CONDUCTION HEAT TRANSFER Heat Transfer The surface area (A) for transferring heat through the pipe (neglecting the pipe ends) is directly proportional to the radius (r) of the pipe and the length (L) of the pipe. A = 2prL As the radius increases from the inner wall to the outer wall, the heat transfer area increases. The  development  of  an  equation  evaluating  heat  transfer  through  an  object  with  cylindrical geometry begins with Fourier’s law Equation 2-5. Q k  A DT Dr From the discussion above, it is seen that no simple expression for area is accurate.  Neither the area of the inner surface nor the area of the outer surface alone can be used in the equation.  For a  problem  involving  cylindrical  geometry,  it is  necessary  to  define  a log  mean  cross-sectional area (A_lm). (2-7) A_lm A_outer A_inner ln A_outer A_inner Substituting  the  expression  2prL  for  area  in  Equation  2-7  allows  the  log  mean  area  to  be calculated from the inner and outer radius without first calculating the inner and outer area. A_lm 2  p  r_outer  L 2  p  r_inner  L ln 2  p  r_outer  L 2  p  r_inner  L 2  p  L r_outer r_inner ln r_outer r_inner This expression for log mean area can be inserted into Equation 2-5, allowing us to calculate the heat transfer rate for cylindrical geometries. HT-02 Page 12 Rev. 0