ADVANCED PROBLEM
PROBLEM 1.1. Length Required for Cooling Coil
𝑇
𝑇 𝑤
= 20 0 C
T = 22 0 C z
Conditions for the flowing liquid
Tref = 0 o C
L…? z + ∆ z
Steady state solution
Heat transfer resistance at the tube-bath interface is minimal
Copper wall resistance can be ignored
𝐶 𝑝
= 1 kcal/kg
0
C
R = 0.01 m 𝑣
0
= 1 m/s 𝜌 = 10
3
kg/m
3
µ = 0.001 kg/m.s k = 1.43. 10
-4
kcal/s.m.K
𝑘𝑐𝑎𝑙 h = 0.980968 𝑚 2 𝑠 𝐾
𝑇
T = 20.5 0 C

PROBLEM 1.2. Heat Transfer in Spherical Boiling Egg
An egg at room temperature (20 o
C ) is submerged in boiling water at t = 0. We assume that the egg is perfectly spherical with radius R, that flow does not play a role in this problem, that the water temperature remains constant at 100 o
C , and that the egg has homogeneous medium properties. a) Give the equation that governs the non-stationary temperature distribution inside the egg.
Argue which terms can be neglected. Specify the initial conditions and the boundary conditions. b) Rewrite the equations into dimensionless form.
Note : Assume if u need to.
PROBLEM 1.3. Laminar flow in a narrow slit (see Fig. below).
Flow through a slit, with B << W << L.
A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls a distance
2B apart. It is understood that B << W, so that "edge effects" are unimportant. Make a differential momentum balance, and obtain the following expressions for the momentum-flux and velocity distribution

SIMPLE PROBLEM
1.
The waste acid from a nitrating process contains 15 percent HN03, 45 percent H2S04, and
40 percent H2O by weight. This acid must be concentrated to 25 percent HN03, 50 percent
H2S04, and 25 percent H2O. Available are concentrated solutions of acid in water, one of
95 percent H2S04 and the other of 85 percent HNO3. If 1500 kg of final product is required, find the mass of each concentrated solution to be added.
2.
Two parallel plates are 10 cm apart. The bottom plate is stationary. The fluid between the plates is water which has a viscosity of 1 centipoise. Calculate the momentum flux and force per unit area necessary to maintain a plate in motion at a velocity of 30 cm s
-1
.
3.
A glass rod of diameter 1.3 mm is 1 m long. One end is maintained at the normal boiling point of toluene, 110.6”C. The other end is affixed to a block of ice. The thermal conduction along the rod is at steady-state. The heat of fusion of ice is 79.7calg
-1
. The thermal conductivity of glass in SI units is 0.86 W m
-1
K
-1
Assume no heat is lost from the exposed surface of the rod. Find:
(a) the amount of heat transferred in joules per second;
(b) the number of grams of ice that melt in 30 minutes.
4.
In the concentration of orange juice a fresh extracted and strained juice containing 7.08 wt
% solids is fed to a vacuum evaporator. In the evaporator, water is removed and the solids content increased to 58 wt % solids. For 1000 kg/h entering, calculate the amounts of the outlet streams of concentrated juice and water.
5.
A fuel gas containing 3,1 % H2, 27,2 %CO, 5,6 %CO2, 0,5 %O2, and 63,6 % N2 is burned with 20 % excess air. The combustion of CO is only 98 % complete. For 100 kg mol of fuel gas, calculate the moles of each component in the exit gas.