Two-Dimensional Steady-State Conduction 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. The animations and images supplement the class interactions and discussions on heat transfer. The images and animations were intended to support the students understanding of the governing equations and also the meaning of various concepts. The animations are available to view at http://www.youtube.com/user/MBRBLU . Suggestions for use The images (and animations) can be displayed and students asked to describe what they see, in relation to the boundary conditions the likely energy balance They might also be asked to describe the relationship between the isotherms and streamlines of heat flux. the relationship between the isotherms and the various boundary conditions Alternatively, the students could be presented with a description of the boundary conditions only and asked, for each case, to plot the likely temperature distribution across the slab (including isotherms) to plot the lines of heat flux The boundary conditions for the cases are shown in table 1 below. Table 1. Boundary conditions Boundary conditions
Two-Dimension Steady-State Conduction
May 31, 2015
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, available at http://www.youtube.com/user/MBRBLU.
The images are accompanied by a collection of supporting animations, available at http://www.youtube.com/user/MBRBLU.
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Two-Dimensional Steady-State Conduction
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.
The animations and images supplement the class interactions and discussions on heat transfer.
The images and animations were intended to support the students understanding of the governing equations and also the meaning of various concepts.
The animations are available to view at http://www.youtube.com/user/MBRBLU.
Suggestions for useThe images (and animations) can be displayed and students asked to describe what they see, in relation to
the boundary conditions the likely energy balance
They might also be asked to describe the relationship between the isotherms and streamlines of heat flux. the relationship between the isotherms and the various boundary conditions
Alternatively, the students could be presented with a description of the boundary conditions only and asked, for each case,
to plot the likely temperature distribution across the slab (including isotherms) to plot the lines of heat flux
The boundary conditions for the cases are shown in table 1 below.
Table 1. Boundary conditions
Boundary conditionsX=0 X=L Y=0 Y=L Thermal conductivity
Case 1 Neumann Neumann Dirichlet (t=0°C)
Dirichlet (t=100°C)
Homogenous
Case 2 Neumann Dirichlet (t=0°C)
Dirichlet (t=0°C)
Dirichlet (t=100°C)
Homogenous
Case 3 Dirichlet (t=0°C)
Dirichlet (t=0°C)
Dirichlet (t=0°C)
Dirichlet (t=100°C)
Homogenous
Case 4 Neumann Dirichlet (t=0°C)
Neumann Dirichlet (t=100°C)
Homogenous
Case 5 Neumann Neumann Dirichlet (t=0°C)
Dirichlet (t=100°C)
Case 6 Neumann Neumann Dirichlet (t=0°C)
Dirichlet (t=100°C)
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
A description of the computer program and the validation of the code can be found at: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.
CreditsThis 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.
© University of Hertfordshire 2010
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