Crono's Brainiac Contest! Question 2

[Crono0001]

After question 1 was solved in 1 day (see here: viewtopic.php?f=23&t=30110) by Schwer_Punkt_91, I thought I'd up the difficulty slightly.  I will wait until the 16th to post the solution.

Difficulty: 6/10

PHYSICS / MECHANICAL ENGINEERING / CHEMICAL ENGINEERING: Transport Phenomena, Thermal Heat Transfer
--------------------------------------------------------------
A step in the manufacture of metallic spherical ball bearings (made of stainless steel 316, density of 8028 kg/m^3) includes thermal treatment, in which
the spheres are heated to a uniform temperature of 843°C in a furnace. The ball bearings that come out
of the furnace are placed on a conveyor belt for transport to an oil bath. The spheres remain 3 minutes
on the conveyor belt where they cool by natural convection (h=1 W/m^2 K) by contact with air at 35°C.
After that, they are dropped into a perfectly mixed oil bath in which the oil is kept at a constant
temperature of 25°C. The motion of the oil in the bath is fast enough to consider that heat transfer by
convection from the spheres to the oil is very fast (assume h = infinity). The spheres remain (briefly) in the bath until the
temperature at their center reaches 28°C. Determine the time that the spheres must remain in the oil
bath. The diameter of the spheres is 2 cm. Other information about the spheres: Cp=503 J/kg K, k=16 W/m K

First person to post the correct time gets the prize.

[Crono0001]

Some tips, since this is actually pretty hard (difficulty is rated on how long it takes to complete the problem by the way):

This is a transient heat transfer problem.  Calculate the Biot number to see whether or not this thing is uniform at both stages.
Start off with these equations:

q = h(T - Ta)
where:
q = heat transferred
h = convective heat transfer coefficient
T = temperature
Ta = temperature of the air

q = -k dT/dr
where:
q = heat transferred
k = conductive heat transfer coefficient
T = temperature
r = radius

Due to the complexity of the formula once you integrate, you may want to move into dimensionless variables.
You can also ask questions, which I'll try my best to answer.

Prize also scales with difficulty.

[kman94]

15 seconds.

[Crono0001]

15 seconds.

Not quite, sorry.
If you give me the answer, I'd also like to see that you've done some work instead of just randomly guessing.  I'm doing these contests for a reason of my own.

[SpartanFett]

Just a random guess... 21 seconds and post the answer soon. I want to know what the real answer is...

[Crono0001]

16 seconds.  I'm going to write the proof on a word document and upload it that way.  Close guess kman

Prize would've been an Umarex PX4 storm CO2 pellet pistol.

[SpartanFett]

16 seconds.  I'm going to write the proof on a word document and upload it that way.  Close guess kman

Prize would've been an Umarex PX4 storm CO2 pellet pistol.

Glad I didn't win than lol...jk I was just throwing a random # out there.

[Dilligaf]

i know the answer even though it was posted already dilligaf read and apply it...