In diesem Kapitel werden grundlegende Begriffe und physikalische Größen zur Beschreibung von Wärme- und Stoffübertragungsvorgängen eingeführt sowie Grundgesetze der Wärme- und Stoffübertragung behandelt. Mit ihrer Hilfe lassen sich bereits technisch wichtige Aufgaben lösen wie die Berechnung des Wärmedurchgangs zwischen zwei Fluiden, die durch eine Wand getrennt sind, oder die Dimensionierung von Apparaten zur Wärme- und Stoffübertragung. Wir behandeln daher solche relativ einfachen Berechnungsverfahren in diesem einführenden Kapitel, während die eingehende Darstellung komplexer Wärme- und Stoffübertragungsprobleme den folgenden Kapiteln überlassen bleibt.
In diesem Kapitel behandeln wir die stationare und instationare Warmeleitung in ruhenden Medien, die vor allem in festen Korpern auftritt. Wir leiten zunachst die grundlegende Differentialgleichung fur das Temperaturfeld her, indem wir den Energieerhaltungssatz mit dem Gesetz von Fourier verknupfen. Die dann folgenden Abschnitte behandeln die stationaren und instationaren Temperaturfelder mit zahlreichen praktischen Anwendungen sowie die numerischen Methoden zur Losung von Warmeleitproblemen, deren Anwendung durch elektronische Rechner erleichtert wird und sich zunehmend verbreitet.
This paper presents an experimental study dealing with the basic nucleate boiling concerning two finned surfaces placed in a narrow channel. The influence of both the channel width and the orientation of the base surface (horizontal or vertical) are discussed. The experiments were performed in a saturated pool of FC-72 while the channel widths investigated were 2.0 mm and 0.5 mm. The experimental data are compared with those obtained in the case of the unconfined situation of the extended surfaces. Channel width reduction does not affect the heat transferred to the liquid in the case of vertical orientation of the base surface, while it causes a drastic reduction in the heat transfer behavior in the case of a horizontal base surface. For the latter situation, vapor stagnation in the gap was observed after the maximum heat flux had been reached.
This work theoretically investigated the thermal performance and stability characteristics of a straight pin fin subject to boiling considering a temperature-dependent thermal conductivity of fin, k=k sat(1+b(T−T sat)). Steady-state temperature distribution and the associated fin base heat flow were for the first time analytically found, whose stability characteristics were evaluated by linear stability analysis. A positive temperature coefficient b will raise both the fin's temperature and base heat flow. The corresponding stability for stable fin boiling was enhanced. A negative b results in an opposite trend. The use of a mean thermal conductivity in fin boiling calculations is discussed.
This paper presents a parametric study of relevant processing parameters found in microcasting Shape Deposition Manufacturing (SDM). Microcasting SDM is a novel, layered manufacturing process capable of rapidly manufacturing near net shape, metal objects. The quality of artifacts built with this process depends on proper metallurgic bonding between impacting molten droplets and previously deposited substrate layers, as well as on the final microstructure of the artifact. Numerical simulations are performed to investigate the effect of operating conditions on the metallurgic bonding induced by substrate remelting and on the microstructure determined by the cooling rates during solidification. Particularly, the effect of droplet impinging temperatures, substrate initial temperatures and combinations of copper and stainless steel materials are investigated. Numerical predictions reveal that impinging droplet temperature variations, within the attainable range in microcasting SDM, have a minimal effect on the cooling rates during solidification. However, droplet temperature has a significant effect on the substrate remelting depth. Furthermore, this investigation quantifies the extent to which substrate preheating lowers the cooling rate during solidification and promotes substrate remelting. The study of the interaction between copper and stainless steel materials shows that the cooling rates during solidification of the deposition material and the occurrence of substrate remelting are both highly dependent on the combination of materials.
A perturbation technique is proposed for solution of the generalized equations governing the thermal behaviour of thin metal films described by a hyperbolic two-step model. The generalized equations of this model contains diffusion terms in both the electron and lattice energy equations and assumes that incident laser radiation is absorbed by both the electron gas and solid lattice to account for the thermal behaviour of semiconducting and impure metals. A perturbation technique is utilized to eliminate the coupling between the electron and phonon energy equations when the normalized temperature difference between electrons and phonons is a small quantity, which is true in materials exhibit high coupling factors.
Transient conjugate natural convection heat transfer in open-ended vertical concentric annuli is investigated numerically. The governing equations of an induced laminar flow for a fluid of Pr=0.7 are solved using a finite-difference technique. The heating is achieved by a step change in the temperature of the outer surface of the outer tube while the inner surface of the inner tube is kept adiabatic. The range of Grashof number considered is 500≤Gr * ≤10 5 . The effects of solid-fluid conductivity ratio and diffusivity ratio on the transient induced flow characteristics are presented.
A three phase mathematical model of simultaneous heat and mass transfer of a batch operation for a fluidized bed is presented. The three phases are a solid free bubble, emulsion and solid phases. The model employs an elaborate five equations porosity model. Various correlations for the minimum fluidization parameters are surveyed and compared with the adequate one is being adopted in the model. The governing equations together with the boundary and initial conditions are presented for a cyclic operation of the bed. These are numerically solved for a test case where the bed is charged with silica gel particles to dehumidify a process air stream. Thus the bed works in an air dehumidification mode/bed regeneration mode cyclic operation with matching conditions.Results for the bed operation are presented as the temperature and humidity ratio variations for the test case. The results indicate the ability of the developed model to provide the␣required data for the concerned batch operated fluidized bed.
This study addresses a distinct, unsophisticated computational procedure for solving approximately, but analytically, the one-dimensional heat equation for circumferential fins of uniform thickness with constant properties. This differential equation with variable coefficients, called the modified Bessel equation of zero order, is subject to a prescribed temperature at the base and zero heat rejection at the tip. Approximate temperature distributions and companion heat transfer rates of excellent quality have been obtained by adequately blending a polynomial curve fit, the method of successive approximations and the method of undetermined coefficients. Detailed error distributions are also presented for real uniform circumferential fins using the exact solution by modified Bessel functions as the baseline case. The calculations of analytic character were carried out with a symbolic algebra software, Maple V, on a personal computer.
A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number, R w the surface temperature parameter, θ w and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of R d ,θ w or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters on the formation of the flow separation are studied.
It is shown that the linear boundary value problems of the heat conduction in a homogeneous slab can be mapped on the initial value problem for a Hamiltonian motion whose phase-space trajectories are subject to an additional restriction, the "arrival condition". The physical consequences of this formal analogy for the macroscopic heat conduction are discussed in detail.
This paper deals with a numerical study of combined convective and radiative heat transfer in a three-dimensional rectangular duct with hydrodynamically and thermally developing laminar flow. The gas is assumed to be an incompressible, absorbing, emitting, isotropically scattering, gray medium. Isothermal, gray, diffuse boundary walls at different temperatures are assumed. The finite-volume method (FVM) is adopted to describe both convective and radiative heat transfer. The coupled continuity and momentum equations are solved by means of SIMPLER algorithm. Numerical results for the radiative flux show very good agreement with the available data. The effects of aspect ratio, optical thickness, scattering albedo and wall emissivity on the mean bulk temperature are also investigated. By splitting the heat flux into convective and radiative contributions, the relative importance of these components is assessed for a typical range of values of the parameters.
This paper deals with the experimental and theoretical investigation of the influence of an electric field on the heat transfer rate during stable film boiling of the electrically insulating fluid FC-72. In particular the case of stable saturated film boiling from a horizontal plate is studied. The experiments show that the heat transfer rate increases ±50 when an electric field of 27.3 kV/cm is applied. A new correlation for the heat transfer rate in the presence of an electric field based on the heat transfer model of Klimenko is derived in this paper. Therefore the behavior of the liquid-vapor interface is studied in more detail. This study shows that the electric field has a two fold effect on the interface. On the one hand the distance between adjacent bubbles decreases and on the other hand the bubbles elongate in the presence of the electric field. The new correlation is in good agreement with the experiments.
The two-equation `low Reynolds number' k-ɛ model of turbulence with a set of universal constants suggested by Launder and Sharma is modified in the present paper. The variability of the turbulent Prandtl number Prt in the energy equation is assumed along with a change of a constant in the dissipation term of the turbulent kinetic energy equation. The turbulent heat transfer is computed for an air flow in a circular pipe for the Reynolds number within the range of 104 < Re < 6.104. The modification considerably improves the agreement between the numerical results and the experiment data published in the available literature.
This paper deals with the one-dimensional transient heat conductivity contact problem of a sliding two semi-spaces, which induces effects of friction, heat generation and water during braking. In the present temperature analysis the capacity of the frictional source on the contact plane dependent on the time of braking. The problem solved exactly using the Laplace transform technique. Numerical results for the temperature are obtained for the different values of the input parameter, which characterise the duration of the increase of the contact pressure during braking from zero to the maximum value. An analytical formulae for the abrasive wear of the contact plane is obtained in the assumption, that the wear coefficient is the linear function of the contact temperature.
This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow.
This paper presents a theoretical study of thermofluid interaction between natural convection in fluid-saturated porous medium and film condensation, coupled through an impermeable vertical wall. The two heat transfer modes are analyzed separately. The solutions are matched on the wall. The complexion of this two-fluid problem is governed by a dimensionless interaction parameter which relates the heat transfer effectiveness of the two heat transfer mechanisms. The effect of this parameter on the flow and heat transfer is documented. Results regarding the overall heat transfer coefficient are obtained for a wide range of the independent parameters.
