Determine the appropriate size of a shell-and-tube heat exchanger with two tube passes and one shell pass to heat 8.82 kg/s of pure ethanol from 15.6 to 60°C. The heating medium is saturated steam at 152 kPa condensing on the outside of the tubes with a condensing coefficient of 15,000 W/(m2K). Each pass of the exchanger has 50 copper tubes with an OD of 1.91 cm and a wall thickness of 0.211 cm. For the sizing, assume the header cross-sectional area per pass is twice the total inside tube cross-sectional area. The ethanol is expected to foul the inside of the tubes with a fouling coefficient of 5678W/(m 2 K). After the size of the heat exchanger, i.e., the length of the tubes, is known, estimate the frictional pressure drop using the inlet loss coefficient of unity. Then estimate the

Question

pumping power required with a pump efficiency of 60% and the pumping cost per year with $0.10 per kw-hr.



GIVEN

• Shell-and-tube heat exchanger, ethanol in copper tubes, steam in shell

• One shell pass and two tube passes

• Ethanol flow rate m e= 8.82 kg/s

• Ethanol temperatures

? Te,in = 15.6°C

? Te,out = 60°C

• Steam pressure = 152 kPa

• Number of tubes (N) = 50

• Tube outside diameter (Do) = 1.91 cm = 0.0191 m

• Tube wall thickness (t) = 0.211 cm = 0.00211 m

• Header area per pass = 2 (total inside cross-sectional area)

• Tube side fouling coefficient (1/Ri) = 5678 W/(m2 K)

• Shell-side transfer coefficient h o= 15,000 W/(m2 K)

FIND

(a) Size: length of one pass (Lp)

(b) The frictional pressure drop (?p)

(c) The pumping power required (Pp) with a pump efficiency (?p) = 60%

(d) Pumping cost per year for energy cost of $0.10/kw-hr

ASSUMPTIONS

• The variation of thermal properties with temperature is negligible

• Shell side fouling is negligible

• The tubes are smooth

• Entrance pressure drop effects are negligible

SKETCH



PROPERTIES AND CONSTANTS

the temperature of saturated steam at 152 kPa (Ts) = 110°C

for ethanol (ethy1 alcohol) at 20°C

Density (?) = 790 kg/m3

Thermal conductivity (k) = 0.182 W/(m K)

Absolute viscosity (?) = 12.0 × 10–4 (Ns)/m2

Prandtl number (Pr) = 16.29 Specific heat (cp) = 2470 J/(kg K)

the thermal conductivity of copper (kc) = 392 W/(m K) at 127°C

Answer 1

The inside diameter of the tubes is



The Reynolds number for the ethanol flow is





The overall heat transfer coefficient with fouling is



The overall heat transfer coefficient with fouling is



The heat capacity rate of the steam is essentially infinite. The heat capacity rate of the ethanol is



Because Z = 0; F = 1 and ?Tmean = LMTD.

The rate of heat transfer is



Solving for the length



The effectiveness, is



NTU ? 0.7



Solving for the length



The length of one pass = L/(# of passes) = (5.42 m)/2 = 2.71 m

This method relies on reading the low and is probably less accurate than the

LMTD method.

(b) the pressure drop is



Where the friction factor, f, is given for turbulent flow



(c) The pumping power required is



(d) The cost to run the pump is