A completely enclosed stirred-tank heating process is used to beat an incoming stream whose flow rate varies. The heating rate from this coil and the volume are both constant.

(a) Develop a mathematical model (differential and algebraic equations) that describes the exit temperature if heat losses to the ambient occur and if the ambient temperature (Ta) and the incoming stream's temperature (Ti) both can vary

(b) Discuss qualitatively what you expect to happen as T and w increase (or decrease). Justify by reference to your model.

Notes:

? and C? are constants.

U, the overall heat transfer coefficient, is constant.

As is the surface area for heat losses to ambient.

Ti > Ta (inlet temperature is higher than ambient temperature).

Ta Heating coil ell