polykin.transport.hmt

U_plane_wall

U_plane_wall(
    h1: float,
    h2: float,
    L: float,
    k: float,
    Rf1: float = 0.0,
    Rf2: float = 0.0,
) -> float

Calculate the overall heat transfer coefficient through a plane wall with convection on both sides.

Under steady-state conditions, the overall heat transfer coefficient is given by the following expression:

\[ U = \left( \frac{1}{h_1} + \frac{1}{h_2} + \frac{L}{k} + R_{f,1} + R_{f,2} \right)^{-1} \]

where \(h_i\) and \(R_{f,i}\) denote, respectively, the heat transfer coefficient and fouling factor at surface \(i\), \(L\) is the wall thickness, and \(k\) is the wall thermal conductivity.

PARAMETER	DESCRIPTION
h1	Heat transfer coefficient at surface 1 (W/(m²·K)). TYPE: float
h2	Heat transfer coefficient at surface 2 (W/(m²·K)). TYPE: float
L	Wall thickness (m). TYPE: float
k	Wall thermal conductivity (W/(m·K)). TYPE: float
Rf1	Fouling factor at surface 1 ((m²·K)/W). TYPE: float DEFAULT: 0.0
Rf2	Fouling factor at surface 2 ((m²·K)/W). TYPE: float DEFAULT: 0.0

RETURNS	DESCRIPTION
float	Overall heat transfer coefficient (W/(m²·K)).

See also

• U_cylindrical_wall: related method for a cylindrical wall.

Examples:

Calculate the overall heat transfer coefficient for a 10 mm-thick plane carbon steel wall subjected to convection on both sides, with heat transfer coefficients of 1000 and 2000 W/(m²·K). Neglect fouling effects.

>>> from polykin.transport import U_plane_wall
>>> h1 = 1e3  # W/(m²·K)
>>> h2 = 2e3  # W/(m²·K)
>>> k = 6e2   # W/(m·K)
>>> L = 10e-3 # m
>>> U = U_plane_wall(h1, h2, L, k)
>>> print(f"U={U:.1e} W/(m²·K)")
U=6.6e+02 W/(m²·K)

Source code in src/polykin/transport/hmt.py

def U_plane_wall(h1: float,
                 h2: float,
                 L: float,
                 k: float,
                 Rf1: float = 0.0,
                 Rf2: float = 0.0) -> float:
    r"""Calculate the overall heat transfer coefficient through a plane wall
    with convection on both sides.

    Under steady-state conditions, the overall heat transfer coefficient is
    given by the following expression:

    $$ U = \left( \frac{1}{h_1} + \frac{1}{h_2} + \frac{L}{k} + R_{f,1} + R_{f,2} \right)^{-1} $$

    where $h_i$ and $R_{f,i}$ denote, respectively, the heat transfer coefficient
    and fouling factor at surface $i$, $L$ is the wall thickness, and $k$ is the
    wall thermal conductivity.

    Parameters
    ----------
    h1 : float
        Heat transfer coefficient at surface 1 (W/(m²·K)).
    h2 : float
        Heat transfer coefficient at surface 2 (W/(m²·K)).
    L : float
        Wall thickness (m).
    k : float
        Wall thermal conductivity (W/(m·K)).
    Rf1 : float
        Fouling factor at surface 1 ((m²·K)/W).
    Rf2 : float
        Fouling factor at surface 2 ((m²·K)/W).

    Returns
    -------
    float
        Overall heat transfer coefficient (W/(m²·K)).

    See also
    --------
    - [`U_cylindrical_wall`](U_cylindrical_wall.md): related method for a
      cylindrical wall.

    Examples
    --------
    Calculate the overall heat transfer coefficient for a 10 mm-thick plane
    carbon steel wall subjected to convection on both sides, with heat transfer
    coefficients of 1000 and 2000 W/(m²·K). Neglect fouling effects.
    >>> from polykin.transport import U_plane_wall
    >>> h1 = 1e3  # W/(m²·K)
    >>> h2 = 2e3  # W/(m²·K)
    >>> k = 6e2   # W/(m·K)
    >>> L = 10e-3 # m
    >>> U = U_plane_wall(h1, h2, L, k)
    >>> print(f"U={U:.1e} W/(m²·K)")
    U=6.6e+02 W/(m²·K)
    """
    return 1/(1/h1 + 1/h2 + L/k + Rf1 + Rf2)