Showing papers on "Heat transfer published in 1980"

Numerical heat transfer and fluid flow

Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.

The heat flow through oceanic and continental crust and the heat loss of the Earth

Abstract: Simple thermal models based on the creation and cooling of the lithosphere can account for the observed subsidence of the ocean floor and the measured decreased in heat flow with age. In well-sedimented areas, where there is little loss of heat due to hydrothermal circulation, the surface heat flow decays uniformly from values in excess of 6 µcal/cm² s (250 mW/m²), for crust younger than 4 Ma (4 m.y. B.P.), to close to 1.1 µcal/cm² s (46 mW/m²) through crust between 120 and 140 Ma. After 200 Ma the heat flow is predicted to reach an equilibrium value of 0.9 µcal/cm² s (38 mW/m²). The surface heat flow on continents is controlled by many phenomena. On the time scale of geological periods the most important of these are the last orogenic event, the distribution of heat-producing elements, and erosion. To better understand the effects of age, each continent is separated into four provinces on the basis of radiometric dates. Reflecting the preponderance of Precambrian crust, two of these provinces cover the Archean to the middle Proterozoic, and the third covers the late Proterozoic to the Mesozoic. The mean heat flow decreases from a value of 1.84 µcal/cm² s (77 mW/m²) for the youngest province to a constant value of 1.1 µcal/cm² s (46 mW/m²) after 800 Ma. The nonradiogenic component of the surface heat flow decays to a constant value of between 0.65 and 0.5 µcal/cm² s (25 and 21 mW/m²) within 200–400 Ma. Using theoretical models, we compute the heat loss through the oceans to be 727 × 1010 cal/s (30.4 × 1012 W). The comparison between the theoretical and measured values allows an estimate of 241 × 1010 cal/s (10.1 × 1012 W) for the heat lost owing to hydrothermal circulation. We show that the heat flow through the marginal basins follows the same relation as that for crust created at a midocean spreading center. These basins have a corresponding heat loss of 71 × 1010 cal/s (3.0 × 1012 W). The heat loss through the continents is calculated from the observations and is 208 × 1010 cal/s (8.8 × 1012 W). Our estimate of the value for the shelves is 67 × 1010 cal/s (2.8 × 1012 W). The total heat loss of the earth is 1002 × 1010 cal/s (42.0 × 1012 W), of which 70% is through the deep oceans and marginal basins and 30% through the continents and continental shelves. The creation of lithosphere accounts for just under 90% of the heat lost through the oceans and hence about 60% of the worldwide heat loss. Convective processes, which include plate creation and orogeny on continents, dissipate two thirds of the heat lost by the earth. Conduction through the lithosphere is responsible for 20%, and the rest is lost by the radioactive decay of the continental and oceanic crust. We place bounds of between 0.6 and 0.9 µcal/cm² s (25 and 38 mW/m²) for the mantle heat flow beneath an ocean at equilibrium and between 0.40 and 0.75 µcal/cm² s (17 and 31 mW/m²) for the heat flow beneath an old stable continent. The computed range of geotherms for an equilibrium ocean overlaps the range of stable continental geotherms below a depth of 100 km. The mantle heat flow beneath a continent decays with a thermal time constant similar to that of the oceanic lithosphere. The continental basins subside with the same time constant. These observations are evidence that there is no detectable difference between the thermal structure of an equilibrium ocean and that of an old continent. Thus the concept of the lithosphere as a combination of a mechanical and a thermal boundary layer can be applied to both oceans and continents. We evaluate the constraints placed on models based on this concept by seismological observations. In the absence of compelling evidence to the contrary we favor these models because they provide a single explanation for the thermal structure of the lithosphere beneath an equilibrium ocean and a stable continent.

Microvascular contributions in tissue heat transfer.

Abstract: Many mathematical formulations of the heat transfer in living tissues'-' have been for the purposes of studying thermal regulation, comfort, or other phenomenon where significant localized (as opposed to whole-body or regional) variations in temperature and heat flux were of little interest. The advent of intensified interest in hyperthermia as a cancer therapy and the safety associated with ultrasound and microwave radiation, as well as attempts at a quantitative interpretation of thermographic measurements, however, have made it highly desirable to have formulations that are valid also for small-scale temperature variations. Living tissues differ from nonbiological materials primarily because of the presence of the vasculature. The large number and the architectural and dimensional variety of blood vessels clearly make it impractical to account for their individual contribution to heat transfer processes in the tissue with the exception, of course, of the larger arteries and veins. In the fields of heat transfer and fluid flow, when one encounters problems with a large number of structures whose individual dimensions are small relative to the macroscopic phenomenon under study, a common practice is to adopt the so-called continuum description. In this description, only the collective behavior of the small structures is taken into consideration in a certain statistical manner. Usually the influence of the small structures are ultimately expressed in terms of continuum properties of the medium, in our case, the thermal conductivity, specific heat, and blood perfusion rate of the tissue. It is the purpose of this report to explore the theoretical basis for the relationship between these properties and the architecture and function of the vasculature. It will be shown that because of the vasculature, and the large rate of blood perfusion, living biological tissues are fundamentally different from inert materials. Consequently, the familiar thermal properties can no longer be assumed to be independent of the parameters of the temperature field. In other words, these properties may vary, depending on the nature of the application. In view of the fact that existing formulations of the bio-heat transfer problem have been found to be more or less satisfactory for the description of heat transfer involving large-scale tempera-

Modeling a variable thickness sea ice cover

Abstract: A numerical model simulating a variable thickness sea ice cover over a seasonal cycle is presented. The model includes a fixed depth mixed-layer formulation with open water heat absorption and lateral melting terms, and a mechanical distribution function consistent with the physics of the ridging process. The equibrium simulation results in realistic geographical ice thickness variations of April ice along the Canadian Archipelago which exceed 7 m, and thicknesses of about 2 m along the Alaskan North Slope. Ice velocity fields were realistic in shape but 25% larger than the net ice station drift over a year; sensitivity simulations indicated a reduced average annual ice export rate of 0.04 Sv as compared to 0.09 Sv for the equilibrium simulation.

Heat transfer model for cw laser material processing

Abstract: (Received 19 September 1979; accepted for publication 12 October 1979)A three‐dimensional heat transfer model for laser material processing with a moving Gaussian heat source is developed using finite difference numerical techniques. In order to develop the model, the process is physically defined as follows: A laser beam, having a defined power distribution, strikes the surface of an opaque substrate of infinite length but finite width and depth moving with a uniform velocity in the positive x direction (along the length). The incident radiation is partly reflected and partly absorbed according to the value of the reflectivity. The reflectivity is considered to be zero at any surface point where the temperature exceeds the boiling point. This is because a ’’keyhole’’ is considered to have formed which will act as a black body. Some of the absorbed energy is lost by reradiation and convection from both the upper and lower surfaces while the rest is conducted into the substrate. That part of the incident r...

Heat transfer to blood vessels

Abstract: Heat transfer to individual blood vessels has been investigated in three configurations: a single vessel, two vessels in counterflow, and a single vessel near the skin surface. For a single vessel the Graetz number is the controlling parameter. The arterioles, capillaries, and venules have very low Graetz numbers, Gz < 0.4, and act as perfect heat exchangers in which the blood quickly reaches the tissue temperature. The large arteries and veins with Graetz numbers over 10(3) have virtually no heat exchange with the tissue, and blood leaves them at near the entering temperature. Heat transfer between parallel vessels in counterflow is influenced most strongly by the relative distance of separation anad by the mass transferred from the artery to the vein along the length. These two effects are of the same order of magnitude, whereas the film coefficients in the blood flow are of significant but lesser importance. The effect of a blood vessel on the temperature distribution of the skin directly above it and on the heat transfer to the environment increases with decreasing depth-to-radius ratio and decreasing Biot number based on radius. The absolute magnitude of these effects is independent of other linear effects, such as internal heat generation or a superimposed one-dimensional heat flux.

Thermal histories of convective Earth models and constraints on radiogenic heat production in the Earth

Abstract: Thermal histories have been calculated for simple models of the earth which assume that heat is transported by convection throughout the interior. The application of independent constraints to these solutions limits the acceptable range of the ratio of present radiogenic heat production in the earth to the present surface heat flux. The models use an empirical relation between the rate of convective heat transport and the temperature difference across a converting fluid. This is combined with an approximate proportionality between effective mantle viscosity and T−n, where T is temperature and it is argued that n is about 30 throughout the mantle. The large value of n causes T to be strongly buffered against changes in the earth's energy budget and shortens by an order of magnitude the response time of surface heat flux to changes in energy budget as compared to less temperature-dependent heat transport mechanisms. Nevertheless, response times with n = 30 are still as long as 1 or 2 b.y. Assuming that the present heat flux is entirely primordial (i.e., nonradiogenic) in a convective model leads back to unrealistically high temperatures about 1.7 b.y. ago. Inclusion of exponentially decaying (i.e., radiogenic) heat sources moves the high temperatures further into the past and leads to a transition from ‘hot’ to ‘cool’ calculated thermal histories for the case when the present rate of heat production is near 50% of the present rate of heat loss. Requiring the calculated histories to satisfy minimal geological constraints limits the present heat production/heat loss ratio to between about 0.3 and 0.85. Plausible stronger constraints narrow this range to between 0.45 and 0.65. These results are compatible with estimated radiogenic heat production rates in some meteorites and terrestrial rocks, with a whole-earth K/U ratio of 1–2×104 giving optimal agreement.

On the calculation of turbulent heat transport downstream from an abrupt pipe expansion

Abstract: A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion Computations employed an adaptation of the TEACH-2E computer program with the standard model of turbulence Emphasis is given to the simulation, from both a physical and numerical viewpoint, of the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion Wall resistance laws or wall functions used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall Predictions of expermental data for a diameter ratio of 054 show generally encouraging agreement with experiment At a diameter of 043 different trends are discernible between measurement and calculation though this appears to be due to effects unconnected with the wall region studied

The role of deep sea heat storage in the secular response to climatic forcing

Abstract: The influence of the world oceans on climatic response is considered here with emphasis on the heat transferred to waters beneath the well-mixed surface layer and to polar bottom water forming zones. An upwelling-diffusing model is formulated to treat this problem whose effective transport properties are calibrated from the steady state vertical profiles of radiocarbon, potential temperature and other tracers measured by chemical oceanographers. The key issue with regard to the question of atmospheric temperature response to external climatic forcing is whether heat is exchanged between the surface mixed layer and deep sea at rates comparable to heat transfer rates between the planetary radiation field and the atmosphere-mixed layer system. An important model parameter appearing in the analysis is the polar sea warming coefficient ∏ equal to the rate of change of polar sea temperature relative to changes in areally averaged mixed layer temperature. For ∏ values in the range of 0 to 2 the models predicts response times in the range of 8 to 20 years to attain 63% of the equilibrium temperature change for a step function climatic forcing, and 50 to 1000 years to get 90% of the equilibrium response. These may be compared with the roughly 4 year response time one gets with an oceanic mixed layer only model. To study the carbon dioxide climate problem, a more realistic time-dependent forcing function is used based on the historical growth of fossil fuel CO2 and a logarithmic scaling law for the temperature increment which would obtain at any instant if the system were in radiative-convective equilibrium. Our results suggest the influence of deep sea thermal storage could delay the full value of temperature increment predicted by equilibrium models by 10 to 20 years in 1980 to 2000 A.D. time frame. Also considered is the model response to periodic forcing, the sensitivity of the results, and the implications of the model results with regard to climatic changes on a decadal to millenial timescale.

An Experimental Study of Endwall and Airfoil Surface Heat Transfer in a Large Scale Turbine Blade Cascade

Abstract: Local rates of heat transfer on the endwall, suction, and pressure surfaces of a large scale turbine blade cascade were measured for two inlet boundary layer thicknesses and for a Reynolds number typical of gas turbine engine operation. The accuracy and spatial resolution of the measurements were sufficient to reveal local variations of heat transfer associated with distinct flow regimes and with regions of strong three-dimensional flow. Pertinent results of surface flow visualization and pressure measurements are included. The dominant role of the passage vortex, which develops from the singular separation of the inlet boundary layer, in determining heat transfer at the endwall and at certain regions of the airfoil surface is illustrated. Heat transfer on the passage surfaces is discussed and measurements at airfoil midspan are compared with current finite difference prediction methods.

Cooling techniques for electronic equipment

Abstract: Evaluating the Cooling Requirements. Designing the Electronic Chassis. Conduction Cooling for Chassis and Circuit Boards. Mounting and Cooling Techniques for Electronic Components. Practical Guides for Natural Convection and Radiation Cooling. Forced--Air Cooling for Electronics. Thermal Stresses in Lead Wires, Solder Joints, and Plated Throughholes. Predicting the Fatigue Life in Thermal Cycling and Vibration Environment. Transient Cooling for Electronic Systems. Special Applications for Tough Cooling Jobs. Effective Cooling for Large Racks and Cabinets. Finite Element Methods for Mathematical Modeling. Environmental Stress Screening Techniques. References. Index.

Heat balance of the Earth

Abstract: Results of improved calculations of the heat balance components of Earth's surface are reported for yearly average conditions The technique used to determine the heat-balance components from land- and sea-based actinometric observations as well as from satellite data on the radiation balance of the Earth-atmosphere system is described, with special attention given to short-wavelength solar radiation on the continents, effective radiation from the land surface, the radiation balance of the ocean surface, heat expended by both evaporation from the ocean surface, and turbulent heat transfer between the ocean surface and the atmosphere World maps of heat-balance components show yearly average values of total radiation, radiation balance, heat expended by evaporation, the turbulent heat flow between Earth's surface and atmosphere, and heat transfer between the ocean surface and underlying waters The global surface heat balance is estimated along with global values of the various components and the heat-balance components for different latitude zones

The Thermodynamics of Aqueous Water Electrolysis

Abstract: Precise definitions are given of three thermodynamic parameters which characterize the water‐electrolysis reaction: the enthalpic voltage, the higher‐heating‐value voltage, and the thermoneutral voltage. Expressions are derived for these parameters and for the reversible potential, as functions of temperature between 25° and 250°C, and of pressure between 1 and 100 atm. Heat losses due to radiation, convection, and conduction are also considered, and a thermal‐balance voltage is defined; representative values are calculated. Electrical‐energy efficiency is related to the characteristic parameters, and thermodynamic limitations on its value are discussed.

Heat-transfer in flow past a continuous moving plate with variable temperature

Abstract: A study of thermal boundary layer on a continuously moving semi-infinite flat plate, whose temperature varies as Axn, where A is a constant and x is measured from the leading edge of the plate, has been presented. Similarity solutions have been derived and the resulting equations are integrated numerically. It has been observed that the value of the Nusselt number increases with increasing n.

Periodic Streamwise Variations of Heat Transfer Coefficients for Inline and Staggered Arrays of Circular Jets with Crossflow of Spent Air

Abstract: Heat transfer characteristics were measured for inline and staggered arrays of circular jets impinging on a surface parallel to the jet orifice plate. The impinging flow was constrained to exit in a single direction along the channel formed by the jet plate and the heat transfer surface. In this configuration the air discharged from upstream transverse rows of jet holes imposes a crossflow of increasing magnitude on the succeeding downstream jet rows. Streamwise heat transfer coefficient profiles were determined for a streamwise resolution of one-third the streamwise hole spacing, utilizing a specially constructed test surface.

An adaptive grid method for problems in fluid mechanics and heat transfer

Abstract: A new method for generating adaptive grids for time-dependent and steady problems in multidimensional fluid mechanics and heat transfer has been developed. The method can be used with many existing grid generation schemes or can be used as an independent grid generation technique. The present adaptive method is based upon the placement of grid points in proportion to the gradients that appear in the dependent variable. The multidimensional results presented in the paper are for the unsteady heat conduction equation and have included steep gradients due to geometry and unsteady boundary conditions. The method has performed in an impressive fashion, although there is a need to control grid skewness better. A study of one-dimensional problems associated with combustion and cell Reynolds number has demonstrated the technique's accuracy and versitility. The paper also discusses the relationship of the method to other grid generation techniques, as well as extensions of the new method.