Temperature distribution at the exit of the leakage gap is of interest for a number of problems. For the calculation of temperatures, the leakage flow may be considered to be a pure drag flow to a good approximation. In the Newtonian case, thermal development length may be expressed in terms of gap height as L ≈ 3/8Pe ·δ ;usually this is less than the available gap length. Pe is the Peclet number and δ the height of leakage gap. Therefore the existing flow may be considered fully developed. For power law fluids, numerical calculations lead to results of the same order. Martin's results therefore may be applied to the flow at the exit of the leakage gap.
Meyer, H. E. H., Ingen Housz, J. F., & Gorissen, W. C. M. (1978). Temperature development in the leakage flow of screw extruders. Polymer engineering and science, 18(4), 288-292. https://doi.org/10.1002/pen.760180409