CONVECTION HEAT TRANSFER Heat Transfer Q k _DrA_lm  (T₂ T₃) Q h₂A₂  (T₃ T₄) DTo can be expressed as the sum of the DT of the three individual processes. DTo (T₁ T₂) (T₂ T₃) (T₃ T₄) If the basic relationship for each process is solved for its associated temperature difference and substituted into the expression for DT_o above, the following relationship results. DTo Q 1 h₁ A₁ Dr k  A_lm 1 h₂ A₂ This relationship can be modified by selecting a reference cross-sectional area A_o. DTo Q A_o A_o h₁ A₁ Dr  Ao k  A_lm A_o h₂ A₂ Solving for results in an equation in the form . Q Q U_o  A_o    DT_o Q 1 A_o h₁ A₁ Dr  Ao k  A_lm A_o h₂ A₂ A_o    DT_o where: (2-10) U_o 1 A_o h₁ A₁ Dr  Ao k  A_lm A_o h₂ A₂ Equation  2-10  for  the  overall  heat  transfer  coefficient  in  cylindrical  geometry  is  relatively difficult to work with.  The equation can be simplified without losing much accuracy if the tube that is being analyzed is thin-walled, that is the tube wall thickness is small compared to the tube diameter.   For a thin-walled tube, the inner surface area (A₁), outer surface area (A₂), and log mean surface area (A_1m), are all very close to being equal.   Assuming that A₁, A₂, and A_1m are equal  to  each  other  and  also  equal  to  A_o  allows  us  to  cancel  out  all  the  area  terms  in  the denominator of Equation 2-11. HT-02 Page 22 Rev. 0