I think this is probably a trivial question, but I am trying to understand how to do a thermodynamic calculation for heat transfer. I want to make a basic resistive heater by shorting a battery, but I want to do it in such a way that the power that goes into heating the battery will be dissipated into the surroundings at a rate such that no heat accumulates in the battery. I have no quantities of resistivity, voltage, or environment temperature, and I am just looking for a general process/equation to use for approximate convective heat transfer.
I think I know how to calculate the rate of heat accumulation in the battery. I do not, however, know how to go about finding the rate of heat transfer to the surroundings given:
Rate of Q_batt, Environment Temp, and any approximate constants for convection through air and the metal battery.
I would appreciate any help understanding that general process! Thank you.
Best Answer
Presumably the power dissipation $\dot{Q}$ inside the battery can be Ohmically modelled using only the current $I$ and the battery's internal resistance $R$.
So now we have two phenomena acting at once:
It's safe to assume that after some time a regime of steady state is achieved where all quantities are constant.
We can then thermodynamically model this in two ways.
$$\frac{\partial T}{\partial t}=\alpha \nabla^2T+\dot{Q}$$
which in steady state reduces to:
$$\alpha \nabla^2T+\dot{Q}=0$$
Depending on geometry this can still be mathematically very demanding.
The law describes convection losses $\dot{Q_{con}}$ to the environment. In steady state we have:
$$\dot{Q_{con}}=\dot{Q}$$
where:
$$\dot{Q_{con}}=k A \left(T_{bat}-T_{env}\right)$$
where $k$ is the convection heat transfer coefficient, $A$ the surface area of the battery, $T_{bat}$ the battery's temperature (presumed uniform) and $T_{env}$ the environment's temperature.
From here $T_{bat}$ can then be estimated.