The effect of wall conductance on heat diffusion in duct flow

SummaryThe 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.

[1]  W. Gill,et al.  Unsteady convective diffusion with interphase mass transfer , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  G. F. Carrier.  On diffusive convection in tubes , 1956 .

[3]  The initial dispersion of contaminant in Poiseuille flow and the smoothing of the snout , 1976 .

[4]  P. C. Chatwin,et al.  On the longitudinal dispersion of passive contaminant in oscillatory flows in tubes , 1975, Journal of Fluid Mechanics.

[5]  M. Lighthill.  Initial Development of Diffusion in Poiseuille Flow , 1966 .

[6]  Ronald Smith.  Longitudinal dispersion of a buoyant contaminant in a shallow channel , 1976, Journal of Fluid Mechanics.

[7]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  R. J. Dewey,et al.  The asymptotic stage of longitudinal turbulent dispersion within a tube , 1977, Journal of Fluid Mechanics.

[9]  P. C. Chatwin,et al.  The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe , 1970, Journal of Fluid Mechanics.

[10]  The initial development of longitudinal dispersion in straight tubes , 1977 .

[11]  J. Philip.  The Theory of Dispersal During Laminar Flow in Tubes. II. , 1963 .

[12]  P. C. Chatwin,et al.  The effects of curvature and buoyancy on the laminar dispersion of solute in a horizontal tube , 1967, Journal of Fluid Mechanics.

[13]  R. Aris.  On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.