Heat Exchanger AnalysisEffectiveness–NTU Method
2. Effectiveness–NTU Method
• It is a simple matter to use the log mean temperature difference(LMTD) method of heat exchanger analysis when;
• the fluid inlet temperatures are known,
• the outlet temperatures are specified,
• the outlet temperatures readily determined from the energy balanceexpressions.
• However, if only the inlet temperatures are known, use of the LMTDmethod requires a cumbersome iterative procedure. It is thereforepreferable to employ an alternative approach termed theeffectiveness-NTU method.
Effectiveness–NTU Method
• To determine the maximum possible heat transfer rate in a heatexchanger, we first recognize that the maximum temperaturedifference in a heat exchanger is the difference between the inlettemperatures of the hot and cold fluids.
• The heat transfer in a heat exchanger will reach its maximum valuewhen the cold fluid is heated to the inlet temperature of the hot fluidor the hot fluid is cooled to the inlet temperature of the cold fluid.These two limiting conditions will not be reached simultaneouslyunless the heat capacity rates of the hot and cold fluids are identical.
Effectiveness–NTU Method
• To define the effectiveness of a heat exchanger, we must firstdetermine the maximum possible heat transfer rate, qmax for theexchanger. This heat transfer rate could, in principle,be achieved in acounterflow heat exchanger.
Effectiveness–NTU Method
• It is now logical to define the effectiveness, ε as the ratio of the actual heat transfer rate for a heat exchanger to the maximum possible heat transfer rate:
Effectiveness–NTU Method
• By definition the effectiveness, which is dimensionless, must be in therange 0≤ε≤1. It is useful because, if , Th,i, and Tc,i are known, the actualheat transfer rate may readily be determined from the expression;
• where Cmin/Cmax is equal to Cc/Ch or Ch/Cc, depending on the relativemagnitudes of the hot and cold fluid heat capacity rates.
Effectiveness–NTU Method
• The number of transfer units (NTU) is a dimensionless parameter that is widely used for heat exchanger analysis and is defined as;
• To determine a specific form of the effectiveness-NTU relation, consider a parallel-flow heat exchanger for which Cmin=Ch, we then obtain;
Effectiveness–NTU Relations
• Substituting the above expression into equations and solving for, we obtain for the;
• parallel-flow heat exchanger;
• counter-flow heat exchanger;
Effectiveness–NTU Relations
• Similar expressions have been developed for a variety of heatexchangers, and representative results are summarized in tablebelow, where Cr is the heat capacity ratio Cr =Cmin/Cmax.
• Note that for Cr =0, as in a boiler, condenser, or single stream heatexchanger effectiveness is given for all flow arrangements.
• Hence, for this special case, it follows that heat exchanger behavior isindependent of flow arrangement.
Effectiveness–NTU Relations
• For the crossflow heat exchanger with both fluids unmixed, relatedequation is exact only for Cr=1.
Effectiveness–NTU Relations
Effectiveness–NTU Relations
Effectiveness–NTU Relations
Effectiveness–NTU Relations
Effectiveness–NTU Relations
