Consider the cross section of a long rectangular metallic plate where the boundaries are subject to three different temperatures in degree Celsius, as shown in figure below. Engineers are interested in knowing the temperature distribution inside the plate in a specific period of time so they can determine the internal thermal stress. Assuming the boundary temperatures are held constant during that specific period of time, the temperature inside the plate wil reach certain equilibrium after some time has passed. Finding this equilibrium temperature distribution at different points on the plate is desirable, but extremely difficult. However, one can consider a few points on the plate and approximate the temperature of these points. This approximation can be done using the mean value approach (the temperature will be approximated by averaging the 4 adjacent temperature, as we have done in class).

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Consider the cross section of a long rectangular metallic plate where the boundaries are subject to three different
temperatures in degree Celsius, as shown in figure below. Engineers are interested in knowing the temperature
distribution inside the plate in a specific period of time so they can determine the internal thermal stress. Assuming
the boundary temperatures are held constant during that specific period of time, the temperature inside the plate will
reach certain equilibrium after some time has passed. Finding this equilibrium temperature distribution at different
points on the plate is desirable, but extremely difficult. However, one can consider a few points on the plate and
approximate the temperature of these points. This approximation can be done using the mean value approach (the
temperature will be approximated by averaging the 4 adjacent temperature, as we have done in class).
a)
b)
20
20
32
Metal Plate
24
32
24
24
24
What are the temperatures at x1 =
°C, x2 =
°C, X3 =
°C, and x4 =
°C?
Note: the answers should be numeric values with 4 significant digit, e.g., 12.34
Transcribed Image Text:Consider the cross section of a long rectangular metallic plate where the boundaries are subject to three different temperatures in degree Celsius, as shown in figure below. Engineers are interested in knowing the temperature distribution inside the plate in a specific period of time so they can determine the internal thermal stress. Assuming the boundary temperatures are held constant during that specific period of time, the temperature inside the plate will reach certain equilibrium after some time has passed. Finding this equilibrium temperature distribution at different points on the plate is desirable, but extremely difficult. However, one can consider a few points on the plate and approximate the temperature of these points. This approximation can be done using the mean value approach (the temperature will be approximated by averaging the 4 adjacent temperature, as we have done in class). a) b) 20 20 32 Metal Plate 24 32 24 24 24 What are the temperatures at x1 = °C, x2 = °C, X3 = °C, and x4 = °C? Note: the answers should be numeric values with 4 significant digit, e.g., 12.34
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