## Heat Exchanger Analysis

Heat Exchanger Analysis based on Effectiveness (ε) – NTU method is done when inlet temperatures are known and outlet temperatures are to be determined.

#### Obtain Process Parameters

Get process stream mass flowrate (M), specific heat (Cp) and inlet temperature (T). Obtain the heat transfer area (A) and overall heat transfer coefficient (U) for the given dimensions of heat exchanger.

Calculate heat capacities and obtain the minimum heat capacity.

`C`

_{H}= M_{H}* Cp_{H}`C`

_{C}= M_{C}* Cp_{C}`C`

_{Min}= Minimum (C_{H}, C_{C})`C`

_{R}= C_{Min}/ C_{Max}

where M_{H}, M_{C} are hot and cold fluid mass flowrate; Cp_{H}, Cp_{C} are hot and cold fluid specific heat.

#### Calculate NTU and Q_{Max}

Number of transfer units ( NTU ) is calculated using following equation :

`NTU = U.A/ C`_{Min}

Maximum heat transfer rate ( Q_{Max} ) is calculated using following equation :

`Q`_{Max} = C_{Min}.(T_{Hot In} - T_{Cold In})

#### Determine Effectiveness

Based on NTU and C_{R} (Ratio of heat capacities) determine heat exchanger effectiveness (ε) from Effectiveness – NTU curves available in literature.

ε – NTU Curve for Cross Flow exchanger Both stream unmixed

#### Calculate Outlet Temperature

Heat exchanger duty is calculated as:

`Q = ε * Q `_{Max}

Outlet temperature are estimated as following :

`T`

_{Hot Out}= T_{Hot In}- Q /( M_{H}.Cp_{H})`T`

_{Cold Out}= T_{Cold In}+ Q /( M_{C}.Cp_{C})

**Example**

*Hot exhaust gases 1.5 kg/s, enter a finned-tube, cross-flow heat exchanger at 250°C and is used to heat pressurized water at a flow rate of 1 kg/s available at 35°C. Exhaust gas specific heat is 1000 J/kg.K and water specific heat is 4197 J/kg.K. Overall heat transfer coefficient is 100 W/m².K and area is 40 m². What is rate of heat transfer by exchanger and gas and water outlet temperatures ?*

**Calculate Heat Capacities**

`C`

_{H}= 1.5 kg/s * 1 kJ/kg.°K`= 1.5 kW/ °K`

`C`

_{C}= 1.0 kg/s * 4.197 kJ/kg.°K`= 4.197 kW/ °K`

`C`

_{R}= 0.36

**Determine NTU and Q _{Max}**

`NTU = 2.67`

`Q`

_{Max}= 322.5 kW

**Determine Effectiveness**

Based on ε – NTU curves for cross flow heat exchanger, determine ε

`ε = 0.845`

**Calculate Outlet Temperature**

Heat duty is calculated as following –

`Q = 272.36 kW`

`T`

_{Hot Out}= 68.43 ° C`T`

_{Cold Out}= 99.89 ° C

### Spreadsheet

All above calculation for some common exchanger geometries have been provided in below spreadsheet.