A Shell and tube heat exchanger consists of a tube(carrying a fluid to be heated

Question

A Shell and tube heat exchanger consists of a tube(carrying a fluid to be heated or cooled) surrounded by another fluid at a different temperature.Consider a chemically reacting flow in such a tube with a velocity of 0.1 m/s. The chemical reaction is exothermic and causes the flow to heat up at some axial position x1 at 15 C/min. Simutaneously, the coolant carries the heat away from the flow such that the temperature inside the tube decreases in the axial direction at 4 C/m. What is the Eulerian derivative DT/Dt at x1?

Answer: -0.15 C/s

Explanation / Answer

DT/Dt= dT/dt + v(dT/dx +dT/dy + dT/dz) (All the R.H.S components are partial derivatives)

dT/dt is the local time derivative and is equal to 15 C/min =0.25 C/s

As the flow is one-dimensional so dT/dy and dT/dz is taken to be zero....

dT/dx= 4 C/m

v=0.1 m/s

the convective component v*dT/dx is negative as the coolant decreases the temperature...

So,

DT/Dt = 0.25-0.1*4 = -0.15 C/s....

If you have any doubts plz comment but rate the answer surely....

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