# Convection to Plate Heat Exchangers (single-phase) (ht.conv_plate)¶

ht.conv_plate.Nu_plate_Khan_Khan(Re, Pr, chevron_angle)[source]

Calculates Nusselt number for single-phase flow in a Chevron-style plate heat exchanger according to [1].

$Nu = \left(0.0161\frac{\beta}{\beta_{max}} + 0.1298\right) Re^{\left(0.198 \frac{\beta}{\beta_{max}} + 0.6398\right)} Pr^{0.35}$
Parameters
Refloat

Reynolds number with respect to the hydraulic diameter of the channels, [-]

Prfloat

Prandtl number calculated with bulk fluid properties, [-]

chevron_anglefloat

Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90. Many plate exchangers use two alternating patterns; use their average angle for that situation [degrees]

Returns
Nufloat

Nusselt number with respect to Dh, [-]

Notes

The viscosity correction power is recommended to be the blanket Sieder and Tate (1936) value of 0.14.

The correlation is recommended in the range of Reynolds numbers from 500 to 2500, chevron angles between 30 and 60 degrees, and Prandtl numbers between 3.5 and 6.

References

1

Khan, T. S., M. S. Khan, Ming-C. Chyu, and Z. H. Ayub. “Experimental Investigation of Single Phase Convective Heat Transfer Coefficient in a Corrugated Plate Heat Exchanger for Multiple Plate Configurations.” Applied Thermal Engineering 30, no. 8 (June 1, 2010): 1058-65. https://doi.org/10.1016/j.applthermaleng.2010.01.021.

Examples

>>> Nu_plate_Khan_Khan(Re=1000, Pr=4.5, chevron_angle=30)
38.40883639103741

ht.conv_plate.Nu_plate_Kumar(Re, Pr, chevron_angle, mu=None, mu_wall=None)[source]

Calculates Nusselt number for single-phase flow in a well-designed Chevron-style plate heat exchanger according to [1]. The data is believed to have been developed by APV International Limited, since acquired by SPX Corporation. This uses a curve fit of that data published in [2].

$Nu = C_1 Re^m Pr^{0.33}\left(\frac{\mu}{\mu_{wall}}\right)^{0.17}$

C1 and m are coefficients looked up in a table, with varying ranges of Re validity and chevron angle validity. See the source for their exact values. The wall fluid property correction is included only if the viscosity values are provided.

Parameters
Refloat

Reynolds number with respect to the hydraulic diameter of the channels, [-]

Prfloat

Prandtl number calculated with bulk fluid properties, [-]

chevron_anglefloat

Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90. Many plate exchangers use two alternating patterns; use their average angle for that situation [degrees]

mufloat, optional

Viscosity of the fluid at the bulk (inlet and outlet average) temperature, [Pa*s]

mu_wallfloat, optional

Viscosity of fluid at wall temperature, [Pa*s]

Returns
Nufloat

Nusselt number with respect to Dh, [-]

Notes

Data on graph from Re=0.1 to Re=10000, with chevron angles 30 to 65 degrees. See PlateExchanger for further clarification on the definitions.

It is believed the constants used in this correlation were curve-fit to the actual graph in [1] by the author of [2] as there is no

As the coefficients change, there are numerous small discontinuities, although the data on the graphs is continuous with sharp transitions of the slope.

The author of [1] states clearly this correlation is “applicable only to well designed Chevron PHEs”.

References

1(1,2,3)

Kumar, H. “The plate heat exchanger: construction and design.” In First U.K. National Conference on Heat Transfer: Held at the University of Leeds, 3-5 July 1984, Institute of Chemical Engineering Symposium Series, vol. 86, pp. 1275-1288. 1984.

2(1,2)

Ayub, Zahid H. “Plate Heat Exchanger Literature Survey and New Heat Transfer and Pressure Drop Correlations for Refrigerant Evaporators.” Heat Transfer Engineering 24, no. 5 (September 1, 2003): 3-16. doi:10.1080/01457630304056.

Examples

>>> Nu_plate_Kumar(Re=2000, Pr=0.7, chevron_angle=30)
47.757818892853955


With the wall-correction factor included:

>>> Nu_plate_Kumar(Re=2000, Pr=0.7, chevron_angle=30, mu=1E-3, mu_wall=8E-4)
49.604284135097544

ht.conv_plate.Nu_plate_Martin(Re, Pr, chevron_angle, variant='1999')[source]

Calculates Nusselt number for single-phase flow in a Chevron-style plate heat exchanger according to [1], also shown in [2] and [3].

$Nu = 0.122 Pr^{1/3} \left[f_d Re^2 \sin (2\phi)\right]^{0.374}$

The Darcy friction factor should be calculated with the Martin (1999) friction factor correlation, as that is what the power of 0.374 was regressed with. It can be altered to a later formulation by Martin in the VDI Heat Atlas 2E, which increases the calculated heat transfer friction slightly.

Parameters
Refloat

Reynolds number with respect to the hydraulic diameter of the channels, [-]

Prfloat

Prandtl number calculated with bulk fluid properties, [-]

chevron_anglefloat

Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90. Many plate exchangers use two alternating patterns; use their average angle for that situation [degrees]

variantstr

One of ‘1999’ or ‘VDI’; chooses between the two Martin friction factor correlations, [-]

Returns
Nufloat

Nusselt number with respect to Dh, [-]

Notes

Based on experimental data from Re from 200 - 10000 and enhancement factors calculated with chevron angles of 0 to 80 degrees. See PlateExchanger for further clarification on the definitions.

Note there is a discontinuity at Re = 2000 for the transition from laminar to turbulent flow, arising from the friction factor correlation’s transition ONLY, although the literature suggests the transition is actually smooth.

A viscosity correction power for liquid flows of (1/6) is suggested, and for gases, no correction factor.

References

1

Martin, Holger. “A Theoretical Approach to Predict the Performance of Chevron-Type Plate Heat Exchangers.” Chemical Engineering and Processing: Process Intensification 35, no. 4 (January 1, 1996): 301-10. https://doi.org/10.1016/0255-2701(95)04129-X.

2

Martin, Holger. “Economic optimization of compact heat exchangers.” EF-Conference on Compact Heat Exchangers and Enhancement Technology for the Process Industries, Banff, Canada, July 18-23, 1999, 1999. https://publikationen.bibliothek.kit.edu/1000034866.

3

Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

Examples

>>> Nu_plate_Martin(Re=2000.0, Pr=.7, chevron_angle=45.0)
30.427601053757

ht.conv_plate.Nu_plate_Muley_Manglik(Re, Pr, chevron_angle, plate_enlargement_factor)[source]

Calculates Nusselt number for single-phase flow in a Chevron-style plate heat exchanger according to [1], also shown in [2].

$Nu = [0.2668 - 0.006967(\beta) + 7.244\times 10^{-5}(\beta)^2] \times[20.7803 - 50.9372\phi + 41.1585\phi^2 - 10.1507\phi^3] \times Re^{[0.728 + 0.0543\sin[(2\pi\beta/90) + 3.7]]} Pr^{1/3}$
Parameters
Refloat

Reynolds number with respect to the hydraulic diameter of the channels, [-]

Prfloat

Prandtl number calculated with bulk fluid properties, [-]

chevron_anglefloat

Angle of the plate corrugations with respect to the vertical axis (the direction of flow if the plates were straight), between 0 and 90. Many plate exchangers use two alternating patterns; use their average angle for that situation [degrees]

plate_enlargement_factorfloat

The extra surface area multiplier as compared to a flat plate caused the corrugations, [-]

Returns
Nufloat

Nusselt number with respect to Dh, [-]

Notes

The correlation as presented in [1] suffers from a typo, with a coefficient of 10.51 instead of 10.15. Several more decimal places were published along with the corrected typo in [2]. This has a very large difference if not implemented.

The viscosity correction power is recommended to be the blanket Sieder and Tate (1936) value of 0.14.

The correlation is recommended in the range of Reynolds numbers above 1000, chevron angles between 30 and 60 degrees, and enlargement factors from 1 to 1.5. Due to its cubic nature it is not likely to give good results if the chevron angle or enlargement factors are out of those ranges.

References

1(1,2)

Muley, A., and R. M. Manglik. “Experimental Study of Turbulent Flow Heat Transfer and Pressure Drop in a Plate Heat Exchanger With Chevron Plates.” Journal of Heat Transfer 121, no. 1 (February 1, 1999): 110-17. doi:10.1115/1.2825923.

2(1,2)

Palm, Björn, and Joachim Claesson. “Plate Heat Exchangers: Calculation Methods for Single- and Two-Phase Flow (Keynote),” January 1, 2005, 103-13. https://doi.org/10.1115/ICMM2005-75092.

Examples

>>> Nu_plate_Muley_Manglik(Re=2000, Pr=.7, chevron_angle=45,
... plate_enlargement_factor=1.18)
36.49087100602062