Summary
The axial diffusion of a passive scalar field (e.g. temperature) in Poiseuille flow through a duct is considered, taking account of leakage of heat through the duct boundary. The cases of the two-dimensional channel and the pipe of circular cross-section are considered in detail, and it is shown that (i) the centroid of the scalar field moves (asymptotically) with a velocity intermediate between the mean and the maximum flow rates and increases with increasing wall conductance, and (ii) the effective diffusivity in the flow direction is a decreasing function of wall conductance.
The temperature field downstream of a maintained heat source is determined as a function of wall conductance.
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Lungu, E.M., Moffatt, H.K. The effect of wall conductance on heat diffusion in duct flow. J Eng Math 16, 121–136 (1982). https://doi.org/10.1007/BF00042550
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DOI: https://doi.org/10.1007/BF00042550