need help, asap deadline in 2 hours

Problem 1 (30 points) Meat balls with a diameter of 30 mm are taken out of the fridge at 5 C and dropped in a pan of boiling pasta sauce (i.e., at 100 C). You can assume that the turbulence of the boiling of the pasta sauce eliminates heat transfer limitations in the sauce. How long does it take for the centre of the meat balls to reach a temperature of 80 C? Properties of the meat balls: cp = 4200 J kg1 K1 = 0.6 W m1 K1 = 1000 kg m3 State any additional assumptions you make. If you use a figure, give sufficient information to support your answer.

Problem 2 (20 points) Calculate the maximum possible dissolution rate (in g/s) of a small sphere of sugar with diameter 1 mm suspended in water in the absence of stirring. Data: The solubility of sugar in water is 250 kg/m3 . The diffusivity of sugar in water is 51010 m2 /s. State your assumptions for full marks. Note: the surface of a sphere is 4r 2 , where r is the radius of the sphere. CHME 6011 continued p. 4 of 5 Name:

Problem 3 Conceptual questions (30 points)

a. (10 points) A cylinder and a sphere with the same radius undergo the same heating process. Which of the two heats up faster? Or do they heat up at the same rate? Justify your answer.

b. (10 points) Explain the concept of contact temperature. Use the concept to explain why you dont burn your hand when you put it in hot air, but you do burn your hand when you put it in hot water of the same temperature.

c. (10 points) Imagine a planet with the same climate and geography and geology as planet earth, but where the year lasts only 3 months. How would the length of the year affect the depth of the freezing line? For instance, on a location where the freezing line on earth is 2 m deep, how deep is the freezing line at the same location on the other planet?

Problem 4 (20 points) A ship has 4000 m2 of hull surface area that is in contact with the water in the ocean. The engine of the ship generates a propulsion force of 4 million newtons, causing the ship to move with a velocity of 10 m/s. The hull of the ship has a roughness length of 10 mm. You can approximate the water as having a density of 1000 kg/m2 and a viscosity of 0.001 Pa s. The water surrounding a moving ship is turbulent.

a. (5 points) What is the shear stress of the water on the hull of the ship?

b. (5 points) What is the friction velocity of the water surrounding the ship? c. (10 points) What is the thickness of the boundary layer surrounding the ship, i.e., at what distance from the hull is the water moving at a velocity of 10 m/s relative to the ship?