Transient natural convection

Free convection in inclined enclosures is discussed by Dropkin and Somerscales [12], Evans and Stefany [9] have shown that transient natural-convection heating or cooling in closed vertical or horizontal cylindrical enclosures may be calculated with... 

Mollendorf, J. C., and B. Gebhart An Experimental Study of Vigorous Transient Natural Convection, ASME Pap. 70-HT-2, May 1970. 

Yang, W. H. and Rao, M. A. 1998b. Transient natural convection heat transfer to starch dispersion in a cylindrical container numerical solution and experiment J. FoodEng. 36 395-415. 

K. C. Cheng, M. Takeuchi, and R. R. Gilpin, Transient Natural Convection in Horizontal Water Pipes With Maximum Density Effect and Supercooling, Num. Heat Transfer (1) 101-115,1978. 

B. Gebhart, Transient Natural Convection from Vertical Elements, J. Heat Transfer (83) 61-70, 1961. 

B. Gebhart and D. E. Adams, Measurements of Transient Natural Convection on Flat Vertical Surfaces, J. Heat Transfer (85) 25-28,1963. 

J. H. Min and F. A. Kulacki, Transient Natural Convection in a Single-Phase Heat Generating Pool Bounded From Below by a Segment of a Sphere, Nucl. Eng. Des. (54) 267-278,1979. 

What Would Make a Sweep Rate Too Slow One general criterion that can be taken here is that the time in which (nDT)l/2 = 8, an assumption used in the theory ofpotentiodynamic transients, remains valid. It is an experimental fact that 8 at an electrode in a still solution for a long time (> 10 s, say) is about 0.05 cm and constant because natural convection stirs the solution and wipes out the concentration gradient set up by diffusion alone. Hence, one can assume that the limit of validity of 8,= (jiDt)m is a time at which becomes 8 equal to 0.05 cm. Using a typical value of D (= 3 x 10-5 cm2 s-1), one obtains... 

The present lecture summarizes some of tiie most recent joint research results from tiie cooperation between the Federal University of Rio de Janeiro, Brasil, and tiie University of Miami, USA, on tiie fransient analysis of both fluid flow and heat transfer within microchannels. This collaborative link is a natural extension of a long term cooperation between the two groups, in the context of fimdamental work on transient forced convection, aimed at tiie development of hybrid numerical-analytical techniques and tiie experimental validation of proposed models md methodologies [1- 9]. The motivation of this new phase of tiie cooperation was thus to extend the previously developed hybrid tools to handle both transient flow and transient convection problems in microchannels within the slip flow regime. 

As explained earlier, in transient electrochemical methods an electrical perturbation (potential, current, charge, and so on) is imposed at the working electrode during a time period 0 (usually less than 10 s) short enough for the diffusion layer 8 (2D0) to be smaller than the convection layer (S onv imposed by natural convection. Thus the electrochemical response of the system investigated depends on the exact perturbation as well as on the elapsed time. This duality is apparent when one considers a double-pulse potentiostatic perturbation applied to the electrode as in the double-step chronoampero-metric method. 

The first section presents some fundamental ideas that are frequently referred to in the remainder of the chapter. The next three sections deal with the major topics in natural convection. The first of these addresses problems of heat exchange between a body and an extensive quiescent ambient fluid, such as that depicted in Fig. 4.1a. Open cavity problems, such as natural convection in fin arrays or through cooling slots (Fig. 4.1fe), are considered next. The last major section deals with natural convection in enclosures, such as in the annulus between cylinders (Fig. 4.1c). The remaining sections present results for special topics including transient convection, natural convection with internal heat generation, mixed convection, and natural convection in porous media. 

An imposed temporal change of Tw, other than the step change, is also of interest. In fact, because the heat capacity of any body or wall is finite, a step change could never be achieved. If the time constant associated with the prescribed change in T is much larger than th the heat transfer at each instant in the transient can be accurately calculated from the steady-state natural convection equation this is called a quasi-static transient. From the above estimates of tt it will be appreciated that the quasi-static approximation will usually be valid for gases. 

Hauf and Grigull [133-135] precisely measured the natural convection heat transfer inside a tube following a step change in the temperature of a fluid in forced convection over the outside of the tube. In this case the heat transfer coefficient on the outer surface is constant throughout the transient, and the heat capacity of the wall plays an important role. Cheng et al. [50] have studied conditions leading to the formation of ice inside horizontal tubes (without throughflow), also with uniform heat transfer coefficient between the outside boundary and a cold environment. 

B. Gebhart, Natural Convection Cooling Transients, Int. J. Heat Mass Transfer (7) 479-483,1964. 

For prediction of subassembly coolant flow rate and temperature distributions a wide range of coolant flow and thermal convection regimes must be considered including laminar and turbulent flow natural, forced and mixed (forced + natural) convection and steady state and transient reactor conditions. 

Based on 2-D RANS and 3-D DNS simulations at meso-scale, it was concluded that 3-dimensional transient RANS simulations are probably the most promising approach for accurate and relatively inexpensive modelling at the macro (whole-body) scale. This approach allows the inclusion of various realistic and important phenomena, such as natural convection and chemical breakthrough. The results of this DNS simulation are nsed (i) to validate RANS and T-RANS simulations for the same conditions and (ii) to guide in choosing a turbulence modelling strategy for the RANS and T-RANS simulations of the flow underneath the porous layer. 

Earlier, a sealing analysis for the passive decay heat cooling system suggested that the AHTR could operate at a thermal power of 2400 MW(t). A more sophisticated analysis was performed that indicates that 2400 MW(t) can indeed be achieved with reasonable RVACS capacity. The analysis showed that for a loss-of-forced-cooling accident (with scram), significant natural convection of the molten salt is established and the eore temperature peaks at only 1160°C, which occurs about 30 hours after the accident. The reactor vessel temperature peaks at 750°C after about 40 hours. This analysis, which did not include a DRAGS, indieates that a 2400 MW(t) AHTR ean easily survive this type of transient. 

LEADIR-PS 200 has a graceful and safe response to all anticipated transients. For example, an overcooling event (as could be caused by loss of feedwater control or spurious opening of steam relief valves in combination with control system failure) causes the core inlet temperature (normally 350°C) to fall as the freezing point of 327°C is approached the coolant viscosity increases, coolant flow decreases, and in the absence of any control system action, the negative temperature coefficients of the fuel and moderator reduce reactor power. Heat removal is maintained by natural convection. 

Soluble boFCHi suppression reduces corrosion and therefore initiator frequency FuU condoisate polishing reduces steam g erator corrosiem and hence, reduces initiator frequency Transients Soluble boron suppression reduces initiator frequency Natural convection ccmling supress initiatcH ... 

Natural convection - L Secondary transients Natural convention - L Loss of electric sources Battery power - R Total loss of heat sink Passive DHR to the air and ground - S Station blackout Not critical ... 

Main and auxiliary cooling systems of the PBWFR are driven by natural convection. The inherent safety features of the core are enhanced to avoid a core disruption accident even in anticipated transients without scram (ATWSs). Specifically, void reactivity for the case when the core, the axial blanket, and the plenum are totally voided is limited by 3 (design modifications are foreseen to make this effect negative). The bum-up reactivity swing during 15 years of operation without refuelling is minimized down to 1.5% AK/K. 

Equation (11.2.7) is known as the Cottrell equation (4) and a typical current transient is shown in Figure 11.1b. For spherical electrodes, the current transient (11.2.14) contains a steady-state term accounting for the effect of radial diffusion. This term wiU dominate at larger t when the Cottrell term tends to zero and the current reaches a steady-state value. The time required to establish the steady state is a function of the electrode radius. The smaller the electrode, the sooner the radial diffusion term becomes dominant (see Section 11.2.4 in this Chapter and Section 2.4 in Chapter 2, and Chapters 6 and 19 on Microelectrodes). To test whether the current response is controlled by diffusion, one plots i vs. For both geometries, the graph should be linear but its intercept will be zero for a planar electrode and equal to the steady-state current for a spherical electrode. For planar electrodes, the current is therefore expected to decay to zero at long times. In practice, this cannot be observed because of the onset of natural convections after 30 s. 

The mechanisms of mass transport can be divided into convective and molecular flow processes. Convective flow is either forced flow, for example, in pipes and packed beds, or natural convection induced by temperature differences in a fluid. For diffusive flow we have to distinguish whether we have molecular diffusion in a free fluid phase or a more complicated effective diffusion in porous solids. Like heat transport, diffusion may be steady-state or transient. 

Investigations of the complete DHR heat sink (DHX, stack and dampers) under steady state, natural convection and transient operation conditions, have shown that no problems... 

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