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David C. Silverman |
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Heat Exchangers-Analysis in the Absence of Fouling Heat is usually exchanged between systems in processing applications. Such applications transcend many industries. The device used in such field applications is the heat exchanger. Though numerous designs exist they tend to have the characteristic that two fluid streams pass by each other separated by a wall. The wall can be metallic or non-metallic. The fluids are normally gas or liquid. Heat is transferred from one stream to the other through the wall. This figure)
shows the overall heat flow between the streams and the resistances involved.
Flow is assumed to be counter-current but co-current and
cross-current flow is possible. The resistance in each fluid is proportional
to the inverse of the convective heat transfer coefficient (h) which is calculated
from the Nusselt number by methodologies discussed in the section
on the thermal boundary layer
and heat transfer coefficient. The resistance in the wall between the two
fluids is proportional to the inverse of the thermal conductivity, a physical
property of the material. All resistances to the total heat flow are also
inversely proportional to the total area for heat transfer.
Details for design of heat transfer equipment of all types can be found in "Perry’s Chemical Engineers Handbook", 7th, McGraw-Hill, 1997 . The underlying equation that calculates the required area from the required heat can be represented as 
(15)where dA is the element of surface area required to transfer an amount of heat equal to dQ and where the overall heat transfer coefficient is U and the temperature difference between the two streams is ΔT. The overall heat transfer coefficient is composed of the heat transfer coefficients of the two fluids and the thermal conductivity of the wall. In terms of this figure
(16)where U is the overall heat transfer coefficient based on the surface exposed to fluid 1. Equation (16) assumes a slab separates the two fluids so the area on each side is the same. In most practical geometries, correction has to be made for differences in area exposed to the two fluids. The heat transfer coefficients hA and hB can be determined by the methods oulined in the section on the thermal boundary layer and heat transfer coefficient using the proper correlation for each geometry. The total area is found by integrating equation (15) from 0 to the total amount of heat required. For most practical considerations, the overall heat transfer coefficient can be considered to be constant (independent of temperature) and equation (15) becomes 
(17)where Qtotal is the total heat load required, Umean is a constant mean overall heat transfer coefficient, and ΔTmean is a corresponding mean temperature difference between the two fluids such that equation (17) is valid. The temperature difference between the two fluids usually varies with position. If the flow is completely countercurrent or completely co-current and the overall heat transfer coefficient is independent of temperature, the correct mean temperature difference to use in equation (17) is calculated using the log mean temperature difference. This figure )
shows the two situations and the temperature profile that results from each. The equation
describing this calculation is
(18)where h and c represent the hot and cold fluids and 1 and 2 represent the positions of the inlet and outlet in the exchanger which correspond to the hot and cold temperatures for the two fluids. The double pipe heat exchanger shown in this figure )
provides a practical example of how to apply the above example. In the figure,
the subscript "ow" stands for "outside wall" and "iw" stands for "inside wall".
Heat is exchanged between the inner fluid and the outer fluid. In terms of the
figure, the overall heat transfer coefficient is 
(19)where UOA is the overall heat transfer coefficient, A is the area of the inner or outer wall, r is the radius of the inner or outer wall, k is the thermal conductivity through the wall, and L is the thickness of the tube wall. The values of h are estimated by the methods outlined in the section The Thermal (Heat Transfer) Boundary Layer and Heat Transfer Coefficient. Example To see how the equations might be applied, assume the following: water at the rate of 3000 kg/min is heated from 25C to 50C by an oil. The fluids are in a counter flow arrangement and the oil enters at 150C and leaves at 100C. The overall heat transfer coefficient as calculated from equation (19) is 2.06x105 cal/hr-m2-C. The assumption is made that equations similar to those outlined in The Thermal (Heat Transfer) Boundary Layer and Heat Transfer Coefficient were used for this estimate. What is the required area? Calculation of Total Heat Transfer q = (mass flow of water)(heat capacity)(change in temperature) = (3x106 g/min)(1/18 cal/gm/C)(25C)(60 min/hr) = 2.50x108 cal/hr. Calculation of Log Mean Temperature Difference 
Calculation of Total Area for Heat Transfer  
From this area, one would have to size the tubes and exchanger. Computer programs are available to properly size and design exchangers. Many types of heat exchangers exist. One of the best sources for a general discussion of the various types of heat exchangers is ”Perry’s Chemical Engineers Handbook”, 7th, McGraw-Hill, 1997 Some examples are:
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David C. Silverman, Ph.D. - Primary Consultant |