Lecture 2 example, thermal system (liquid cooling) (ENGR5001) - Revisica

Lecture 2 example, thermal system (liquid cooling)TutorialCurrent spec2:28 min

ENGR5001 Lecture 2 worked example 4, thermal system (slides 23-25)

A container of liquid at temperature $\theta$ stands in surroundings at temperature $\theta_S$ (for example a cup of coffee cooling in a room).

Formulas you may need

Newton's law of cooling: rate of change of temperature proportional to the excess temperature (learn this)
Generalised first order form $\tau\dfrac{dx}{dt} + x = Ku(t)$ (learn this)

(a)
State the modelling assumption (Newton's law of cooling) and write it as a differential equation with a model coefficient $K'$ . Identify the output and the input.
(b)
Put the model into the generalised first order form and give the time constant and steady state gain. What sign must $K'$ have, and why?

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