Problem 1.
a) Derive an equation which describes cooling of an object which is a good
thermal conductor. Assume uniform heat transfer outside the surface of the
object.
b) Spherical iron ball with diameter of 1 cm is initially at 100 oC temperature. Air
at temperature 20 oC flows outside it. Calculate temperature of the ball after
one minute, when the heat transfer coefficient between the ball and the flowing
air is 50 W/m2K.
c) Calculate the same thing numerically directly from the time dependent
energy balance by using ten second time steps.
Problem 2.
Stirred tank with 2300 kg of liquid is being heated from initial temperature of
15°C to a final temperature of 120°C. Saturated steam at 350 kPa(abs) is being
fed to the jacket of the tank. Heat capacity of the liquid is 2.0 kJ/kg K. Heat
transfer area is 5m2 and overall heat transfer coefficient 300 W/m2K.
a) How long does the heating take in this batch operation
b) What is steam mass flow in the beginning and in the end?
c) If the vessel would be fully mixed and operated in a continuous mode, how
big much cold flow could be heated?
d) How much of the feed could be heated with a countercurrent heat exchanger
of similar area?
Problem 3 &4.
Problem 3.
Derive an equation describing concentration changes in a batch reactor with
first order irreversible reaction to the reactant.
Problem 4.
Derive an equation for concentration changes in a steady state isothermal plug
flow reactor, and compare it to the previous result. Calculate concentration
changes with Excel, and study the effect of the step size and reaction kinetic
parameter.
Problem 5 & 6.
Problem 5.
a) Derive compositions at the vapor-liquid interface according to the two film
mass transfer theory.
b) Derive an equation for the overall mass transfer coefficient in the same
situation
Problem 6.
Calculate instantaneous mass transfer rate (g/s) for a spherical water droplet
falling in completely dry air at atmospheric pressure at terminal velocity of 6
m/s. Temperature of the droplet is 20 oC.
Newton’s law of cooling
A pot of liquid is put on the stove to boil. The temperature of the liquid
reaches 1700F and then the pot is taken off the burner and placed on a
counter in the kitchen. The temperature of the air in the kitchen is 760F.
After two minutes the temperature of the liquid in the pot is 1230F. How
long before the temperature of the liquid in the pot will be 840F ?
Mixtures
A large tank holds 300 gallons of brine solution. Salt was entering and
leaving the tank; A concentration of 2 lbs/gal is pumped into the tank at
a rate of 3 gal/min; it mixed with the solution there, and then the mixture
was pumped out at the rate of 3 gal/min. If 50 pounds of salt were
dissolved initially in the 300 gallons, how much salt is in the tank after a
long time?
Mixtures
Mixtures
A large tank holds 300 gallons of brine solution with 40 lbs of salt. A
concentration of 2 lbs/gal is pumped in at a rate of 4 gal/min. The
concentration leaving the tank is pumped out at a rate of 3 gal/min.
How much salt is in the tank after 12 min?
Mixtures
Consider a large tank holding 1000 L of pure water into which a brine
solution of salt begins to flow at a constant rate of 6 L/min. The solution
inside the tank is kept well stirred, and is flowing out of the tank at a rate of
6 L/min. If the concentration of salt in the brine solution entering the tank is
0.1 Kg/L, determine when the concentration of salt will reach 0.05 Kg/L?