Por Gltimo, hacemos notar que e l estado Mrcado en l a Figura 3.4 con V es e l estado de detonación a volumen constante, conocfdo en buena part e de los trabajos sobre explosivos como 'estado de explosiÓn", frente al t í m i n o 'estado de ~tonación',que se suele reservar a l estado C-J.Este estado de " e ~p l o ~l Ó n ' es un caso teórico, pues l a velocidad de -choque sería Inf!nlti. como se puede comprobar haciendo en 3-12 v=vo: Este proceso debe considerarse como e1 caso lfmtte de aquellas detonaciones que tienen lugar con ligeros aumentos de volumen y velocida-/ das muy grandes. Cálculo del estado de detonación C-JE l sistema de ecuaciones a resolver es e l slgulente:Cbnfie se tienen como incógnitas: P. v. T. u. U.Las energlas internas e y e , son funciones de l a s otras variables termodinámicas (P. v, T) en l o s estados f i n a l e i n i c i a l . En c i tn CO De en ec 1 n qu En la expresión para la ecuación de estado se han hecho aparecer e x p l i citamente ni, indicando con ello que en la ecuación que utiliza estetrabajo, la relación entre P, v y T depende. entre otras cosas, de la composiciÓn del producto de la explosión. Dejando las dos ecuaciones mecánicas del choque aparte, y centrándonos en las tres Últimas , que ligan P, v y T, se tiene un sistema de tres ecuaciones para estas tres incógnitas. ~Ó t e s e que existe una serie de incógnitas intermedias, que son las ni cantidades de cada compuesto -que forman parte del producto en equilibrio. Este sistema se resuelve de la siguiente forma: supóngase una T, un v y una composición cualquiera. De la ecuaciónde estado se tiene asi también una P. Con estas condiciones temodinimicas se calcula el equi 1 i brio quimico correspondiente. La expresión de trabajo de la condición de Chapman-Jouguet se obtendrá en su momento. Por el momento, baste con decir que puede expresarse, como es lÓgico, en función de P. v. T y la composición. Asi pues, fijo dos P, T y obtenidc la composición de equilibrio, esta condición se rg duce a una ecuación en una variable, v. Su resolución proporciona una aproximación del volumen especifico. Con el volumen asi calculado y la correspondiente presión, se procede a obtener la composición de equilibrio, y resolviendo nuevamente laecuación C-J, se calcula un nuevo v, continuando este proceso hasta -' Y .

Recently, an orthogonal expansion technique was used to describe the temperature distribution in laminar flow double-pipe heat exchangers ( 2 ) . One of the difficulties with this approach is the calculation of the expansion coefficients, since they cannot be determined by standard techniques. A computational scheme for obtaining the expansion coefficients was described in this paper, and the expansion coefficients thus calculated were used to obtain the effectiveness for counterflow exchangers.In a later issue of the Journal Stein ( 4 ) presented an alternate computational scheme for solving the same system of equations for the expansion coefficients. Called the Argonne procedure by Stein, this scheme, along with the initial one, named by Stein the Nunge-Gill procedure, was applied to a countercurrent plu flow system. From a Gill procedure fails to give accurate numerical values under certain conditions in the plug flow case. Furthermore, Stein states on page 1219, "The reader is invited to study the results shown in these tables as related to the treatment of Equation ( 2 2 ) of reference 2 and Equation (38) in reference 4 as well as the tabulations of the expansion coefficients in references 2 and 3." This implies that one can extrapolate the plug flow case, which has a finite discontinuity in the velocity profile, to estimate the accuracy of the laminar flow calculations. In contrast, we will show that the two computational schemes yield essentially the same effectiveness for those cases considered in references 1, 2, and 2a. Also, some of the local temperature distributions and Nusselt numbers given in these references were compared with finite-difference calculations, and in all cases the comparisons were favorable (1, 2a).Thus, the purpose of this communication is to present a comparison of the effectiveness of the two computational schemes for the laminar flow case, a comparison similar to that made by Stein, for the plug flow exchanger. We shall restrict our attention to those results which are already in the literature ( 2 ) and cover the range 0.8 4 K H 5 4.5. For the comparison, the problem of calculating the exchanger effectiveness, which requires the computation of the expansion coefficients, was reworked for Iaminar countercurrent flow in a concentric tube exchanger comparison of the results, Stein conc B uded that the Nungeaccording to the Argoniie procedure. The main conclusion to be drawn from these calculations is that, for the laminar flow cases studied previously, both procedures yield essentially the same effectiveness and that our original results ( 2 ) are accurate enough for the practical calculation of effectiveness, temperature distributions, and Nusselt numbers. DISCUSSION OF SERIES CONVERGENCEBecause of the form of the equations which must be solved for the expansion coefficients, for example, Equation (38) of reference 2, the addition of successive terms to the series can affect the lower-order expansion coefficients. The convergence and accuracy of the results can be judged by inspe...

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