Calculating the boil-off rate of liquid helium

[NZPhysics]

Homework Statement

An aluminum rod 0.500 m in length and with a cross-sectional area of 2.60 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at340 K. (Aluminum has thermal conductivity of 3,100 W/m · K at 4.20 K; ignore its temperature variation. Aluminum has a specific heat of 0.215 cal/g · °C and density of 2.70 g/cm3.The density of liquid helium is 0.125 g/cm3.)

(a) If the circular surface of the upper end of the rod is maintained at 340 K, what is the approximate boil-off rate of liquid helium in litres per second after the lower half has reached 4.20 K?
___________ litres/s

Homework Equations

ΔL/L₀ = αΔT, I'm not really sure what else would be applicable.

The Attempt at a Solution

I honestly have no idea where to start with this question so any help would be really appreciated.

Thanks

 

[haruspex]

Unless you are expected to solve the diffusion equation using Fourier series, I would assume that only the lower tip of the rod is in the helium. So it becomes a question about rate of conduction of heat along a rod with the ends at fixed temperatures.
You must have been taught something about conduction and temperature gradients.