1000 Solved Problems In Heat Transfer Pdf
AbstractThis text is a collection of solutions to a variety of heat conduction problems found in numerous publications, such as textbooks, handbooks, journals, reports, etc. Its purpose is to assemble these solutions into one source that can facilitate the search for a particular problem solution. New blue color fast keygen crack.
SCHAUM’S OUTLINE OF THEORY AND PROBLEMS OF HEAT TRANSFER Second Edition DONALD R. Professor Emeritus of Mechanical and Aerospace Engineering and Engineering Science The University of Tennesse -Knoxville LEIGHTON E, SISSOM, Ph.D., P.E.
Generally, it is intended to be a handbook on the subject of heat conduction. There are twelve sections of solutions which correspond with the class of problems found in each. Geometry, state, boundary conditions, and other categories are used to classify the problems. Each problem is concisely described by geometry and condition statements, and many times a descriptive sketch is also included. The introduction presents a synopsis on the theory, differential equations, and boundary conditions for conduction heat transfer.
Some discussion is given on the use and interpretation of solutions. Supplementary data such as mathematical functions, convection correlations, and thermal properties are included for aiding the user in computing numerical values from the solutions. 155 figs., 92 refs., 9 tabs. This text is a collection of solutions to a variety of heat conduction problems found in numerous publications, such as textbooks, handbooks, journals, reports, etc.
Its purpose is to assemble these solutions into one source that can facilitate the search for a particular problem solution. Generally, it is intended to be a handbook on the subject of heat conduction. This material is useful for engineers, scientists, technologists, and designers of all disciplines, particularly those who design thermal systems or estimate temperatures and heat transfer rates in structures. More than 500 problem solutions and relevant data are tabulated for easy retrieval.
There are twelve sections of solutions which correspond with the class of problems found in each. Geometry, state, boundary conditions, and other categories are used to classify the problems. A case number is assigned to each problem for cross-referencing, and also for future reference. Each problem is concisely described by geometry and condition statements, and many times a descriptive sketch is also included.
At least one source reference is given so that the user can review the methods used to derive the solutions. Problem solutions are given in the form of equations, graphs, and tables of data, all of which are also identified by problem case numbers and source references.
With advances in commercially available finite element software and computational capability, engineers can now model large-scale problems in mechanics, heat transfer, fluid flow, and electromagnetics as never before. With these enhancements in capability, it is increasingly tempting to include the fundamental process physics to help achieve greater accuracy (Refs. While this goal is laudable, it adds complication and drives up cost and computational requirements. Practical analysis of welding relies on simplified user inputs to derive important relativistic trends in desired outputs such as residual stress or distortion due to changes in inputs like voltage, current, and travel speed.
Welding is a complex three-dimensional phenomenon. The question becomes how much modeling detail is needed to accurately predict relative trends in distortion, residual stress, or weld cracking?
In this work, a HAZ (Heat Affected Zone) weld-cracking problem was analyzed to rank two different welding cycles (weld speed varied) in terms of crack susceptibility. Figure 1 shows an aerospace casting GTA welded to a wrought skirt. The essentials of part geometry, welding process, and tooling were suitably captured lo model the strain excursion in the HAZ over a crack-susceptible temperature range, and the weld cycles were suitably ranked. The main contribution of this work is the demonstration of a practical methodology by which engineering solutions to engineering problems may be obtained through weld modeling when time and resources are extremely limited. Typically, welding analysis suffers with the following unknowns: material properties over entire temperature range, the heat-input source term, and environmental effects. Material properties of interest are conductivity, specific heat, latent heat, modulus, Poisson's ratio, yield strength, ultimate strength, and possible rate dependencies.
Boundary conditions are conduction into fixturing, radiation and convection to the environment, and any mechanical constraint. If conductivity, for example, is only known at a few temperatures it can be linearly extrapolated from the highest known temperature to the liquidus temperature. Over the liquidus to solidus temperature the conductivity is linearly increased by a factor of three to account for the enhanced heat transfer due to convection in the weld pool. Above the liquidus it is kept constant. Figure 2 shows an example of this type of approximation.
Other thermal and mechanical properties and boundary conditions can be similarly approximated, using known physical material characteristics when possible. Sensitivity analysis can show that many assumptions have a small effect on the final outcome of the analysis. In the example presented in this work, simplified analysis procedures were used to model this process to understand why one set of parameters is superior to the other. From Lin (Ref. 8), mechanical strain is expected to drive HAZ cracking. Figure 3 shows a plot of principal tensile mechanical strain versus temperature during the welding process. By looking at the magnitudes of the tensile mechanical strain in the material's Brittle Temperature Region (BTR), it can be seen that on a relative basis the faster travel speed process that causes cracking results in about three times the strain in the temperature range of the BTR.
In this work, a series of simplifying assumptions were used in order to quickly and accurately model a real welding process to respond to an immediate manufacturing need. The analysis showed that the driver for HAZ cracking, the mechanical strain in the BTR, was significantly higher in the process that caused cracking versus the process that did not. The main emphasis of the analysis was to determine whether there was a mechanical reason whether the improved weld parameters would consistently produce an acceptable weld, The prediction of the mechanical strain magnitudes confirms the better process.
A fast growing volume of literature in various fields of composite materials and structures has inspired the authors to attempt to assemble all major books and review papers in a concise compendium presented here. This could give researchers, engineers, designers, and graduate students a rapid access to the vast volume of references on any specific topic in the field of composites and thereby satisfy their research requirements. The compendium includes encyclopedias, handbooks, design guides, textbooks, reference books, review papers and also a few collections of papers. The topics span theory, modeling and analysis of composite materials, processing and manufacturing, properties and characterization, theory and analysis of composite structures, joints and connections, designing with composites, and composites applications. The compendium includes over 400 references, which are arranged in alphabetical order within each topic under consideration. Additionally, the reader can find, in this compendium, the lists of major conferences, journals, and ASTM STP publications on composites. The major objective of this work is not critically reviewing or discussing specific research approaches and results.
The authors have rather intended to provide extensive bibliographic information that may help the reader to get familiar with the primary literature and, in necessary, undertake further literature search on any particular problem of interest. This NEUP funded project, NEUP 12-3630, is for experimental, numerical and analytical studies on high-pressure steam condensation phenomena in a steel containment vessel connected to a water cooling tank, carried out at Oregon State University (OrSU) and the University of Wisconsin at Madison (UW-Madison). In the three years of investigation duration, following the original proposal, the planned tasks have been completed: (1) Performed a scaling study for the full pressure test facility applicable to the reference design for the condensation heat transfer process during design basis accidents (DBAs), modified the existing test facility to route the steady-state secondary steam flow into the high pressure containment for controllable condensation tests, and extended the operations at negative gage pressure conditions (OrSU).
(2) Conducted a series of DBA and quasi-steady experiments using the full pressure test facility to provide a reliable high pressure condensation database (OrSU). (3) Analyzed experimental data and evaluated condensation model for the experimental conditions, and predicted the prototypic containment performance under accidental conditions (UW-Madison). A film flow model was developed for the scaling analysis, and the results suggest that the 1/3 scaled test facility covers large portion of laminar film flow, leading to a lower average heat transfer coefficient comparing to the prototypic value. Although it is conservative in reactor safety analysis, the significant reduction of heat transfer coefficient (50%) could under estimate the prototypic condensation heat transfer rate, resulting in inaccurate prediction of the decay heat removal capability. Further investigation is thus needed to quantify the scaling distortion for safety analysis code validation. Experimental investigations were performed in the existing MASLWR test facility at OrST with minor modifications.
A total of 13 containment condensation tests were conducted for pressure ranging from 4 to 21 bar with three different static inventories of non-condensable gas. Condensation and heat transfer rates were evaluated employing several methods, notably from measured temperature gradients in the HTP as well as measured condensate formation rates. A detailed mass and energy accounting was used to assess the various measurement methods and to support simplifying assumptions required for the analysis.
Condensation heat fluxes and heat transfer coefficients are calculated and presented as a function of pressure to satisfy the objectives of this investigation. The major conclusions for those tests are summarized below: (1) In the steam blow-down tests, the initial condensation heat transfer process involves the heating-up of the containment heat transfer plate. An inverse heat conduction model was developed to capture the rapid transient transfer characteristics, and the analysis method is applicable to SMR safety analysis.
(2) The average condensation heat transfer coefficients for different pressure conditions and non-condensable gas mass fractions were obtained from the integral test facility, through the measurements of the heat conduction rate across the containment heat transfer plate, and from the water condensation rates measurement based on the total energy balance equation. 15 (3) The test results using the measured HTP wall temperatures are considerably lower than popular condensation models would predict mainly due to the side wall conduction effects in the existing MASLWR integral test facility. The data revealed the detailed heat transfer characteristics of the model containment, important to the SMR safety analysis and the validation of associated evaluation model. However this approach, unlike separate effect tests, cannot isolate the condensation heat transfer coefficient over the containment wall, and therefore is not suitable for the assessment of the condensation heat transfer coefficient against system pressure and noncondensable gas mass fraction.
(4) The average condensation heat transfer coefficients measured from the water condensation rates through energy balance analysis are appropriate, however, with considerable uncertainties due to the heat loss and temperature distribution on the containment wall. With the consideration of the side wall conduction effects, the results indicate that the measured heat transfer coefficients in the tests is about 20% lower than the prediction of Dehbi’s correlation, mainly due to the side wall conduction effects. The investigation also indicates an increase in the condensation heat transfer coefficient at high containment pressure conditions, but the uncertainties invoked with this method appear to be substantial.
(5) Non-condensable gas in the tests has little effects on the condensation heat transfer at high elevation measurement ports. It does affect the bottom measurements near the water level position. The results suggest that the heavier non-condensable gas is accumulated in the lower portion of the containment due to stratification in the narrow containment space. The overall effects of the non-condensable gas on the heat transfer process should thus be negligible for tall containments of narrow condensation spaces in most SMR designs. Therefore, the previous correlations with noncondensable gas effects are not appropriate to those small SMR containments due to the very poor mixing of steam and non-condensable gas. The MELCOR simulation results agree with the experimental data reasonably well. However, it is observed that the MELCOR overpredicts the heat flux for all analyzed tests.
The MELCOR predicts that the heat fluxes for CCT’s approximately range from 30 to 45 kW/m2 whereas the experimental data (averaged) ranges from about 25 to 40 kW/m2. This may be due to the limited availability of liquid film models included in MELCOR. Also, it is believed that due to complex test geometry, measured temperature gradients across the heat transfer plate may have been underestimated and thus the heat flux had been underestimated. The MELCOR model predicts a film thickness on the order of 100 microns, which agrees very well with film flow model developed in this study for scaling analysis. However, the expected differences in film thicknesses for near vacuum and near atmospheric test conditions are not significant. Further study on the behavior of condensate film is expected to refine the simulation results.
Possible refinements include but are not limited to, the followings: CFD simulation focusing on the liquid film behavior and benchmarking with experimental analyses for simpler geometries. 16 1 INTRODUCTION This NEUP funded project, NEUP 12-3630, is for experimental, numerical and analytical studies on high-pressure steam condensation phenomena in a steel containment vessel connected to a water cooling tank, carried out at Oregon State University (OrSU) and the University of Wisconsin at Madison (UW-Madison). The experimental results are employed to validate the containment condensation model in reactor containment system safety analysis code for integral SMRs. Such a containment condensation model is important to demonstrate the adequate cooling. In the three years of investigation, following the original proposal, the following planned tasks have been completed: (1) Performed a scaling study for the full pressure test facility applicable to the reference design for the condensation heat transfer process during design basis accidents (DBAs), modified the existing test facility to route the steady-state secondary steam flow into the high pressure containment for controllable condensation tests, and extended the operations at negative gage pressure conditions (OrSU). (2) Conducted a series of DBA and quasi-steady experiments using the full pressure test facility to provide a reliable high pressure condensation database (OrSU). (3) Analyzed experimental data and evaluated condensation model for the experimental conditions, and predicted the prototypic containment performance under accidental conditions (UW-Madison).
1000 Solved Problems In Heat Transfer Pdf Book Free
The results are applicable to integral Small Modular Reactor (SMR) designs, including NuScale, mPower, Westinghouse SMR, Holtec-160 and other integral reactors with small containments of relatively high pressures under accidental conditions. Testing has been conducted at the OrSU laboratory in the existing MASLWR (Multi-Application Small Light Water Reactor) integral test facility sponsored by the US Department of Energy.
Its highpressure stainless steel containment model (2 MPa) is scaled to the NuScale SMR currently under development at NuScale Power, Inc. Minor modifications to the model containment have been made to control the non-condensable gas fraction and to utilize the secondary loop stable steam flow for condensation testing. UW-Madison has developed a containment condensation model, which leveraged previous validated containment heat transfer work carried out at UW-Madison, and extended the range of applicability of the model to integral SMR designs that utilize containment vessels of high heat transfer efficiencies. In this final report, the research background and literature survey are presented in Chapter 2 and 3, respectively. The test facility description and modifications are summarized in Chapter 4, and the scaling analysis is introduced in Chapter 5.
The tests description, procedures, and data analysis are presented in Chapter 6, while the numerical modeling is presented in Chapter 7, followed by a conclusion section in Chapter 8. In this paper the use of the boundary integral equation method (BIEM) for multidimensional problems with moving phase change interface is explored. The method is shown to be suited for heat transfer problems where the field equations are linear in each region and the boundary or interface matching conditions are both highly irregular and non-linear. For moving interface problems the BIEM technique both reduces the dimensions of the problem by one, thus decreasing storage requirements, and directly solves for the unknown normal temperature gradient on each side of the interface for the determination of the instantaneous interface velocity.
To illustrate the versatility of this technique the BIEM is applied to a previously unsolved problem; the melting/freezing around a pipe buried in a semi-infinite domain where the melting/freezing is initiated at the free surface and the medium is initially not at the phase change temperature. For simplicity a quasi-steady heat conduction is assumed in both the thawed and frozen zones. Solutions are presented for various values of the governing parameters.