Turbulent heat flux

Internal Regenerator Bed Colls. Internal cods generate high overall heat-transfer coefficients [550 W / (m -K)] and typically produce saturated steam up to 4.6 MPa (667 psi). Lower heat fluxes are attained when producing superheated steam. The tube banks are normally arranged horizontally in rows of three or four, but because of their location in a continuously active bubbling or turbulent bed, they offer limited duty flexibdity with no shutdown or start-up potential. 

Temperature and contaminant gradients along the room height and separation stability between the upper and lower zones are influenced by turbulent exchange between these zones. The heat flux density due to turbulent exchange can be determined as ... 

A massive amount of propane is instantaneously released in an open field. The cloud assumes a flat, circular shape as it spreads. When the internal fuel concentration in the cloud is about 10% by volume, the cloud s dimensions are approximately 1 m deep and 100 m in diameter. Then the cloud reaches an ignition source at its edge. Because turbulence-inducing effects are absent in this situation, blast effects are not anticipated. Therefore, thermal radiation and direct flame contact are the only hazardous effects encountered. Wind speed is 2 m/s. Relative humidity is 50%. Compute the incident heat flux as a function of time through a vertical surface at 100 m distance from the center of the cloud. 

The method is based on the calculation of the total temperature difference between the fluid and the surface, by adding the components attributable to the laminar sub-layer, the buffer layer and the turbulent region. In the steady state, the heat flux (<70) normal to the surface will be constant if the effects of curvature are neglected. 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

The quantity G of the effective mixing mass flux is determined by the turbulent velocity fluctuations at the bubble-layer edge. The distance of the edge of the bubble layer from the wall is taken as the distance at which the size of the turbulent eddies is k times the average bubble diameter. Weisman and Pei have determined empirically that k equals 2.28. Only a fraction of the turbulent velocity fluctuations produced are assumed to be effective in reaching the wall. The effective velocity fluctuations are those in which the velocity exceeds the average velocity away from the wall produced by evaporation heat flux q"b. At the bubble layer-core interface, the effective mass flux to the wall is computed as... 

These results appear to indicate that flow turbulences in the whole channel can improve the critical heat fluxes. 

Dwyer, O. E., G. Strickland, S. Kalish, and P. J. Schoen, 1973a, Incipient-Boiling Superheat for Sodium in Turbulent Channel Flow Effects of Heat Flux and Flow Rate, Int. Heat Mass Transfer 16 911-984. (4)... 

The model includes a dynamic thermodynamic sea ice model. The dynamics of sea ice are formulated using viscous-plastic rheology [Hibler (1979)]. The thermodynamics relate changes in sea ice thickness to a balance of radiant, turbulent, and oceanic heat fluxes. The effect of snow accumulation on sea ice is included, along... 

It has been shown that in small-scale experiments with turbulent fires, the flame heat flux approaches its asymptotic value for oxygen concentrations greater than about 30% the asymptotic value is very close to the value expected in very large fires (7). 

For laminar conditions of slow flow, as in candle flames, the heat transfer between a fluid and a surface is predominately conductive. In general, conduction always prevails, but in the unsteadiness of turbulent flow, the time-averaged conductive heat flux between a fluid and a stationary surface is called convection. Convection depends on the flow field that is responsible for the fluid temperature gradient near the surface. This dependence is contained in the convection heat transfer coefficient hc defined by... 

Convective heating in fire conditions is principally under natural convection conditions where for turbulent flow, a heat transfer coefficient of about 10 W/m2 K is typical. Therefore, under typical turbulent average flame temperatures of 800 °C, we expect convective heat fluxes of about 8 kW/m2. Consequently, under turbulent conditions, radiative heat transfer becomes more important to fire growth. This is one reason why fire growth is not easy to predict. 

Heat flux is an important variable in fire growth and its determination is necessary for many problems. In general, it depends on scale (laminar or turbulent, beam length ), material (soot, combustion products) and flow features (geometric, natural or forced). We... 

Predicted Nusselt numbers for turbulent flow with constant wall heat flux (John Wiley and Sons from Bird et al., 1964). Abbreviations Nu = Nusselt number Re = Reynolds number Pr = Prandtl number. 

Dengler and Addoms 8 measured heat transfer to water boiling in a 6 m tube and found that the heat flux increased steadily up the tube as the percentage of vapour increased, as shown in Figure 14.4. Where convection was predominant, the data were correlated using the ratio of the observed two-phase heat transfer coefficient (htp) to that which would be obtained had the same total mass flow been all liquid (hi) as the ordinate. As discussed in Volume 6, Chapter 12, this ratio was plotted against the reciprocal of Xtt, the parameter for two-phase turbulent flow developed by Lockhart and Martinelli(9). The liquid coefficient hL is given by ... 

When the turbulence in the atmospheric boundary layer is maintained largely by buoyant production, the boundary layer is said to be in a convective state. The source of buoyancy is the upward heat flux originating from the ground heated by solar radiation. Convective turbulence is relatively vigorous and causes rapid vertical mixing in the atmospheric boundary layer. 

The rate of heat transfer from the tubes to the fluid depends primarily on turbulence and the magnitude of the heat flux itself. Turbulence is a... 

In the present study, numerical techniques capable of explicitly tracking the receding solid propellant boundary in turbulent reacting flows are developed. With this capability, nonuniform and time dependent heat fluxes along the propellant interface can be predicted, and a two-way coupling between gas-phase and solid-phase is established. A number of areas requiring further efforts can be identifled. 

Owing to vertical (turbulent) diffusion, heat is transported from regions of warm water to adjacent colder layers. Mathematically this appears as a heat flux against the vertical temperature gradient (remember Fick s first law, Eq. 18-6). Thus, at a later time, ti+u we expect to find warmer water between z and zB. The change of the heat content with time A is ... 

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