Question

5. To warm up some milk for a baby, a caregiver pours milk into a thin-walled glass whose diameter is 6 cm. The height of the milk in the glass is 7 cm. The caregiver then places the glass into a large pan filled with hot water at 60 °C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the hot water and the glass is 120 W/m2-°C determine how long it wil take for the milk to warm up from 3 °C to 38 °C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Why? [Ans: 5.8 min] 6. Let's suppose that in Problem 5 that you decided that it wasn't necessary to stir the milk, so that the assumption of "lumped capacity" might not be valid. Treat the milk as a solid having properties equal to those of water at the average temperature of 20°C. Neglect end effects, so that the glass of milk can be considered to be a one-dimensional cylinder of diameter 6 cm. The outside heat transfer coefficient between the milk and the glass is still 120 W/m2-C. Estimate how long it will take for the centerline of this milk cylinder to reach 38 °C when its initial temperature is 3 °C. What will be the temperature at the glass-milk interface? [Hint: Your instructor hasn't worked this out yet, so it might not be a realistic problem. Note that you are neglecting the thermal resistance of the glass, which is probably not too bad.]
need the solution to problem 6. I already did problem 5 --> solution to problem 5 is 5.8 minutes.

Answer 1

Solis properties of water at Arg. temp. of 20'c are unit M (dysianic viscosite ) = 1002 RC Kinanutic viscoside) = lood unit Specific bead, co 4.18 KJ/KgK. Thermal Conductivity, K S 598-4 un P = 0.998 kg/m3 X17 Sence lumbed capacity is not valid here, so - we use Now o Hessler chert 3 5 98.4 - 6.993 X4170 X 100 0.143 X10-] .: D-143103 x + = 0.03484 t fo = 0.039844 t' is the time which he have to .0 calculate

Biot mo. Bir nec Bist No. Bir hike 120x0:06 * 1000 - 12:53 3984 i = 0082 = 0+1 Messeter's chart: Noves being . for Bi" = 0.082 and be = 0.395, he geti fo = 28 (from Hessehr charts fo: 0.02930 29 > t = 2.8 - 70-35 sec D: 5299 1. So, tiny tukea to centreline y the milk Cylinder is 70:25 sec. Now, to calculate glass-milk interface temp. DE LAAT = 120x (0-06)? (38-1) @=11.86 watt

NOW: Baka da 196 = 0.599 x 20:00 AT24125 R 219.25°C 5 T-20 = 21921's 33 T- 112C interface temperature will be 23825°C ca