Mass - adiabatic

The procedure to determine the adiabatic mass flow rate through a pipe or hole is as follows ... 

Eqns (20) and (21) are solved simultaneously by the Newton-Raphson iteration with respect to the two unknown variables y and x. The results are shown in figure 2 where the choking pressure drop and the temperature are shown as functions of the pipe length. The deviation between the isothermal and adiabatic mass flux at zero pipe length reflects the ratio between the adiabatic and isothermal speed of pressure propagation. Furthermore, at a pipe length of about 100 diameters, the discrepancy between the various models to predict the mass flux is not very significant. 

In Section 5.3.6, activation-energy asymptotics have been applied to the adiabatic version of equation (9) for a particular rate function w burning-rate formulas are given in Section 5.3.6 for this rate function and in Section 5.3.7 for others. Here it is convenient to presume that for L = 0, the burning rate is known on the basis of these results and to employ the known adiabatic mass burning rate for the purpose of nondimensionalization. Thus, in analogy with equation (5-18), we introduce the nondimensional stream wise coordinate = m CpX/X and obtain the equation... 

For adiabatic mass transfer the rate of heat transfer due to the latent heat in the water vapor being transferred can be obtained from Eq. (9.3-16) by rearranging and using a volumetric basis. 

When the rate of accumulation dpjdt of all quantities in the system is zero, the condition is known as the steady state. All other systems are time dependent. Stationary flames supported on burners are steady-state phenomena, and so for a quasi-one-dimensional stationary flame d AMy)/dy = 0 and AMy = constant. In the hypothetical case of a true one-dimensional adiabatic flame the constant My is the adiabatic mass burning velocity. It is an eigenvalue solution of the physical problem, equal to the product of the density and linear velocity of the gas at any position in the flame. Thus... 

Reactor heat carrier. Also as pointed out in Sec. 2.6, if adiabatic operation is not possible and it is not possible to control temperature by direct heat transfer, then an inert material can be introduced to the reactor to increase its heat capacity flow rate (i.e., product of mass flow rate and specific heat capacity) and to reduce... 

Accurate enthalpies of solid-solid transitions and solid-liquid transitions (fiision) are usually detennined in an adiabatic heat capacity calorimeter. Measurements of lower precision can be made with a differential scaiming calorimeter (see later). Enthalpies of vaporization are usually detennined by the measurement of the amount of energy required to vaporize a known mass of sample. The various measurement methods have been critically reviewed by Majer and Svoboda [9]. The actual teclmique used depends on the vapour pressure of the material. Methods based on... 

Finally, we shall look briefly at the form of the non-adiabatic operators. Taking the kinetic energy operator in Cartesian form, and using mass-scaled coordinates where Ma is the nuclear mass associated with the ath... 

If the parameter r is very small, we are in the case of M being much larger than m. Thus, the limit f —> 0 is the limit of infinite mass M, i.e., the adiabatic... 

The enthalpy hberated on the VDP of parylene is real and in an adiabatic situation causes a rise in temperature of the coated substrate. For Parylene C, 229.1 kj/mol (54.7 cal/mol) corresponds to 1654 J/g (395 cal/g) whereas its specific heat at 25°C is only 1.00 J/(g-K) [0.239 cal/(g-K)] (33). In most practical situations, however, the mass of parylene deposited is dwarfed by the substrate mass, and the heat of polymeriza tion is dissipated within the coated substrate over the time required to deposit the coating with minimal actual temperature rise. 

The specific enthalpies ia equation 9 can be determined as described earUer, provided the temperatures of the product streams are known. Evaporative cooling crystallizers operate at reduced pressure and may be considered adiabatic (Q = 0). As with of many problems involving equiUbrium relationships and mass and energy balances, trial-and-error computations are often iavolved ia solving equations 7 through 9. 

An equation representing an energy balance on a combustion chamber of two surface zones, a heat sink Ai at temperature T, and a refractory surface A assumed radiatively adiabatic at Tr, inmost simply solved if the total enthalpy input H is expressed as rhCJYTv rh is the mass rate of fuel plus air and Tp is a pseudoadiabatic flame temperature based on a mean specific heat from base temperature up to the gas exit temperature Te rather than up to Tp/The heat transfer rate out of the gas is then H— — T ) or rhCp(T f — Te). The... 

Measurement of Performance The amount of useful work that any fluid-transport device performs is the product of (1) the mass rate of fluid flowthrough it ana (2) the total pressure differential measured immediately before and after the device, usually expressed in the height of column of fluid equivalent under adiabatic conditions. The first of these quantities is normally referred to as capacity, and the second is known as head. 

For systems other than air-water vapor, the value of h /k c, may differ appreciably from unity, and the wet-bulb and adiabatic-saturation temperatures are no longer equal. For these systems the psychrometric ratio may be obtained by determining h /k from heat- and mass-transfer an ogies such as the Chilton-Colburn analogy [Ind. Eng. Chem., 26, 1183 (1934)]. For low humidities this analogy gives... 

Local equilibrium theory Shows wave character—simple waves and shocks Usually indicates best possible performance Better understanding Mass and heat transfer very rapid Dispersion usually neglected If nonisothermal, then adiabatic... 

High mass-transfer rates in both vapor and hquid phases. Close approach to eqiiilihriiim. Adiabatic contact assures phase eqiiilihriiim, Only moderate mass-transfer rate in liquid phase, zero in sohd. Slow approach to equilibrium achieved in brief contact time. Included impurities cannot diffuse out of solid. Sohd phase must be remelted and refrozen to allow phase equilibrium. 

Estimation of operating data (usually consisting of a mass and energy in which the energy balance decides whether the absorption balance can be considered isothermal or adiabatic)... 

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