## Temp to raise fluid temp inside a container - Heat transfer & thermodynamics

1. The problem statement, all variables and given/known data
Hi all, I have this problem statement with variables:

20" Diameter, 2000mm (length, L) cylindrical container with 8mm thickness made of plastic
Container 3/4 filled with gasoline.

Question: What is the immediately surrounding temperature required outside the container to raise the temperature of gasoline, initially at 50 F, 6 F per minute.

How will the pressure change/minute inside the tank as temperature of gasoline rises.

Known: Thermal conductivity, k, of plastic (for conduction heat transfer)
Heat capacity of gasoline

Assumptions: Equal heat transfer from outside to inside through all sides
At atmospheric pressure outside
Tank fully closed (no vents, etc.)

2. Relevant equations

I know this equation q = (mass) (temp change) (Cp)
But I don't know how to incorporate heat transfer through the thickness of the container to the fluid inside the tank.

I also know that the heat transfer rate through cylindrical shell is Q(dot)= 2k(pi)L(T1-T2)/ln(r2/r1)
But how do I take into account heat transfer through circular end caps on each end of the cylinder?

3. The attempt at a solution

I have no idea how to combine heat transfer and thermodynamic aspects of this problem together to solve for what the statement is asking for, outside temperature and pressure change

Any ideas or direction will be greatly appreciated!

Thanks,
Abe

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 Any ideas? Any help or direction will be appreciated. UPDATE: In addition to the information above, I can figure out the mass of the gasoline from the volume and density, and use q=m*cp*(T2-T1), and this will give me heat in Joules, but I don't know how to take into account the temperature raise by 6 F (3.33K) PER minute. That throws me off as well. I guess for the end caps, I can use 2*q(conduction through wall) and for the shell, I can use q(conduction through cylinder). Since I am looking for temperature immediately surrounding the tank, is it safe to ignore ambient air convection? Pretty much this tank will be engulfed in flames. So then my unknown would be the outside surface temperature of the tank, assuming evenly distributed flame, thus evenly distributed outside surface temperature. My other question is since the tank is only 3/4 full with gasoline initial temp at 50 F (283.15K), what would my inside surface temp be? If the density of gasoline is 840 Kg/m^3 and volume of 3/4 full tank is 0.426m^3, mass is 358kg. Using q=m*cp*(detla T), 358kg*1750J/kg-K*3.33K = 2086.245KJ.
 Anyone?