Q_RAD

This function computes net radiative heat flux between a surface and its surroundings using emissivity and absolute temperatures. It applies the Stefan-Boltzmann relation and supports back-radiation from a surrounding temperature.

The governing expression is:

q = \epsilon \sigma \left(T_1^4 - T_2^4\right)

where \epsilon is emissivity, \sigma is the Stefan-Boltzmann constant, T_1 is surface temperature, and T_2 is surrounding temperature.

Excel Usage

=Q_RAD(emissivity, T, T_two)

emissivity (float, required): Surface emissivity fraction (-).
T (float, required): Surface temperature (K).
T_two (float, optional, default: 0): Surroundings temperature (K).

Returns (float): Radiant heat flux in W/m^2, or an error message if invalid.

Example 1: Blackbody radiation at 400 K

Inputs:

emissivity	T
1	400

Excel formula:

=Q_RAD(1, 400)

Expected output:

1451.61

Example 2: Gray surface with 305 K surroundings

Inputs:

emissivity	T	T_two
0.85	400	305

Excel formula:

=Q_RAD(0.85, 400, 305)

Expected output:

816.782

Example 3: Moderate temperature difference

Inputs:

emissivity	T	T_two
0.5	350	250

Excel formula:

=Q_RAD(0.5, 350, 250)

Expected output:

314.705

Example 4: High temperature surface

Inputs:

emissivity	T	T_two
0.9	1200	800

Excel formula:

=Q_RAD(0.9, 1200, 800)

Expected output:

84919.4

Python Code

Show Code

from ht.radiation import q_rad as ht_q_rad

def q_rad(emissivity, T, T_two=0):
    """
    Compute radiant heat flux between a surface and surroundings.

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

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

    Args:
        emissivity (float): Surface emissivity fraction (-).
        T (float): Surface temperature (K).
        T_two (float, optional): Surroundings temperature (K). Default is 0.

    Returns:
        float: Radiant heat flux in W/m^2, or an error message if invalid.
    """
    try:
        emissivity_val = float(emissivity)
        T_val = float(T)
        T_two_val = float(T_two)
        if emissivity_val < 0 or emissivity_val > 1:
            return "Error: emissivity must be between 0 and 1"
        if T_val < 0 or T_two_val < 0:
            return "Error: temperatures must be non-negative"
        return ht_q_rad(emissivity=emissivity_val, T=T_val, T2=T_two_val)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

emissivity *

Surface emissivity fraction (-).

T *

Surface temperature (K).

T_two

Surroundings temperature (K).