Very simple question on heat transfer / thermal conductivity

Hi people! This is my first time and so on...don't kill me it isn't the
right place yada yada
<THE ACTUAL QUESTION IS DOWN AT THE BOTTOM>

I'm trying to evaluate the temperature inside an ('empty') aluminium
cylinder as a function of the external one. I'm using a naive model
assuming the inside is isolated and the temperature in the cylinder is
the same at every point (i.e temperature is a function of time only).
Anyhow, this assumption (that one may call "a thin boundry assumption":
Rin ~ Rout) ends with a simple ODE

My question - We usually take the heat flux to be lineary proportional
to the derivitive of temperature along the axis of heat flow
Jq = -K*Tx
but I don't have this derivitive having assumed temperature to be
constant inside the cylinder. I think in this case I should take the
heat flux to be of the form:
Jq = -K*(T(t) - Tout)/L
Where L is some typical distance constant. But what is a good
assumption about this L? Should it be the thickness of the cylinder
Rout-Rin? Maybe better to take half of it? I'm realy not sure

Would much appreciate any help

.

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