A mathematical analysis based on Monin-Obukhov similarity (MOS) is carried out to validate the observed behavior of H with stability parameter within the framework of commonly used linear and non-linear similarity functions. The mathematical analysis reveals that the MOS theory is able to capture the observed behavior of H with ζ in stable conditions if the linear similarity functions are incorporated. However, in the case of non-linear similarity functions, the relationship between heat flux and stability parameter appears to breakdown for sufficiently large value of ζ. In unstable conditions, H is expressed as a function of ζ and temperature gradient and the behavior is analyzed by considering vertical surface layer potential temperature gradient as (i) a constant and (ii) a power-law function of heat flux. The analysis reveals that the nature of H with ζ in unstable conditions is consistent with that obtained theoretically from MOS equations by considering the vertical temperature gradient as a power-law function of heat flux having the exponent larger than 2/3.