A comprehensive account of the emerging concept of dispersion of heat along the axial direction as a fluid flows through a passage bounded by solid wall has been presented with its most recent and remarkable advancement. This new proposition takes axial dispersion as a disturbance which propagates as a wave with a finite velocity. It has been proposed that this sound like propagation be named as the "third sound wave in flowing fluid". The fundamental analysis of this theory has been presented with particular emphasis on the boundary condition which plays a key role in the propagation of the wave. A general flux formulation has been used for this purpose. Analysis has also been presented for a two fluid situation. It has been found that the 'subsonic' and 'super sonic' flow with respect to third sound wave behave difFerently particularly at entry and exit. The theoretical background developed has been substantiated by three examples-one purely theoretical condition, one comparison with numerical analysis and finally application to a complete apparatus. it' 199X Elsevier Science. All rights reserved. Nomenclature A parameter, equation (44) a fluid diffusivity based on dispersion = ;z; [m' s '1 I' a* a Auid diffusivity based on molecular conduction, [m' s '1 a, thermal diflusivity of the wall B,, & breadth of the flow channels, Fig. 5 [m] Md, B' parameter = ~-~~ W(',' C' propagation velocity of third sound wave [m s '1 ('P specific isobaric heat capacity of the fluid [J kg-' Km '1 c',, second sound velocity in wall [m s '1 l', specific heat of the solid wall [J kg ' K '1 n parameter. equation (44) *Corresponding author. ' Lecture presented by W. Roetzel at the Internal meeting oE VDIiGVC committee 'Heat and Mass Transfer'. Lahnstein. Germany.