Overall Heat Transfer Coefficient

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