As seen from the ammonium chloride experiment (Chen & Chen [1], Roberts & Loper [11], the interface near chimneys has an up-rising shape and we observe thickening of mush next to chimney. We analyze the thermal boundary layer around chimney that forms as the mush is cooled locally by the fluid rising through the chimney. We obtain solutions of the temperature, the solid fraction, and the pressure in the chimney wall. Also, our expression of the pressure shows that the fluid flow can require a huge pressure in order to pass through the chimney wall if its permeability is very small. We present a simple analytic description of the up-rising shape near the exit of the chimney, due to the fact that the comparatively solute (i.e. $NH_4Cl$ in the case of the ammonium chloride experiment)-rich fluid near the chimney tends to crystallize as it is chilled by the rising jet of cold fluid in the chimney.