# Heat Exchangers | Gate

covered topics

- Logarithmic Mean Temperature Difference
- Number of transfer units

**1. Heat exchanger:** heat exchanger is a device which is designed for effective heat transfer between two fluids. the flow of heat transfer is from high temperature to low-temperature fluid.

Ex. Boilers, condenser, etc.

**2. Logarithmic mean temperature difference (LMTD):** the temperature difference which, if constant would give the same rate of heat transfer as actually occurs under variable conditions of temperature difference.

heat transfer by the heat exchanger

**Q = UAdTm**

# LMTD in parallel flow heat exchanger

**ΔT1 = Th1-Tc1**

**ΔT2 = Th2-Tc2**

# LMTD in counter flow heat exchanger

**ΔT1 = Th1-Tc2**

**ΔT2 = Th2– Tc1**

# LMTD

**ΔTm = ΔT1-ΔT2 / ln(ΔT1/ΔT2)****Q (heat transfer) = UAΔTm**

**3. Heat capacity ratio:** it is denoted by C, and defined by the ratio of minimum heat capacity rate to maximum heat capacity rate of two fluids.

**C= Cmin/ Cmax**

**4. Effectiveness:** it is defined as the ratio of actual heat transfer rate to the maximum possible heat transfer rate of any heat exchanger.

ε = a**ctual heat transfer/ maximum possible heat transfer**** **

# if (mCp)hot > (mCp)cold,

** ε = (Tc1-Tc1)/ (Th1-Tc1)**

# if (mCp)hot < (mCp)cold,

** ε = ****(Th1-Th2)/(Th1-Tc1)**

**5. Number of transfer units(NTU):** NTU is the measure of heat transfer size of a heat exchanger.

**NTU = UA/Cmin**

# effectiveness from NTU method for parallel flow

** ε = 1 – e^{-NTU(1+C) }/ (1 + C)**

# effectiveness from NTU method for counter flow

**ε = 1 – e^{-(1-C)NTU }/ 1 + Ce^{-(1-C)NTU}**

## Questions:

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