# Heat transfer question: Finding the convection coefficient

1. Feb 28, 2009

### Seraph042

1. The problem statement, all variables and given/known data

In Betty Crocker's cookbook, it is states that it takes 2h 45 min to roast a 3.2kg rib initially at 4.5 Celsius "rare" in an oven maintained at 163 Celsius. It is recommended that a meat thermometer be used to monitor the booking, and the rib is considered rare done with the thermometer inserted into the center of the thickest part of the meat registers at 60 Celsius. The rib can be treated as a homogeneous spherical object.

Here are the given variables:
$$\rho$$=1200 kg/m3
cp=4.1 kJ/kg C
k=0.45 W/m C
$$\alpha$$=0.91 x 10-7 m2/2
t = 2hr45min = 9900s
Ti = 4.5 C
Tinf = 163 C
T(0, t) = 60 C

a) FIND THE HEAT TRANSFER COEFFICIENT AT THE SURFACE OF THE RIB

2. Relevant equations
The chapter which this goes in has the following equations
$$\theta$$o=(T(0,t) - Tinf) / (Ti - Tinf)=A1e-$$\lambda$$12 * $$\tau$$

$$\tau$$ = $$\alpha$$ * t / ro2

Bi = hLc / k

3. The attempt at a solution
The book gives us that h = 156.9 W/m2 C

I've tried -k * dT(ro, 0) / dt = h * (T(ro, 0) - Tinf)

Where T(ro, 0) = Ti = 4.5 C

But if I plug in my known value of h that the book gives us, then dT(ro, 0) / dt must be = 55263.7

I found $$\theta$$o = 0.6498, but we cannot get A1 or $$\lambda$$1 until we find the Biot number

I've also tried looking at the Heisler charts, but they have been no use without having both $$\tau$$ and the Bi number

There are other questions to this problem but I can figure those out, I just have no idea what to do for this