Log Mean Temperature Difference Application to Heat Exchangers

In order to resolve certain heat exchanger troubles, a log mean temperature difference (i.e., LMTD or ΔT_lm) should be computed before the heat elimination from the heat exchanger is examined.  The illustration below elaborates like computation.

The answer to the heat exchanger problem might be simple adequate to be symbolized by a straight-forward overall balance or might be therefore detailed as to need integral calculus.  A steam generator, for illustration, can be examined by an overall energy balance from the feed-water inlet to the steam outlet in which the quantity of heat transferred can be stated simply as Q = m Δh, where m is the mass flow rate of the secondary coolant and Δh is the change in enthalpy of the fluid.  The similar steam generator can also be examined by an energy balance on the main flow stream by the equation Q = m c_p ΔT, where m, c_p , and ΔT are the mass flow rate, specific heat capacity & temperature transform of the prime coolant.  The heat transfer rate of the steam generator can also be established by comparing the temperatures on the primary and secondary parts with the heat transfer characteristics of the steam generator by using the equation Q = u_o A_o ΔT_lm.

The condensers are also illustrations of components found in nuclear facilities where the idea of LMTD is required to address certain problems.  Whenever the steam enters the condenser, it provides up its latent heat of vaporization to the circulating water and changes phase to a liquid. Since condensation is occurring, it is suitable to term this the latent heat of condensation. Subsequent to the steam condenses, the saturated liquid will carry on to transfer some heat to the circulating water system since it continues to fall to the bottom (hot well) of the condenser.  This sustained cooling is termed as sub-cooling and is essential to prevent cavitation in the condensate pumps. The answer to condenser problems is approached in the similar manner as those for steam generators.