Virginia Polytechnic and State University
Computer Assignment 1
Department of Aerospace and Ocean Engineering
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Craig Sossi
Craig Sossi
904512344
September 27, 2009
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PROBLEM DESCRIPTION
Finding simple solutions to heat conduction problems has been an issue for over a
century.
Simple geometric objects have been used as representations of objects for many
practical situations, however the analytical solution for these representations are so complex that
a numerical approach is not feasible.
To obtain solutions, the finite difference method is often
used.
The finite difference method approximates an object with a grid which is then used to
approximate the differential increments of temperature in the overall object.
The purpose of this problem is to investigate the heat flow through a two dimensional
object for steady heat conduction and unsteady heat conduction with various representation
accuracies.
We wish to determine the temperature at the nodes circled in green in figure 1.
The
figure represents the two grid sizes which will be compared to determine the effects of object
representation accuracy on heat flow.
Figure 1
Object Representation for Heat Conduction
This problem utilizes the 2D Steady Heat Conduction and 2D Unsteady Heat
Conduction applets available on the Virginia Tech Engineering Applets webpage.
These applets
take a user input of geometric representation and initial temperatures and compute the final
temperature distribution.
INPUT INFORMATION
To use the applet, a chart representing the grid and initial temperatures must be created
using Microsoft Excel.
The input format consists of defining the grid spacing (x direction and y
direction) and then starting at the bottom left corner and working in a clockwise direction,
specify the x and y coordinate points and temperature.
This is done for the perimeter of the
object only; the program automatically distributes internal points on the grid based on the user
defined grid spacing.
Figure 2 shows the format for the applet input and tables 1 and 2 show the
information used for all computations for this problem.
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 Fall '08
 Schetz,J
 Thermodynamics, Heat, Heat Transfer, Steady heat conduction

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