Question

Data for carbon dioxide:

Molecular weight:44.0

Heat capacity of gas phase: 0.036+4.23 x10^-5T   (in kJ/mole^oC, T is in ^oC)

Viscosity                                 Pr                    k (W/m K)

180^oC2.13 x10^-5kg/(m s)                  0.721               0.029

130^oC  1.93x10^-5kg/(m s)                  0.738               0.025

  80^oC  1.72x10^-5kg/(m s)                  0.755               0.020

Approximate density: 2.0 kg/m³

Data for water:

Molecular weight:18.0

Heat capacity for liquid water: 0.0754 kJ/mole ^oC  

Viscosity:

Viscosity                                 Pr                    k (W/m K)

180^oC139 x10^-6kg/(m s)                   0.94                 0.665

130^oC  278x10^-6kg/(m s)                   1.72                 0.682

  80^oC  472x10^-6kg/(m s)                   3.00                 0.658

Ideal gas constant:

0.08206 L atm/(mol K)

Carbon dioxide, with flow rate of 0.10 kg/s, is to be cooled from 180 ^oC to 80 ^oC.  The utility stream is cold water, which enters the shell at 15 ^oC and leaves at 60 ^oC.    The carbon dioxide flows through the tubes and the water flows through the shell. The heat exchanger is a 1-1 shell and tube design (i.e. one shell pass, one tube pass).  The flow is counter-current.  The number of tubes is unknown.

Data (additional data on previous pages):

Heat transfer coefficient of the water in the shell: 500 W/m^2oC

Re in the tubes is 15,000

Assume the resistance to heat transfer of the pipe wall is negligible.

tube dimensions:  0.716 cm ID,   1.271 cm OD

tube pitch/diameter ratio=1.5

Pressure everywhere is approximately 1.5 atm

Assume carbon dioxide is an ideal gas.

Note—you do not need to interpolate physical properties; use values at the closest temperature given.

a. expected rate of energy transfer from the hot to the cold stream, in W:______________

b. mass flow rate of the water, in kg/s:______________________

c. heat transfer coefficient in the tubes (hint, tube Re=15,000):___________units of:____________

d. mass flow rate of the CO₂in each tube, in kg/s:_____________

e. overall heat transfer coefficient, Uo___________units of:____________

f. area needed for heat transfer, Ao, m²________________

g. Number of tubes needed, (round the number to nearest integer):_________

h. Length of each tube (using integer number of tubes, from part (g), m:___________

Answer 1

1. Expected rate of energy transfer from the hot to the cold stream, in W:______________

For this we will use, mCpdT for CO2 side as we know, Q= mCpdT (hot) = mCpdT (Cold)

Step1 :For CO2 , T1 = 180 C and T2 = 80, so dT = 100C

Step2 : Cp= 0.036+4.23 x10^-5T

        Cp1 = 0.036+ 4.23 x10^-5(180) =0.043614 kJ/mole^oC

              Cp2 = 0.036+ 4.23 x10^-5(80) =0.039384 kJ/mole^oC

Thus Cp (avg) = 0.041499 kJ/mol^oC

Step3 : m = 0.10 kg/s * 3600 = 360 kg/hr =8.18 kmol/hr =8180mol/hr

Step 4 : Q = mCpdT = 8180* 0.0415* 100 = 33497 kJ/hrC = 9304 W /c

2. mass flow rate of the water, in kg/s:

As we know, Q= mCpdT (hot) = mCpdT (Cold)

Thus , 33497 kJ/hr C = m (water ) Cp( water ) dt(water )

m = 9.872 kmol/hr = 0.049 kg/s