S_SPHERE_TO_PLANE

Computes the conduction shape factor for an isothermal sphere near an isothermal plane. The result is used in simplified conduction models for buried or embedded spherical geometries.

Heat transfer can then be estimated with:

Q = Sk(T_1 - T_2)

Excel Usage

=S_SPHERE_TO_PLANE(D, Z)

D (float, required): Sphere diameter (m).
Z (float, required): Distance to plane (m).

Returns (float): Shape factor (m).

Example 1: Example sphere to plane

Inputs:

D	Z
1	100

Excel formula:

=S_SPHERE_TO_PLANE(1, 100)

Expected output:

6.29893

Example 2: Closer plane distance

Inputs:

D	Z
0.4	4

Excel formula:

=S_SPHERE_TO_PLANE(0.4, 4)

Expected output:

2.57772

Example 3: Small sphere near plane

Inputs:

D	Z
0.2	2

Excel formula:

=S_SPHERE_TO_PLANE(0.2, 2)

Expected output:

1.28886

Example 4: Moderate geometry values

Inputs:

D	Z
0.6	8

Excel formula:

=S_SPHERE_TO_PLANE(0.6, 8)

Expected output:

3.84195

Python Code

Show Code

from ht.conduction import S_isothermal_sphere_to_plane as ht_S_isothermal_sphere_to_plane

def S_sphere_to_plane(D, Z):
    """
    Compute the shape factor for a sphere near a plane.

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

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

    Args:
        D (float): Sphere diameter (m).
        Z (float): Distance to plane (m).

    Returns:
        float: Shape factor (m).
    """
    try:
        return ht_S_isothermal_sphere_to_plane(D=D, Z=Z)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

D *

Sphere diameter (m).

Z *

Distance to plane (m).