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Presentation transcript:

Bring it together

Why do we use numerical methods?

Why use Numerical Methods? To solve problems that cannot be solved exactly

Why use Numerical Methods? To solve problems that have exact solutions but are otherwise intractable!

Assembling a fulcrum for a bascule bridge Girder Trunnion Hub

What model should I use?

Finding the fluid temperature to get enough contraction

Finding the expression for thermal expansion coefficient

How long does it take a trunnion to cool down? http://numericalmethods.eng.usf.edu

Example A solid steel shaft at room temperature of 27°C is needed to be contracted so that it can be shrunk-fit into a hollow hub. It is placed in a refrigerated chamber that is maintained at −33°C. The rate of change of temperature of the solid shaft q is given by Using Euler’s method, find the temperature of the steel shaft after 86400 seconds. Take a step size of h = 43200 seconds. http://numericalmethods.eng.usf.edu

Comparison of Exact and Numerical Solutions Figure 3. Comparing exact and Euler’s method http://numericalmethods.eng.usf.edu