# Counterflow, crossflow and cocurrent flow heat transfer in heat exchangers: analytical solution based on transfer units

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## Abstract

By means of analysis equations for heat transfer performance based on number of heat transfer units were found, that allow to solve in a simple way single-pass and multipass heat exchanger problems when there are counterflow, crossflow and cocurrent modes of flow in any combination. There is no need to use external information such as the effectiveness concept or the correction factor *F*. The analysis gives new results which are at variance with traditional heat exchanger analysis when crossflow or cocurrent flow is involved.

## Keywords

Heat Transfer Heat Exchanger Transfer Unit Heat Transfer Area Cocurrent Flow## List of symbols

*A*Overall heat transfer area

*A*_{cc}Heat transfer area where the mode of flow is counterflow

*A*_{cf}Heat transfer area where the mode of flow is crossflow

*A*_{coc}Heat transfer area where the mode of flow is cocurrent

*Cp*_{c}Specific heat of cold stream, energy/mass–temperature difference

*Cp*_{h}Specific heat of hot stream, energy/mass–temperature difference

*F*Correction factor for the counterflow logarithmic mean temperature difference

*m*_{c}Main cold stream, mass flow into the heat echanger (mass/time)

*m*_{h}Main hot stream. mass flow into the heat echanger (mass/time)

*m*_{c}Main cold stream, mass flow per unit area, mass/area–time

*m*_{h}Main hot stream, mass flow per unit area, mass/area–time

- mscc
_{c} Cold stream, mass flow in a counterflow section (mass/time)

- mscc
_{h} Hot stream, mass flow in a counterflow section (mass/time)

- mscf
_{c} Cold stream, mass flow in a crossflow section (mass/time)

- mscf
_{h} Hot stream, mass flow in a crossflow section (mass/time)

- mscoc
_{c} Cold stream, mass flow in a cocurrent flow section (mass/time)

- mscoc
_{h} Hot stream, mass flow in a cocurrent flow section (mass/time)

- NHTUA
Number of heat transfer units available

- NHTUR
Number of heat transfer units required

*Q*Heat load, energy/time

*T*_{c}Cold stream temperature in the exchanger, average over the axis

*x*at a point in the axis*y*for crossflow. For counterflow and cocurrent flow average in the axis transversal to flow at a point in the axis parallel to flow*T*_{c0}Average inlet cold stream temperature

*T*_{c1}Average outlet cold stream temperature

*T*_{c loc}Local cold stream temperature

*T*_{h}Hot stream temperature in the exchanger, average over the axis

*x*at a point in the axis*y*for crossflow. For counterflow and cocurrent flow average in the axis transversal to flow at a point in the axis parallel to flow*T*_{h0}Average outlet hot stream temperature

*T*_{h1}Average inlet hot stream temperature

*T*_{h loc}Local hot stream temperature

*U*_{a}Volumetric overall heat transfer coefficient, energy/time–volume–temperature difference

*U*Overall heat transfer coefficient, energy/time–area–temperature difference

*U*_{cc}Overall heat transfer coefficient in a counterflow section

*U*_{cf}Overall heat transfer coefficient in a crossflow section

*U*_{coc}Overall heat transfer coefficient in a cocurrent flow section

*x*Dimension in the direction of

*m*_{c}flow in crossflow*y*Dimension in the direction of

*m*_{h}flow in crossflow*z*Dimension of the active volume, perpendicular to

*y*and*x*- Δ
*x* Length of stream

*m*_{c}flow path in a cross-flow stage- Δ
*y* Length of stream

*m*_{h}flow path in a cross-flow stage or in counter or cocurrent flow

## References

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