def bartz_sigma_sanchez(T_e, T_avg, w=0.6):
    """Correction factor for the Bartz equation.

    Reference:
      [1] M. Martinez-Sanchez, "Convective Heat Transfer: Reynolds Analogy,"
        MIT 16.512 Lecture 7. https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-512-rocket-propulsion-fall-2005/lecture-notes/lecture_7.pdf

    Arguments:
        T_e (scalar): Static temperature of the fluid external to the boundary layer
            [units: kelvin].
        T_avg (scalar): Average temperature through the boundary layer, used to adjust
            the effective density and viscosity of the boundary layer. Martinez-Sanchez
            suggests :math:`T_{avg} = (T_e - T_w)/2` for flow around Mach 1.
        w (scalar): Viscosity is assumed to vary as :math:`T^w`. Martinez-Sanchez
            suggests :math:`w = 0.6` [units: dimensionless].

    Returns:
        scalar: The Bartz equation correction factor :math:`\sigma`.
    """
    return (T_e / T_avg)**(0.8 - 0.2 * w)