taken of the top surface during casting. The results indicate that the model is able to quantitatively predict the steady state sump depth and profile and is able to qualitatively predict aspects of the top surface temperature distribution. The model has also been used to conduct a process heat balance and sensitivity analyses. The process heat balance conducted on the model domain indicates that at steady state the liquid metal inlet contributes 88% of the total power input, while the electron beam provides net 12% after accounting for radiation losses from the top surface; 62% of the heat is lost through the ingots sides and the balance is lost via bulk transport of sensible heat through the bottom of the domain. The results of the sensitivity analysis on pool depth indicate that casting rate has the largest effect followed by metal inlet superheat. The thermal, flow and pressure fields predicted by the steady state model serves as the initial conditions for a transient hot-top model, which is the subject of a forth-coming paper.     

Phase transition in binary systems and the binary alloy problem

In this paper we consider a phase transition in binary systems describing the solidification of a dilute alloy in one space dimension, in which the equations of heat and mass transfer are coupled through the conditions at the free boundary. A kinetic condition is introduced to suggest a regularization of the model, which admits a unique solution, and to obtain the generalized solution of the dilute-alloy problem under an additional assumption.     

A 3-colour ink jet plotter for computer graphics

A new plotter for hard copy colour display of digital computer outputs has been developed. The plotter uses three intensity modulated ink jets with the colours red, yellow and blue, which plot the information on a normal A 4 paper (210×297 mm) fastened to a rotating drum. The ink jets are individually controlled from a magnetic tape unit which is loaded with a tape prepared by the computer. The total plotting time is 85 seconds independent of the complexity of the picture to be plotted. The total information contents plotted in one 85 second run is 3.7·10⁶ bits.     

A mathematical model of the heat transfer process in a shell and tube condenser for use in refrigeration applications

This paper describes a mathematical model that may be used in predicting the heat transfer performance of a shell and tube condenser. The model uses the Effectiveness-Number of Transfer Units (E-NTU) method of heat exchanger analysis. Given the geometric characteristics, the flow conditions and inlet fluid temperatures the model determines, (a), the necessary heat transfer coefficients; (b), the fractions of the condenser devoted to desuperheating, condensing and subcooling the condensing medium; (c), the total heat rejection; and (d), the exit fluid temperatures.The model has been validated by testing a typical condenser at various operating conditions. The measured performance has been compared with that predicted theoretically and a close correlation has been found to exist between the two.