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Schedule online. The transfer of energy as heat plays a key role, not only in technical applications energy production, engines, cooling of electronic components, buildings, It is almost impossible to find examples where heat transfer is absent. It is also directly linked to today's challenges of energy and environment. Heat transfer is therefore a key subject in the curriculum of engineers and architects. Heat transfer represents the transfer of thermal energy from a warm body to a colder one. The objective of the course is thus to quantitatively relate heat fluxes to temperature gradients.

There are three main heat transfer modes: conduction, convection and radiation. The course focuses first on each mode separately, and then on multimode heat transfers. For each mode, the underlying physical processes are described and quantitative laws are developped. Theoretical notions are illustrated through numerous practical examples from our daily life. In particular, following topics are covered: Physical origin of the different heat transfer mechanisms conduction, convection, radiation and key definitions flux, heat, temperature Conduction: Fourier's law, heat diffusion equation 1D, 2D, unsteady , shape factor, analogy with electrical circuits Convection: velocity and thermal boundary layer, convection coefficient, Nusselt number, laminar vs.

At the end of the course, students should be able to quantify the heat transfer in a large range of practical applications. To efficiently follow this course, it is preferable to have some basic knowledge of Thermodynamics e. The course is divided into 13 lectures that take place each Monday morning. The material covered in each lecture corresponds to one or two chapters of the textbook, successively covering the three main parts of the course: conduction, convection and radiation.

Each lecture is divided in two parts. Theoretical results are also discussed in details and illustrated through practical examples. This session is chaired by the course assistants, and is done in smaller groups, either in French or in English. The last lecture of the course is dedicated to solving more complex problems, where different heat transfer modes are present. It also serves as questions-answers session for the final exam. Learning activities also include three homework at the end of each part of the course to be solved individually at home. These homework are evaluated and count towards the final grade.

Their objective is to ensure a continuous learning of the subject, to allow a self-evaluation for the students, and to help the instructors in identifying the difficulties encounted by the students.

A detailed calendar of the course material and deadlines will be presented during the first lecture et distributed electronically to all registered students. Both the theoretical lectures and the exercise sessions are face-to-face. The theoretical lectures are taught in English, and the exercise sessions in French or in English depending on the choice of the student.

## Heat Transfer - Exercises, 1st ed - PDF Free Download

All modules have been enhanced continuously and extensively as a result of these experiences. Many of the original Fortran programs were developed and used as lecture demonstrations in distance education courses in Computational Fluid Dynamics and Heat Transfer taught through the Virginia Commonwealth Graduate Engineering Program.

Then as facilities became available, they were used in a similar mode for a number of years in a projector-equipped, local classroom. The development of the graphical-user-interfaces during the academic year made them appropriate for student use as well, both on their own, or as we use them, in a scheduled "studio" session. Students attend two minute-long, traditional classes a week, but also have a two-hour working session in one of our computer classrooms.

### Description

Originally Watcom Fortran 77 was used for the intense numerical computations and for generation of the color plots, while a tailored Visual Basic executable was used for the user interface. Later all modules were ported to Visual Basic 6, allowing for much more interactivity than in the past. The development of the underlying computational routines, the user-interface, on-line help file, the supporting documentation, the student exercises, and in many cases a journal article is extremely time-consuming.

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Consequently the topics for modules were chosen with great care. Only fundamental subjects that cover at least ten pages in a typical textbook were selected. In several cases virtually all the concepts from a whole chapter in a graduate-level text can be illustrated using one module. In addition, several of the modules are sufficiently general that they may be used in a variety of related courses, both graduate and undergraduate, in mathematics, science and engineering.

General References. Ribando, R. Witte , Nov. Noor and J. Malone , pp.

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Return to Top Two-Dimensional, Steady-State Conduction. Transient Conduction in a Finite Cylinder Cooking. External Flows Flat Plate.

Internal Flows Pipe Flow. Natural Convection in a Saturated Porous Layer. This module covers natural convection in a fluid-saturated, porous material, a topic covered in a number of recent graduate-level heat transfer texts. The problem is analogous to classical Rayleigh-Benard natural convection in homogeneous fluid layers. The fluid is assumed to be "Boussinesq," i. Fluid motion is assumed governed by the Darcy equations.

Heating may be either from the bottom of the layer or from side to side. Module Description. Before any run the user selects the aspect ratio of the layer and the number of grid points to be used in the vertical direction. The same grid spacing is used in both directions, so different aspect ratios are obtained simply by adding or subtracting columns of grid points in the horizontal direction.

These two parameters may not be changed once a calculation is begun. Before as well during a run the user may set the Rayleigh number for the calculation and also change the heating mode from either bottom-to-top or side-to-side. The remaining sides are taken as adiabatic.

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Natural Convection in a Saturated Permeable Layer. Unless the user elects to stop prematurely, the program runs to a prescribed non-dimensional time. During that interval a succession of color contour plots of temperature are drawn in the left-hand window creating an animation effect. Contours of streamfunction are superimposed on top if the user selects that option. The Nusselt number computed at both the bottom and top or at the left and right sides if that heating option has been selected is plotted in the right hand window as a function of time.

Switching the heating direction or changing the Rayleigh number in the midst of a run produces interesting transients which may be monitored in both windows. Very thorough implementation instructions of this algorithm are included on the HTT CD-ROM, making it suitable as a several-week-long project in a graduate-level computational methods or convection heat transfer course.

## Syllabus of ME 631 - Conductive Heat Transfer

Heat Exchangers. The usual treatment of heat exchanger thermal design and analysis is based on two analytically-based solution methods applied to the governing, coupled heat balance equations for the two fluids. Because the solution of these differential equations by analytical means is challenging for all but the simplest configurations, the numerical results have been graphed in non-dimensional form and the resulting charts have been used routinely for the last half century. The LMTD method is commonly used for heat exchanger design , that is, determining the required thermal size, while the Effectiveness - NTU method is used for performance calculations.

Unfortunately the charts and equations associated with these two methods do not give a complete picture of what is happening inside the exchanger, only a single overall measure. In these two modules, the same governing heat balance equations are solved in discretized form using modern numerical techniques, yielding not only the same "bottom line" results as the traditional methods, but giving a complete picture of what is happening within the device.

## Intro to Thermodynamics & Heat Transfer 2nd Edition

Both algorithms solve discretized, coupled heat-balance equations along the paths of the two fluids as they each traverse the heat exchanger. Separate algorithms on the two tabs have been developed because in one case, a coupled set of ordinary differential equations apply, while in the other a coupled set of partial differential equations govern. The detailed temperature distribution is presented to the user in both tabs, and the performance and design numbers associated with the conventional LMTD and effectiveness-NTU methods are reported in both cases for comparison.

Samples of the main user-interface for both algorithms are shown below. Both algorithms allow for several geometric options. The single pass, cross-flow heat exchanger module allows the four generic textbook options: neither fluid mixed, both fluids mixed and either one or the other, but not both mixed. A fifth selection, a two-pass geometry related to an experiment we have done in our undergraduate lab, is also included. The user selects this option in the top left corner and a small schematic of the selected geometry appears. The 1-D option tab seen below allows for several generic geometries, including double pipe designs parallel and counterflow , shell-and-tube designs and 2-pass, 2-pass plate configurations.

After selection of the "Configuration" option, the user specifies a few other inputs relevant to that particular case. In the case of a shell-and-tube configuration, the baffle arrangement is used as a convenient means of discretizing the shell for the numerical solution. In both modules after the geometry has been selected, the user specifies the heat-capacity rates for both fluids and indicates which of the two calculation methods to use. For the Performance option the user inputs the product of the overall heat transfer coefficient and area UA product.

Input boxes are shown in white on all user interfaces while numbers appearing on the gray background are program outputs. Based on this user input, the temperature distributions in both fluids are computed and displayed in a fraction of a second. For the cross-flow module the temperature distribution in both fluids is depicted in the form of color contour plots as seen above. The hot fluid is shown flowing vertically in the leftmost plot.

The cold fluid flows from left to right and is shown in the center. The local mean temperature of the two fluids, which can be helpful in assessing the quality of a design, is shown in the right hand plot.