According to the weather forecast, tomorrow the temperature atpointA will increa

Question

According to the weather forecast, tomorrow the temperature atpointA will increase from -10C at 8:00 AM to 0C at 16:00 PM, and the temperature at point B will change from -5C at 8:00 AM to 5C at 16:00 PM. Consider the distance between A and B as 400 km, we can approximate the temperature variation T (x t), by T (x,t) = 0. 0125x + 25.1 t ?20 , where x represents the location ( x = 0 for A and x = 400 for B), and t is time (t = 8 at 8:00 AM and t =16 at 16:00 PM). Assume you are leaving A at 10:00 AM to B and driving at a speed of 100 km/hr, please find the temperature increase rate you will experience on your trip using

(a) the material derivative (15 marks) and

(b) the local temperature difference at the beginning and end of your trip and the time you spend on the trip (10 marks).

Explanation / Answer

Please write T(x,t) clearly. a. Material Derivative: DT/Dt = Partial T/ Partial t + (dx/dt)*(Partial T/ Partial x) Substitute the speed u=27.77 m/s b. Rate = (T(400,16)-T(0,8)) / Time taken for trip

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