T_{2}400- F 120- F 280- FT_{1}500- F 310- F 190- FT_{lm}( T_{2}T_{1})lnT_{2}T_{1}(280- F 190- F)ln280- F190- F232- FQ m hmQ m c_{p}TmHEAT EXCHANGERSHeat TransferHT-02 Page 36Rev. 0chimney effect of the warm humid air in the tower or by fans at the bottom (forced draft) or atthe top (induced flow) of the tower. Mechanical draft towers are more economical to constructand smaller in size than natural-convection towers of the same cooling capacity.LogMeanTemperatureDifferenceApplicationToHeatExchangersIn order to solve certain heat exchanger problems, a log mean temperature difference (LMTDor T ) must be evaluated before the heat removal from the heat exchanger is determined. Thelmfollowing example demonstrates such a calculation.Example:A liquid-to-liquid counterflow heat exchanger is used as part of an auxiliary system ata nuclear facility. The heat exchanger is used to heat a cold fluid from 120- F to 310- F.Assuming that the hot fluid enters at 500- F and leaves at 400- F, calculate the LMTDfor the exchanger.Solution:The solution to the heat exchanger problem may be simple enough to be represented by astraight-forward overall balance or may be so detailed as to require integral calculus. A steamgenerator, for example, can be analyzed by an overall energy balance from the feedwater inletto the steam outlet in which the amount of heat transferred can be expressed simply as, where is the mass flow rate of the secondary coolant and h is the change inenthalpy of the fluid. The same steam generator can also be analyzed by an energy balance onthe primary flow stream with the equation , where , c , and T are the masspflow rate, specific heat capacity, and temperature change of the primary coolant. The heat