Fundamentals of Heat Exchanger Theory and Design written by: Harlan Bengtson • edited by: Lamar Stonecypher • updated: 10/6/2010 Heat exchanger theory leads to the heat exchanger design equation that relates the overall heat transfer coecient, heat transfer surface area, and log mean temperature dierence to the rate of heat transfer. This heat exchanger design equation is used to nd the area needed for heat exchangers.
Introduction The heat exchanger design equation can be used to calculate the required heat transfer surface area for a variety of specied uids, inlet and outlet temperatures and types and congurations of heat exchangers, including countero or parallel o. ! value is needed for the overall heat transfer coecient for the given heat exchanger, uids, and temperatures. Heat exchanger calculations could be made for the required heat transfer area, or the rate of heat transfer for a heat exchanger of given area.
The Heat Exchanger Design Equation Heat exchanger theory leads to the basic heat exchanger design equation" # $ % ! &T lm, here # is the rate of heat transfer beteen the to uids in the heat exchanger in 'ut(hr, * o % is the overall heat transfer coecient in 'tu(hr)ft ) +, * ! is the heat transfer surface area in ft , and &Tlm is the log mean temperature dierence ino+, calculated from the inlet and outlet temperatures of both uids. +or design of heat exchangers, the basic heat exchanger design equation can be used to calculate the required heat exchanger area for non or estimated values of the other three parameters, #, %, and &Tlm. -ach of those parameters ill no be discussed briey.
Log Mean Temperature Diference
The driving force for any heat transfer process is a temperature dierence. +or heat exchangers, there are to uids involved, ith the temperatures of both changing as they pass
through the heat exchanger, so some type of average temperature dierence is needed. any heat transfer textboos have a derivation shoing that the log mean temperature dierence is the right average temperature to use for heat exchanger calculations. That log mean temperature is dened in terms of the temperature dierences as shon in the equation at the right. THin and THout are the inlet and outlet temperatures of the hot uid and /in T and T/out are the inlet and outlet temperatures of the cold uid. Those four temperatures are shon in the diagram at the left for a straight tube, to pass shell and tube heat exchanger ith the cold uid as the shell side uid and the hot uid as the tube side uid.
Heat Transer Rate, Q Heat exchanger calculations ith the heat exchanger design equation require a value for the heat transfer rate, #, hich can be calculated from the non o rate of one of the uids, its heat capacity, and the required temperature change. +olloing is the equation to be used" # $ mH /pH 0THin ) THout1 $ m/ /p/ 0T/out ) T/in1, here mH $ mass o rate of hot uid, slugs(hr, /pH $ heat capacity of the hot uid, 'tu(slug)o+ m/ $ mass o rate of cold uid, slugs(hr, o /p/ $ heat capacity of the cold uid, 'tu(slug) +, and the temperatures are as dened in the previous section. The required heat transfer rate can be determined from non o rate, heat capacity and temperature change for either the hot uid or the cold uid. Then either the o rate of the other uid for a specied temperature change, or the outlet temperature for non o rate and inlet temperature can be calculated.
Oera!! Heat Transer "oe#cient, $ The overall heat transfer coecient, %, depends on the conductivity through the heat transfer all
separating the to uids, and the convection coecients on both sides of the heat transfer all. +or a shell and tube heat exchanger, for example, there ould be an inside convective coecient for the tube side uid and an outside convective coecient for the shell side uid. The heat transfer coecient for a given heat exchanger is often determined empirically by measuring all of the other parameters in the basic heat exchanger equation and calculating %. Typical
ranges of % values for various heat exchanger(uid combinations are available in textboos, handboos and on ebsites. ! sampling is given in the table at the right for shell and tube heat exchangers"
%ummar& 2reliminary heat exchanger design to estimate the required heat exchanger surface area can be done using the basic heat exchanger equation, # $ % ! &T lm, if values are non or can be estimated for #, % and &Tlm. Heat exchanger theory tells us that &T lm is the right average temperature dierence to use. +or example preliminary heat exchanger design calculations, see the article,2reliminary 3 Heat -xchanger 4esign -xample.3 +or -xcel spreadsheet templates that can be donloaded to mae preliminary heat exchanger design calculations, see the article" 3-xcel 5preadsheet Templates for 2reliminary Heat -xchanger 4esign .3
Reerences and Image "redit 6eferences for +urther 7nformation" 8. 'engtson, H., +undamentals of Heat -xchangers, an online, continuingeducation course for 24H credit *. 9aac, 5. and :iu, H.,Heat Exchangers: Selection, Rating and Thermal Design , /6/ 2ress, *;;*. <. 9uppan, T., Heat Exchanger Design Handbook, /6/ 2ress, *;;;. 7mage /redit" 5traight tube, to pass, shell and tube heat exchanger"http"((.e) steamboilers.com(en(shell=tube=heat=ex.asp
HEAT EXCHANGER DESGN Heat echanger design includes estimation o! the heat trans!er area needed !or "nown or estimated heat trans!er rate# o$erall heat trans!er coe!!icient and log mean temperature di!!erence% &he tube or pipe diameters and length also need to be determined# as well as the pressure drop
