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Computer Problem 1 - Virginia Polytechnic and State...

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Virginia Polytechnic and State University Computer Assignment 1 Department of Aerospace and Ocean Engineering Honor Pledge: By submitting this document I pledge I have neither given nor received unauthorized aid. 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 2-D Steady Heat Conduction and 2-D 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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