A turbulent diffusion flame adjacent to a solid fuel in a parallel airflow is studied analytically. The flow is assumed to be of boundary-layer type where the mean properties of flowfield are predicted by a low-Reynolds-number K-ε two-equation model. The chemical reaction is approximated as one-step and infinite-fast. The mean mass-fraction distribution in the boundary layer is described by probability density function (p.d.f.). Four kinds of p.d.f.s are used and they are beta, clipped Gaussian, double delta, and ten-point delta p.d.f.s respectively. The general features of each flame structure by applying corresponding p.d.f.s are quite similar. An overlap exists between fuel and oxidizer mean mass-fraction distributions. The maximal flame temperature is below the value of adiabatic one and its profile is rounded. The velocity, mixture fraction and its fluctuation, and total enthalpy are found to be almost invariant with the form of p.d.f.s. The mass fraction and temperature profiles appear nearly identical by the uses of beta and clipped Gaussian p.d.f.s. In application of double delta p.d.f., discontinuity shows up in these profiles. The modified ten-point delta p.d.f. has the maximum flame temperature due to its smallest overlap of Y¯F and ¯O among these p.d.f.s.