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Heat - A Primer!

Here is some information about heat transfer and heat exchangers, two related and interesting topics!  What follows is a brief and simplified look at these concepts.

 Heat transfer can be classified in two ways:

Sensible heat transfer, also known as temperature change.   For example, it takes one BTU to raise one pound of water one °F.  The key relationship here is:   

Q = C_p • M • TD

Where:
  Q is BTU/hr
  C_p is heat capacity in BTU/lb-F (the C_p of water is 1)
  M is mass flow in lb/hr
  TD is Temperature difference in °F

Latent heat transfer, also known as phase change.  For example, it takes 1000 BTUs to boil one pound of liquid water into steam - at the same temperature.  The key relationship here is:

Q = H_fg • M

Where:
  Q is BTU/hr
  H_fg is the latent heat of vaporization in BTU/lb (the H_fg of water is 1000)
  M is mass flow in lb/hr

Heat exchanger design starts looking just as simple, but it gets much more interesting!  Heat exchangers are machines that get fluids to transfer their heat.  Most heat exchangers work with two fluids flowing separate passages, for example cold water flowing inside a tube and warm air flowing outside the tube.  When this happens, the cold fluid warms up and the hot fluid cools off.  The key relationship here is:

Where:
  A is the required amount of surface area in ft²
  Q is duty in BTU/hr
  U is the performance of the heat exchanger in BTU/hr-ft²-°F 
  LMTD is the mean temperature difference throughout the heat exchanger in °F

The LMTD is a computation that takes the inlet and outlet temperatures of both fluids and reduces them to one number, which is the average temperature difference:



     T₁ = Hot Stream Inlet Temp.
     T₂ = Hot Stream Outlet Temp.
       t₁ = Cold Stream Inlet Temp.
       t₂ = Cold Stream Outlet Temp.

The U value is the heat exchanger's performance coefficient, it's based on the unit's design, materials and the fluids that flow through.  A heat exchanger made from aluminum, will have a higher U value than one made of plastic, because aluminum is a better conductor of heat.  A heat exchanger using water as coolant will have a higher U value than it would using air as coolant, because water is a better coolant.  The key relationship here is:

 
Where:
  U is the performance coefficient for the heat exchanger in BTU/hr-ft²-°F
  h₁, h₂, h₃, etc. for a fin tube, air-to-water heat exchanger are heat transfer coefficients typically:
air, fin, tube, water.
 R₁, R₂, R₃, etc. is the thermal resistance of the various aspects of the heat exchanger in hr-ft²-°F/BTU, typically:
Internal fouling factor, metal contact resistance, external fouling factor

The number and type of heat transfer coefficients and thermal resistances will vary from one heat exchanger design to the next.  In a simple unit where two fluids flow on opposite sides of a metal plate, there might be an h_cold-fluid, R_metal-plate and h_hot-fluid.  The metal resistance is trivial because the thermal conductivity of metals is well known.  The fluid heat transfer coefficients depend not only on the fluid, but on it's level of turbulence as it flows through the heat exchanger.  Determining fluid heat transfer coefficients is often the crux of designing heat exchangers.