Appendix D
Appendix D
ELABORATE DESIGN OF MULTIPASS COUNTER
FLOW HEAT EXCHANGER
D.1 Design of Multipass counter flow (shell &tube type) heat
exchanger
A multipass counter flow (shell & tube type) heat exchanger is selected for
preheating the air which shall be supplied to the furnace. In designing of this
heat exchanger following parameters are consideredMass flow rate of air at inlet.
Mass flow rate of flue gases at inlet.
Logarithmic mean temperature difference.
Correction factor.
Number and arrangement of tubes depending upon surface area.
Dimensions of heat exchanger
Efficiency of heat exchanger
Area density β (Surface area of heat transfer/volume of heat transfer)
Dimensions of ducts
Fouling factor
Refractory lining and construction
The following data’s are considered for designingAir density =1.1774kg/m3,
Approximate Volume of air =1000.0m3,
Approximate time of one heat = 40.0 minutes,
Atmospheric air temperature at inlet of exchanger = 27.00C,
Air temperature at exit from exchanger = 350.00C,
Specific heat at constant pressure for air Cpc = 1.005kj/kg,
Specific heat at constant pressure for hot gases Cph =1.100kj/kg.
D.1.1 DESIGN PARAMETERS
(1) Mass flow rate of air at inlet:
= (1000x1.1774)/ (40x60) =0.490 kg/sec
D.1
Appendix D
Amount of heat absorbed Q =0.490 kg/sec x 1.005kj/kg x (350-27)0C
=159.061 Kw
(2) Mass flow rate of flue gases at inlet:
Approximate fuel (Biodiesel) per heat = 80.0 liters,
Density of Biodiesel =0.88kg/liter
Mass flow rate of flue gases at inlet
= [0.490+ (80x0.87)/ (40x60)]=0.519kg/sec
Temperature of hot gases at exit from heat exchanger
Q= m x s x t
159.061Kw=0.519 kg/sec x 1.100 x(1100- th2) or
th2=821.385oC
th1 =Temperature of hot gases at inlet of exchanger=11000C
th2 =Temperature of hot gases at outlet of exchanger=821.3850C
tc1= Temperature of fresh air at inlet of exchanger=270C
tc2= Temperature of fresh air at outlet of exchanger= 3500C
(3) Logarithm mean temperature difference T(lm)- The temperature
difference of the hot and cold fluids varies along the heat exchanger and a
mean temperature difference known as Logarithmic mean temperature
difference denoted by T(lm) is the difference of hot and cold fluid
T(lm) = (t1-t2)/ln (t1/t2)
Where t1 = (th1 _ tc2) and t2 = (th2_ tc1)
Logarithmic mean temperature difference T(lm) = t1-t2 / In t1/t2
t1 = (th1 _tc2) (1100-350) =7500c
t2 = (th2 _ tc1) = (821.3850c -27) =794.380c
T (lm) = (750-794.38)/ ln (750/794.38) = [- 44/-0.057]
= 771.920C
(4) Correction factor- For heat exchangers equivalent temperature
difference is related to Logarithm mean temperature difference by
T (lm) = F x Tmcf
Where Tmcf = mean temperature difference, and F=correction factor.
D.2
Appendix D
Correction factors have been published in the form of charts by Bonman,
Mueller, and Nagle and by TEMA. The data is presented as a function of
following two non-dimensional variables(a) P= Temperature ratio and
(b) R= Capacity ratio
(a) Temperature ratio (P)
is defined as the ratio of the rise in
temperature of cold fluid to the difference in the inlet temperatures of the
hot and cold fluids, thus
P= (tc2 _ tc1) /(th1 _ tc1)
Where subscripts h and c denote the hot and cold fluid respectively and
subscripts 1and 2 refer to the inlet and outlet conditions respectively.
The Temperature ratio P indicates cooling or heating effectiveness and it can
vary from zero, for constant temperature of one of the fluids, to unity for the
case, when inlet temperature of the hot fluid equals the outlet temperature
of the cold fluid.
P= [(tc2 _ tc1)/ (th1 _ tc1) = [(350-27)/ (1100 -27)] =323/1073
= 0.301
(b) Capacity ratio (R) - It is defined as the ratio of temperature drop of the
hot fluid to the temperature rise in cold fluid, of the two fluids, thus
R = (th1 _ th2)/(tc2 _ tc1)
= [(1100-821.385)]/[(350 -27)]= 278.615/323
=0.862
Corresponding to these values of P and R from curve (Figure D-1) F=0.99
D.3
Appendix D
Figure D-1 P and R curve for correction factor for multipass counter flow
heat exchanger
(5) Number and arrangement of tubes depending on surface area
Q = UAFT(lm),
U=overall heat transfer coefficient =30w/m2 0C
A=surface area
F=correction factor=0.95,
T(lm)=logarithm mean temperature difference =771.920C
A= Q/UFT (lm)= 159.06 x103 watt/0.99 x30w/m2 0C x771.920C
=6.937m2
Diameter of tube = =0.04m,
Length of one tube =1.0m
Surface area of one tube= 0 .1257m2
No of tubes = 6.937 m2/0.1257m2 =55.19
If length of tube =1.0m, No of tubes=56
56 tubes are arranged in 4 passes of 14 tubes in each pass
(6) Dimensions of heat exchanger
Total length of heat exchanger=1m+0.20m+0.20m=1.40m
Diameter of heat exchanger—
D.4
Appendix D
Total 56 tubes are arranged in 4 passes of 14 tubes each (diameter 4.0 cms
separated by baffle plates of 2.0 cms each).
Pass 1 =34.0 cms
Pass 2= 16.0 cms
Pass 3= 16.0 cms
Pass 4= 34.0 cms
Diameter=100.0 cms
Length of heat exchanger==1.40m & diameter =1.00m
Shape of heat exchanger is cylindrical
(7) Efficiency of heat exchanger =
Efficiency of heat exchanger is given by ή=Q*/Q max
Where Q*=actual heat transfer and
Qmax=maximum possible heat transfer
Q* =159.061kW,
Qmax =Cmin (th1- tc1)
where Cmin is smaller of Ch and Cc
Ch =mh*Cph
and Cc= mc* Cpc
Ch =mh*Cph = 0.519 kg/sec x1100 j/kg =570.9 j/sec
Cc= mc*Cpc = 0.490 kg/sec x1005 j/kg = 492.45 j/sec
Cmin = 492.45 j/sec
Qmax =Cmin (th1- tc1)
=492.45 j/sec (1100-27)0C
=528.398kW
Efficiency (ή) = Q*/ Qmax =159.061/528.398 =0.3010
= 30.10 %
(8) Area density β
β=Surface area of heat transfer/volume of heat transfer
(a) Surface area of heat transfer
Area of 1 tube = π d l=0.1257 m2
Area of 56 tubes =56x0.1257m2 =7.0399 m2
(b) Volume of heat transfer
D.5
Appendix D
Volume of 1 tube =π d2 l/4
= 0.001256 m3
Volume of 56 tubes (volume of heat transfer) =56 x 0.001256 m3
=0.0703m3=
Area density β = surface area of heat transfer/volume of heat transfer
=7.0399 m2 /0.0703m3 = 100.14
(9) Diameter of cylindrical duct for fresh air inlet and exit=8.0 cms.
Diameter of cylindrical duct for hot flue gases at inlet/exit = 20cm /10 cm
(10) Fouling factor-The performance of heat exchanger usually
deteriorates with time as a result of accumulation of deposits on heat
transfer surfaces. The layer of deposits represents additional resistance to
heat transfer and causes the rate of heat transfer in a heat exchanger to
decrease. The net effect of these accumulations on heat transfer is
represented by a fouling factor Rf which is a measure of thermal resistance
introduced by fouling. The representative fouling factor Rf (thermal
resistance due to fouling for a unit surface area) for air, as given by tubular
exchangers manufacturers association (USA) is 0.0004m2 0C/W. It has been
already considered in overall heat transfer coefficient.
(11) Refractory lining and its installation–Normally the refractory
lining of exchanger is being done with monolithic silica brick lining of
thickness 60.0 mm followed by rammed silica mass of thickness 40.0 mm,
which is available in the market.
Dimensions (after brick lining), length =1.60 m and diameter=1.20 m
The exchanger is fabricated with heavy duty Ni Cr steel (25% Ni, 20%Cr)
plates of 5.0 mm thickness, reinforced with steel rings on both sides, and
strengthened with flats.
D.6