Computational Methods EML3041

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Presentation transcript:

Computational Methods EML3041 Bring it together Computational Methods EML3041

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!

Bascule Bridge THG http://nm.MathForCollege.com

Bascule Bridge THG Hub Trunnion Girder THG picture http://nm.MathForCollege.com

Trunnion-Hub-Girder Assembly Procedure Step1. Trunnion immersed in dry-ice/alcohol Step2. Trunnion warm-up in hub Step3. Trunnion-Hub immersed in dry-ice/alcohol Step4. Trunnion-Hub warm-up into girder http://nm.MathForCollege.com

After Cooling, the Trunnion Got Stuck in Hub Problem After Cooling, the Trunnion Got Stuck in Hub http://nm.MathForCollege.com

Why did it get stuck? Magnitude of contraction needed in the trunnion was 0.015” or more. Did it contract enough? http://nm.MathForCollege.com

What model should I use to calculate contraction of trunnion?

Finding the fluid temperature to get enough contraction

Finding the expression for thermal expansion coefficient

What is the temperature of the trunnion after half an hour? http://numericalmethods.eng.usf.edu

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

Temperature vs. Time http://numericalmethods.eng.usf.edu

What is the rate of change of heat stored in the cylinder? http://numericalmethods.eng.usf.edu

Can you identify? We talked about 7 mathematical procedures in this course. Write them down. Now connect the problem just discussed to these 7 mathematical procedures on each of the previous slides.

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