(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two students, A and B, are discussing a heat transfer problem regarding what the surface temperature of a cartridge electrical heater would be when exposed to a water flow (CASE 1) and an air flow (CASE 2).

Case 1:

h_{w}= 5000 W / (m^{2}* K); T_{surr}= 20ºC

Case 2:

h_{a}= 50 W / (m^{2}* K); T_{surr}= 20ºC

Student A insists that the surface temperature of the cartridge will be larger in CASE 2 than in CASE 1, while student B states the opposite.

The cartridge is shaped as a solid cylinder of length L=200 mm and diameter D=20 mm, which is known to dissipate 2 kW irrespective of the case. Find the surface temperature of the cartridge in each case to find out if student A is right or wrong.

2. Relevant equations

q_{tot}= q_{conv}+ q_{rad}

q_{tot}= A * q^{''}_{conv}+ A * q^{''}_{rad}

I assumed that since [itex]\alpha[/itex] wasn't mentioned, [itex]\epsilon[/itex] = [itex]\alpha[/itex] and I could use this form:

q_{tot}= 2[itex]\pi[/itex]RL * h(T_{s}-T_{surr}) + 2[itex]\pi[/itex]RL * [itex]\epsilon[/itex] [itex]\sigma[/itex] (T_{s}^{4}- T_{surr}^{4})

3. The attempt at a solution

So really, given the above equations, this should be a "plug and chug" problem by saying that q_{tot}= 2 kW and solving the equation for T_{s}. However, I cannot do that because the surface emissivity (or absorption) is not given. So I started to think whether or not the cartridge had any radiation at all. I looked through my notes and the textbook and could not find a way to quantify [itex]\epsilon[/itex] using the given information. That's when I came here. Am I wrong to assume that there is any radiation? Or am I doing something completely wrong?

Thanks for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Heat Transfer Problem - Radiation missing Emissivity value

**Physics Forums | Science Articles, Homework Help, Discussion**