Originally Posted by **Ryudamasu** For example, if there are two heated coils, one that is room temperature and one that is 100 degrees Fahrenheit. In the same instance, there are two heat guns aimed at the heater coils at the same settings. Would the 100 degree heat coil be slower to climb in temperature, or gain at the same rate as the room temperature coil? |

In practise, heating coil temperatures are dominated by the actual heat rate of the technology, so they're not affected much by the surroundings. Therefore, for convenience, heat problems tend to neglect the temperature of the actual heating coil and just assume that the heat is provided by an constant injection. However, if its desirable to model the temperature of the coil itself, what happens depends on the temperature of the air inside the cavity.

If the temperature inside the room is intermediate between the two coil temperatures, then one heat rate will increase and the other will decrease. The difference in temperature growth rates then depends on how much convection is happening (high surface area and high heat transfer coefficient).

If the temperature in the room is not intermediate between the two coils, then the growth rates can both be boosted or damped by the effect of convection, since heat will go into or out of the room air.

Let's say we have two parallel heating coils separated by an air gap (with adiabatic side walls) with temperature $\displaystyle T_{room}$. If each coil has a constant heat rate $\displaystyle \dot{q_{heat}}$, and variable temperatures $\displaystyle T_{1}$ and $\displaystyle T_{2}$, then

$\displaystyle \dot{q_1} = \dot{q_{heat}} + hA(T_{room} - T_{1})$

$\displaystyle \dot{q_2} = \dot{q_{heat}} + hA(T_{room} - T_{2})$

since in our problem set-up we have $\displaystyle T_{1} > T_{room}$ and $\displaystyle T_{2} < T_{room}$, we expect $\displaystyle \dot{q_2} < \dot{q_1}$.

A more standard problem is to consider two plane walls separated by an air gap and then embed the heating coils in the plane walls. Then, the heating coils are just modelled as injections of heat into the walls. Then, you can include the effect of conduction across the wall in addition to the convection from the surface.