Thermal flows, simultaneous

A high precision electronic integrator is directly connected to the thermoelectric captors so as to record simultaneously the thermal flow and its integral curve versus time. Figure 5 shows the thermograms given by this apparatus. 

S.P. Guidice, C. Nonino, and S. Savino, Effects of viscous dissipation and temperature dependent viscosity in thermally and simultaneously developing laminar flows in microchannels. International Journal of Heat and Fluid Flow 28, 15-27 (2007). 

The term x, denoting thermally and simultaneously developing flows, is expressed as ... 

Simultaneously Developing Flow. Simultaneously developing flow usually occurs when the fluid exhibits a moderate Prandtl number. In such a flow, the velocity and the temperature profiles develop simultaneously along the flow direction. Therefore, the heat transfer rate strongly depends on the Prandtl number of the fluid and the thermal boundary condition. 

Thermally and Simultaneously Developing Flows. Hydrodynamically developing laminar flow in triangular ducts has been solved by different investigators as is reviewed by Shah and London [1]. Wibulswas [160] obtained a numerical solution for the problem of simultaneously... 

TABLE 5.41 Local and Mean Nusselt Numbers for Thermally and Simultaneously Developing Laminar Flows and Equilateral Triangular Ducts [160]... 

In many industrially important situations, it is impossible to maintain geometric, mechanical (kinematic/hydrodynamic and turbulence similarities), and thermal similarities simultaneously. Consider a stirred tank reactor with heat exchange only through a jacket on its external surface. The jacket heat transfer area to vessel volume ratio is proportional to (l/T). Evidently, with scale-up, this ratio decreases, and it is difficult to maintain the same heat transfer area per unit volume as in the small-scale unit. Additional heat transfer area is required to cater to the extra heat load resulting from increase in reactor volume. This area can be provided in the form of a coil inside the reactor or an external heat exchanger circuit. In both cases, the flow patterns are significantly different than the model contactor used in bench-scale studies and kinematic similarity is violated. This is the classic dilemma of a chemical engineer it is impossible to preserve the different types of similarities simultaneously. 

In this situation, e.g. heat is briefly more quickly released than heat—which up to now has been relevant for the maintenance of thermal equilibrium— flows simultaneously from the measuring kettle into the intermediate thermostat. But the momentarily changed temperature difference T2(t)-F... 

Clearly, the maximum degree of simplification of the problem is achieved by using the greatest possible number of fundamentals since each yields a simultaneous equation of its own. In certain problems, force may be used as a fundamental in addition to mass, length, and time, provided that at no stage in the problem is force defined in terms of mass and acceleration. In heat transfer problems, temperature is usually an additional fundamental, and heat can also be used as a fundamental provided it is not defined in terms of mass and temperature and provided that the equivalence of mechanical and thermal energy is not utilised. Considerable experience is needed in the proper use of dimensional analysis, and its application in a number of areas of fluid flow and heat transfer is seen in the relevant chapters of this Volume. 

The determination of these curves requires not only the measurement of small amounts of heat in a microcalorimeter, but also the simultaneous determination of the corresponding quantity of adsorbed gas. Volumetric measurements are to be preferred to gravimetric measurements for these determinations because it would be very difficult indeed to ensure a good, and reproducible, thermal contact between a sample of adsorbent, hanging from a balance beam, and the inner cell of a heat-flow calorimeter. 

Thermal decomposition was performed using a SDT Q-600 simultaneous DSC-TGA instrument (TA Instruments). The samples (mass app. 10 mg) were heated in a standard alumina 90 il sample pan. All experiments were carried out under air with a flow rate of 0.1 dm3/min. Non-isothermal measurements were conducted at heating rates of 3, 6, 9, 12, and 16 K/min. Five experiments were done at each heating rate. 

Table El4.1 A shows various feeds and the corresponding product distribution for a thermal cracker that produces olefins. The possible feeds include ethane, propane, debutanized natural gasoline (DNG), and gas oil, some of which may be fed simultaneously. Based on plant data, eight products are produced in varying proportions according to the following matrix. The capacity to run gas feeds through the cracker is 200,000 lb/stream hour (total flow based on an average mixture). Ethane uses the equivalent of 1.1 lb of capacity per pound of ethane propane 0.9 lb gas oil 0.9 lb/lb and DNG 1.0.

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