Steady state convective heat transfer on either side of a heat exchanger (hot or cold side) can be expressed with following figure and equation,

The steady state convective heat transfer can be mathematically captured by following equation,

Q = h×A×(T_{1} - T_{2})

where Q : heat transfer rate in Joules/hr

A : Effective heat transfer area of the solid surface in m^{2}

T_{1} & T_{2} : Steady state temperatures of solid and fluid bodies respectively in ^{0}C

h : Heat transfer coefficient in Joule/(^{0}C×m^{2})

For heat transfer equipments, separate 'heat transfer coefficients' (h) can be defined for the hot and cold media of the equipment. These heat transfer coefficients can be used to describe the heat transfer on each side of the heat exchanger. In addition an 'overall heat transfer coefficient' (U) can be defined which describes the overall heat transfer occurring in the exchanger.

For example in shell and tube exchangers, heat transfer coefficients on shell side and tube side describe the heat transfer as,

Q = h_{S}×A_{S}×(T_{S}-T_{SW}) - shell side heat transfer

Q = h_{T}×A_{T}×(T_{TW}-T_{T}) - tube side heat transfer

where Q : heat transfer rate in Joules/hr

A_{S} & A_{T} : Effective heat transfer areas on shell side and tube side respectively

T_{S} and T_{SW} : Steady state temperatures on shell side fluid and wall surface on shell side in ^{0}C

T_{T} and T_{TW} : Steady state temperatures on tube side fluid and wall surface on tube side in ^{0}C

h_{S} : Shell side heat transfer coefficient in Joule/(^{0}C×m^{2})

h_{T} : Tube side heat transfer coefficient in Joule/(^{0}C×m^{2})

For steady state heat transfer in an exchanger, the heat coming to the tube wall trough shell side is equal to the heat transferred through the tube wall by conduction, and is equal to the heat going out to the tube side. The conductive heat transfer rate through the tube wall is given by,

where N is the tube length and 'r' stands for tube radius. The subscripts 1 and 2 stand for inner and outer tube wall respectively. Tube metal conductivity is expressed as 'k'.

The overall heat transfer in the heat exchanger then may be expressed as,

Q = U×A×(T_{S}-T_{T}) - overall heat transfer rate

U : overall heat transfer coefficient

A : effective overall heat transfer area

Usually for heat exchanger design, the product UA is expressed as a single entity. The overall heat transfer coefficient depends on several factors affecting the individual heat transfer coefficients on both sides (shell side heat transfer coefficient and tube side heat transfer coefficient), as well as conduction in the tube wall.

## Related reading

- Surface area available for heat transfer is quite an important determinant of the overall heat transfer rate. Understand the importance of this factor with a small thought experiment.