Conv Plate

Overview

Plate heat exchangers are compact thermal systems where corrugated plates create large surface area and strong mixing for efficient energy exchange. In this category, single-phase convection in chevron plate channels is modeled with empirical correlations for both heat transfer and pressure drop. These tools matter because exchanger sizing, pump power, and thermal duty are coupled in process design, HVAC, refrigeration, and energy systems. Using consistent correlations helps engineers compare designs and operating points with fewer trial-and-error iterations.

Core Concepts: The shared foundation is the relationship among Reynolds number (Re), Prandtl number (Pr), plate chevron angle (\beta), and dimensionless response metrics. Heat-transfer performance is represented by the Nusselt number (Nu), while hydraulic penalty is represented by the Darcy friction factor (f). In practice, these quantities are evaluated together because increased turbulence often improves Nu while also increasing f and pressure drop. A typical design tradeoff can be summarized as maximizing thermal effectiveness for a given pumping constraint.

Implementation: These functions are implemented with the Python ht library, specifically the ht.conv_plate module for single-phase plate-exchanger convection. The library provides engineering correlations from published literature in a consistent API, making it suitable for screening calculations, sensitivity analysis, and spreadsheet integration workflows.

For hydraulic resistance, FRIC_PLATE_MARTIN99 and FRIC_PLATE_MARTINV estimate Darcy friction factor for chevron channels using Martin-style formulations (1999 and VDI variant). These functions are used when estimating channel pressure drop and required pumping power before committing to geometry or flow targets. The two variants are closely related but use different coefficient sets, so they are useful for uncertainty checks and standard-specific comparisons. Their outputs also feed directly into Martin-based heat-transfer prediction.

For direct heat-transfer estimation with broadly used empirical forms, NU_PLATE_KHAN_KHAN and NU_PLATE_KUMAR compute Nu from Re, Pr, and chevron angle. NU_PLATE_KHAN_KHAN is commonly applied in its reported validity window for moderate Re, Pr, and angle ranges, while NU_PLATE_KUMAR supports optional viscosity wall correction via (\mu/\mu_w)^{0.17}. These tools are practical for fast rating calculations and for comparing how fluid properties and corrugation angle influence convective performance.

For coupled or geometry-sensitive predictions, NU_PLATE_MARTIN and NU_PLATE_MULEYMANG provide two complementary approaches. NU_PLATE_MARTIN ties heat transfer to a friction-factor-driven term and allows selecting the Martin friction variant, which is valuable when thermal and hydraulic models need to stay internally consistent. NU_PLATE_MULEYMANG adds explicit dependence on plate enlargement factor, making it useful when corrugation geometry and effective area amplification are key design levers. Together, these methods support practical correlation selection across early sizing, benchmarking, and detailed exchanger optimization.

FRIC_PLATE_MARTIN99

This function computes the Darcy friction factor for single-phase flow in chevron-style plate heat exchangers using the Martin (1999) correlation. The model combines angle-dependent terms with Reynolds-number-dependent sub-correlations for laminar and turbulent regimes.

The correlation is commonly represented in reciprocal square-root form:

\frac{1}{\sqrt{f}} = \frac{\cos\phi}{\sqrt{a(\phi) + f_0/\cos\phi}} + \frac{1-\cos\phi}{\sqrt{3.8f_1}}

where f_0 and f_1 are piecewise functions of Reynolds number and \phi is the chevron angle. This function is useful for estimating pressure-drop-related flow resistance in compact plate heat exchanger channels.

Excel Usage

=FRIC_PLATE_MARTIN99(Re, chevron_angle)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).

Returns (float): Darcy friction factor, or error message if invalid.

Example 1: Example from documentation

Inputs:

Re chevron_angle
20000 45

Excel formula:

=FRIC_PLATE_MARTIN99(20000, 45)

Expected output:

0.781892

Example 2: Laminar Reynolds number range

Inputs:

Re chevron_angle
1000 30

Excel formula:

=FRIC_PLATE_MARTIN99(1000, 30)

Expected output:

0.45632

Example 3: Turbulent Reynolds number range

Inputs:

Re chevron_angle
5000 60

Excel formula:

=FRIC_PLATE_MARTIN99(5000, 60)

Expected output:

1.83307

Example 4: Very low Reynolds number

Inputs:

Re chevron_angle
200 15

Excel formula:

=FRIC_PLATE_MARTIN99(200, 15)

Expected output:

0.501842

Python Code

Show Code 
from ht.conv_plate import friction_plate_Martin_1999 as ht_friction_plate_Martin_1999

def fric_plate_martin99(Re, chevron_angle):
    """
    Calculate Darcy friction factor for chevron plate exchangers (Martin 1999).

    See: https://ht.readthedocs.io/en/latest/ht.conv_plate.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).

    Returns:
        float: Darcy friction factor, or error message if invalid.
    """
    try:
        result = ht_friction_plate_Martin_1999(Re=Re, chevron_angle=chevron_angle)
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Plate chevron angle relative to flow direction (degrees).

FRIC_PLATE_MARTINV

This function computes the Darcy friction factor for single-phase flow in chevron-style plate heat exchangers using the VDI Heat Atlas variant of Martin’s formulation. It uses the same overall structure as the Martin model but with revised coefficients to predict somewhat higher friction in many operating ranges.

The formulation is written in terms of reciprocal square root friction factor:

\frac{1}{\sqrt{f}} = \frac{\cos\phi}{\sqrt{b(\phi) + f_0/\cos\phi}} + \frac{1-\cos\phi}{\sqrt{3.8f_1}}

with f_0 and f_1 defined piecewise by Reynolds number and \phi as the chevron angle. This is used to characterize hydraulic resistance and pressure-drop behavior in plate channels.

Excel Usage

=FRIC_PLATE_MARTINV(Re, chevron_angle)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).

Returns (float): Darcy friction factor, or error message if invalid.

Example 1: Example from documentation

Inputs:

Re chevron_angle
20000 45

Excel formula:

=FRIC_PLATE_MARTINV(20000, 45)

Expected output:

0.781589

Example 2: Laminar Reynolds number range

Inputs:

Re chevron_angle
1000 30

Excel formula:

=FRIC_PLATE_MARTINV(1000, 30)

Expected output:

0.456322

Example 3: Turbulent Reynolds number range

Inputs:

Re chevron_angle
5000 60

Excel formula:

=FRIC_PLATE_MARTINV(5000, 60)

Expected output:

1.83215

Example 4: Very low Reynolds number

Inputs:

Re chevron_angle
200 15

Excel formula:

=FRIC_PLATE_MARTINV(200, 15)

Expected output:

0.501844

Python Code

Show Code 
from ht.conv_plate import friction_plate_Martin_VDI as ht_friction_plate_Martin_VDI

def fric_plate_martinV(Re, chevron_angle):
    """
    Calculate Darcy friction factor for chevron plate exchangers (VDI Heat Atlas variant).

    See: https://ht.readthedocs.io/en/latest/ht.conv_plate.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).

    Returns:
        float: Darcy friction factor, or error message if invalid.
    """
    try:
        result = ht_friction_plate_Martin_VDI(Re=Re, chevron_angle=chevron_angle)
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Plate chevron angle relative to flow direction (degrees).

NU_PLATE_KHAN_KHAN

This function estimates the Nusselt number for single-phase convection in chevron-style plate heat exchangers using the Khan and Khan correlation. It relates convective heat transfer to Reynolds number, Prandtl number, and chevron angle.

The correlation form is:

Nu = \left(c_1\frac{\beta}{\beta_{max}} + c_2\right)Re^{\left(c_3\frac{\beta}{\beta_{max}} + c_4\right)}Pr^{0.35}

where \beta is chevron angle and the constants are empirical. This function is typically applied within the reported validity region for Reynolds number, Prandtl number, and plate angles.

Excel Usage

=NU_PLATE_KHAN_KHAN(Re, Pr, chevron_angle)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • Pr (float, required): Prandtl number calculated with bulk fluid properties (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).

Returns (float): Nusselt number with respect to hydraulic diameter, or error message if invalid.

Example 1: Example from documentation

Inputs:

Re Pr chevron_angle
1000 4.5 30

Excel formula:

=NU_PLATE_KHAN_KHAN(1000, 4.5, 30)

Expected output:

38.4088

Example 2: Mid-range Reynolds and Prandtl numbers

Inputs:

Re Pr chevron_angle
1500 3.5 45

Excel formula:

=NU_PLATE_KHAN_KHAN(1500, 3.5, 45)

Expected output:

70.1524

Example 3: Higher chevron angle with larger Reynolds number

Inputs:

Re Pr chevron_angle
2000 5 60

Excel formula:

=NU_PLATE_KHAN_KHAN(2000, 5, 60)

Expected output:

149.382

Example 4: Lower Reynolds number within recommended range

Inputs:

Re Pr chevron_angle
500 4 40

Excel formula:

=NU_PLATE_KHAN_KHAN(500, 4, 40)

Expected output:

27.6417

Python Code

Show Code 
from ht.conv_plate import Nu_plate_Khan_Khan as ht_Nu_plate_Khan_Khan

def Nu_plate_Khan_Khan(Re, Pr, chevron_angle):
    """
    Calculate Nusselt number for single-phase flow in a chevron-style plate heat exchanger (Khan and Khan).

    See: https://ht.readthedocs.io/en/latest/ht.conv_plate.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        Pr (float): Prandtl number calculated with bulk fluid properties (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).

    Returns:
        float: Nusselt number with respect to hydraulic diameter, or error message if invalid.
    """
    try:
        result = ht_Nu_plate_Khan_Khan(Re=Re, Pr=Pr, chevron_angle=chevron_angle)
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Prandtl number calculated with bulk fluid properties (-).
Plate chevron angle relative to flow direction (degrees).

NU_PLATE_KUMAR

This function computes Nusselt number for single-phase flow in well-designed chevron plate heat exchangers using the Kumar correlation. The model uses empirical coefficients selected by Reynolds-number and angle ranges, with an optional viscosity wall correction.

A common representation is:

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

where the viscosity ratio term is applied when both bulk and wall viscosities are supplied. The result is a hydraulic-diameter-based Nusselt number for heat transfer estimation.

Excel Usage

=NU_PLATE_KUMAR(Re, Pr, chevron_angle, mu, mu_wall)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • Pr (float, required): Prandtl number calculated with bulk fluid properties (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).
  • mu (float, optional, default: null): Viscosity at bulk temperature (Pa*s).
  • mu_wall (float, optional, default: null): Viscosity at wall temperature (Pa*s).

Returns (float): Nusselt number with respect to hydraulic diameter, or error message if invalid.

Example 1: Example without wall correction

Inputs:

Re Pr chevron_angle
2000 0.7 30

Excel formula:

=NU_PLATE_KUMAR(2000, 0.7, 30)

Expected output:

47.7578

Example 2: Example with wall correction

Inputs:

Re Pr chevron_angle mu mu_wall
2000 0.7 30 0.001 0.0008

Excel formula:

=NU_PLATE_KUMAR(2000, 0.7, 30, 0.001, 0.0008)

Expected output:

49.6043

Example 3: Low Reynolds number case

Inputs:

Re Pr chevron_angle
300 2 45

Excel formula:

=NU_PLATE_KUMAR(300, 2, 45)

Expected output:

16.5498

Example 4: Higher Reynolds number case

Inputs:

Re Pr chevron_angle
5000 0.9 60

Excel formula:

=NU_PLATE_KUMAR(5000, 0.9, 60)

Expected output:

41.5623

Python Code

Show Code 
from ht.conv_plate import Nu_plate_Kumar as ht_Nu_plate_Kumar

def Nu_plate_Kumar(Re, Pr, chevron_angle, mu=None, mu_wall=None):
    """
    Calculate Nusselt number for a well-designed chevron plate heat exchanger (Kumar correlation).

    See: https://ht.readthedocs.io/en/latest/ht.conv_plate.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        Pr (float): Prandtl number calculated with bulk fluid properties (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).
        mu (float, optional): Viscosity at bulk temperature (Pa*s). Default is None.
        mu_wall (float, optional): Viscosity at wall temperature (Pa*s). Default is None.

    Returns:
        float: Nusselt number with respect to hydraulic diameter, or error message if invalid.
    """
    try:
        result = ht_Nu_plate_Kumar(
            Re=Re,
            Pr=Pr,
            chevron_angle=chevron_angle,
            mu=mu,
            mu_wall=mu_wall,
        )
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Prandtl number calculated with bulk fluid properties (-).
Plate chevron angle relative to flow direction (degrees).
Viscosity at bulk temperature (Pa*s).
Viscosity at wall temperature (Pa*s).

NU_PLATE_MARTIN

This function calculates the Nusselt number for single-phase flow in chevron-style plate heat exchangers using the Martin correlation. It combines Reynolds and Prandtl effects with a friction-factor-based term and supports either the 1999 or VDI friction variant.

The Martin heat transfer form is:

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

where f_d is the Darcy friction factor from the selected variant and \phi is the chevron angle. This is used for compact exchanger thermal performance estimation.

Excel Usage

=NU_PLATE_MARTIN(Re, Pr, chevron_angle, martin_variant)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • Pr (float, required): Prandtl number calculated with bulk fluid properties (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).
  • martin_variant (str, optional, default: “1999”): Friction factor correlation variant (-).

Returns (float): Nusselt number with respect to hydraulic diameter, or error message if invalid.

Example 1: Example with default variant

Inputs:

Re Pr chevron_angle
2000 0.7 45

Excel formula:

=NU_PLATE_MARTIN(2000, 0.7, 45)

Expected output:

30.4276

Example 2: VDI variant selection

Inputs:

Re Pr chevron_angle martin_variant
2000 0.7 45 VDI

Excel formula:

=NU_PLATE_MARTIN(2000, 0.7, 45, "VDI")

Expected output:

30.4187

Example 3: Lower Reynolds number case

Inputs:

Re Pr chevron_angle
500 2.5 30

Excel formula:

=NU_PLATE_MARTIN(500, 2.5, 30)

Expected output:

13.1012

Example 4: Higher Reynolds number with VDI variant

Inputs:

Re Pr chevron_angle martin_variant
8000 0.7 60 VDI

Excel formula:

=NU_PLATE_MARTIN(8000, 0.7, 60, "VDI")

Expected output:

105.462

Python Code

Show Code 
from ht.conv_plate import Nu_plate_Martin as ht_Nu_plate_Martin

def Nu_plate_Martin(Re, Pr, chevron_angle, martin_variant='1999'):
    """
    Calculate Nusselt number for chevron plate exchangers using the Martin correlation.

    See: https://ht.readthedocs.io/en/latest/ht.conv_plate.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        Pr (float): Prandtl number calculated with bulk fluid properties (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).
        martin_variant (str, optional): Friction factor correlation variant (-). Valid options: Martin 1999, VDI. Default is '1999'.

    Returns:
        float: Nusselt number with respect to hydraulic diameter, or error message if invalid.
    """
    try:
        result = ht_Nu_plate_Martin(
            Re=Re,
            Pr=Pr,
            chevron_angle=chevron_angle,
            variant=martin_variant,
        )
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Prandtl number calculated with bulk fluid properties (-).
Plate chevron angle relative to flow direction (degrees).
Friction factor correlation variant (-).

NU_PLATE_MULEYMANG

This function estimates the Nusselt number for single-phase flow in chevron-style plate heat exchangers using the Muley-Manglik correlation. It accounts for Reynolds number, Prandtl number, chevron angle, and plate enlargement factor.

The correlation uses multiplicative empirical polynomials and a Reynolds exponent term:

Nu = A(\beta)\,B(\phi_e)\,Re^{n(\beta)}Pr^{1/3}

where A(\beta) and n(\beta) depend on chevron angle and B(\phi_e) depends on enlargement factor. This gives a hydraulic-diameter-based convection estimate for corrugated plate geometries.

Excel Usage

=NU_PLATE_MULEYMANG(Re, Pr, chevron_angle, plate_enlargement_factor)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • Pr (float, required): Prandtl number calculated with bulk fluid properties (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).
  • plate_enlargement_factor (float, required): Surface area enlargement factor due to corrugations (-).

Returns (float): Nusselt number with respect to hydraulic diameter, or error message if invalid.

Example 1: Example from documentation

Inputs:

Re Pr chevron_angle plate_enlargement_factor
2000 0.7 45 1.18

Excel formula:

=NU_PLATE_MULEYMANG(2000, 0.7, 45, 1.18)

Expected output:

36.4909

Example 2: Higher Reynolds number with larger enlargement

Inputs:

Re Pr chevron_angle plate_enlargement_factor
5000 0.7 60 1.3

Excel formula:

=NU_PLATE_MULEYMANG(5000, 0.7, 60, 1.3)

Expected output:

138.478

Example 3: Lower chevron angle case

Inputs:

Re Pr chevron_angle plate_enlargement_factor
1500 1.2 30 1.1

Excel formula:

=NU_PLATE_MULEYMANG(1500, 1.2, 30, 1.1)

Expected output:

23.1601

Example 4: Mid-range inputs

Inputs:

Re Pr chevron_angle plate_enlargement_factor
3000 2 45 1.4

Excel formula:

=NU_PLATE_MULEYMANG(3000, 2, 45, 1.4)

Expected output:

123.19

Python Code

Show Code 
from ht.conv_plate import Nu_plate_Muley_Manglik as ht_Nu_plate_Muley_Manglik

def Nu_plate_MuleyMang(Re, Pr, chevron_angle, plate_enlargement_factor):
    """
    Calculate Nusselt number for chevron plate exchangers using the Muley-Manglik correlation.

    See: https://ht.readthedocs.io/en/latest/ht.conv_plate.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        Pr (float): Prandtl number calculated with bulk fluid properties (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).
        plate_enlargement_factor (float): Surface area enlargement factor due to corrugations (-).

    Returns:
        float: Nusselt number with respect to hydraulic diameter, or error message if invalid.
    """
    try:
        result = ht_Nu_plate_Muley_Manglik(
            Re=Re,
            Pr=Pr,
            chevron_angle=chevron_angle,
            plate_enlargement_factor=plate_enlargement_factor,
        )
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Prandtl number calculated with bulk fluid properties (-).
Plate chevron angle relative to flow direction (degrees).
Surface area enlargement factor due to corrugations (-).