This document presents solutions to two-dimensional heat transfer calculations, accompanied by images and animations intended to enhance students' understanding of governing equations and concepts. It includes various boundary conditions and suggests activities for students to analyze temperature distributions and heat flux based on these conditions. The resource, created by the University of Hertfordshire, is part of an open educational project and provides a computer program for heat conduction analysis.

1. Two-Dimensional Steady-State Conduction<br />The following images represent the solutions to a series of two-dimensional heat transfer calculations. The images are accompanied by a collection of supporting animations.<br />The animations and images supplement the class interactions and discussions on heat transfer.<br />The images and animations were intended to support the students understanding of the governing equations and also the meaning of various concepts.<br />The animations are available to view at http://www.youtube.com/user/MBRBLU. <br />Suggestions for use<br />The images (and animations) can be displayed and students asked to describe what they see, in relation to<br />the boundary conditions<br />the likely energy balance<br />They might also be asked to describe<br />the relationship between the isotherms and streamlines of heat flux.<br />the relationship between the isotherms and the various boundary conditions<br />Alternatively, the students could be presented with a description of the boundary conditions only and asked, for each case, <br />to plot the likely temperature distribution across the slab (including isotherms)<br />to plot the lines of heat flux<br />The boundary conditions for the cases are shown in table 1 below.<br />Table 1. Boundary conditions<br />Boundary conditionsX=0X=LY=0Y=LThermal conductivityCase 1Neumann QUOTE Neumann QUOTE Dirichlet (t=0°C)Dirichlet (t=100°C)HomogenousCase 2Neumann QUOTE Dirichlet (t=0°C)Dirichlet (t=0°C)Dirichlet (t=100°C)HomogenousCase 3Dirichlet (t=0°C)Dirichlet (t=0°C)Dirichlet (t=0°C)Dirichlet (t=100°C)HomogenousCase 4Neumann QUOTE Dirichlet (t=0°C)Neumann QUOTE Dirichlet (t=100°C)HomogenousCase 5Neumann QUOTE Neumann QUOTE Dirichlet (t=0°C)Dirichlet (t=100°C)Case 6Neumann QUOTE Neumann QUOTE Dirichlet (t=0°C)Dirichlet (t=100°C)<br />Case 1 Case 2Case 3Case 4Case 5Case 6<br />A description of the computer program and the validation of the code can be found at:<br />Russell, M.B., Probert, S.D., FDiff3: A finite difference solver for facilitating understanding of heat conduction and numerical analysis, Applied Energy Vol 79. 2004.Credits<br />This resource was created by the University of Hertfordshire and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.<br />© University of Hertfordshire 2010<br />This work is licensed under a Creative Commons Attribution 2.0 Licence. <br />The name of the University of Hertfordshire, UH and the UH logo are the name and registered marks of the University of Hertfordshire. To the fullest extent permitted by law the University of Hertfordshire reserves all its rights in its name and marks which may not be used except with its written permission.<br />The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence. All reproductions must comply with the terms of that licence.<br />The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.<br />