Effect of dissipation and compression work on the eddy conductivity calculated from experimental temperature data for gases

Abstract

T h e effect of dissipation and compression work on the eddy conductivity calculated from experimental temperature distribution data for gases is examined i n detail, and it is shown that these effects are significant even i n relatively low Reynolds number flows, say greater than 30,000. The inclusion of dissipation and compression work i n the energy equation for gaseous flows is shown to lead to the determination of symmetrical eddy diffusivities from experimental data.The temperature distribution in the fully developed thermal region for a fluid flowing turbulently between two walls maintained at uniform but different temperatures i s a function of the transverse coordinate only, and therefore both the wall temperature and heat flux are independent of the axial coordinate. The heat entering at one wall is effectively "conducted" away by the fluid and then lost to the other wall; the fluid i s heated by contact with one wall and cooled by contact with the other, This mode of convective heat transfer i s particularly favorable for determining the behavior of the eddy conductivity at the center of the channel, a s was recognized by Harrison and Menke ( 9 ) and Corcoran, Sage, and co-workers ( 3 to 6, 12,13,14, 16).of the fluid and consequently alters the temperature gradient distribution for heating and cooling in opposite directions. A parallel argument holds for the effects of corn pression work, which behaves as an energy sink. An asymmetrical arrangement is thus particularly interesting because the fluid is simultaneously heated at one wall and cooled at the other, and therefore dissipation and compression work may introduce asymmetries in the temperature gradient distribution even if the fluid properties are assumed independent of temperature. For these reasons, the asymmetrical arrangement discussed above, which was studied experimentally by Corcoran, Sage, and co-workers ( 3 to 6,11,13,14, 16) with the objective of determining the eddy diffusivity distribution, i s also particularly interesting from the point of view of investigating the presence of dissipation and compression work and the extent to which these effects may intervene in the heat transfer process .Previous theoretical developments (22, 27, 28) indicate that for gaseous flows, dissipation and compression work may affect measured temperature profiles. The effects of compression work on the temperature distribution are important for compressible flows whenever the dissipative effects cannot be neglected; the latter are of the same order of magnitude as the other terms in the equation of energy when the Eckert number is on the order of unity. Dissipation in turbulent gaseous flows was introduced by Venezian Dissipation, an energy source, increases the temperature Jose A. Blanco is with the International Nickel