Answer to Question #299433 in Inorganic Chemistry for Pink

Question

Write the dynamic model in eqn. 1 in terms of the deviation variables 0*(t), q*(t), and 0*(t)

Answer 1

Let $\theta=\theta(t)[°C]$ be temperature of a component.

Let the component be generating heat as it is used at rate

$q=q(t)[J/s]$

Air is blown over the component to cool it.

Temperature of air $\theta_a=\theta_a(t)[°C]$

Temperature of air $\theta_a(t)$ and heat generated by component , $q(t)$ affect temperature of component $\theta(t)$

The dynamic model for the output $\theta(t)$ in response to $q(t)$ and $\theta_a(t)$ is

$C\>\frac{d\theta}{dt}=q(t)+UA[\theta_a(t)-\theta(t)]$

Where C, U and A are [Constant] parameters.