Turbulent thermal conductivity

Kl Turbulent thermal conductivity of Pk Kinetic stress tensor of particles... 

It is at = At/gc with the turbulent thermal conductivity or eddy diffusivity for heat transfer1 At (SI units W/K m). The total heat flux is... 

If one doesn t take into account the longitudinal heat transfer by turbulent thermal conductivity inside the reactor, then temperature change (cooling) at the expense of external heat removal is determined as following ... 

Convection Heat Transfer. Convective heat transfer occurs when heat is transferred from a soHd surface to a moving fluid owing to the temperature difference between the soHd and fluid. Convective heat transfer depends on several factors, such as temperature difference between soHd and fluid, fluid velocity, fluid thermal conductivity, turbulence level of the moving fluid, surface roughness of the soHd surface, etc. Owing to the complex nature of convective heat transfer, experimental tests are often needed to determine the convective heat-transfer performance of a given system. Such experimental data are often presented in the form of dimensionless correlations. 

Figure 10-50C. Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm . A fluid inside pipes/tubes, turbulent flow only. Note h= average film coefficient, Btu/hr-ft -°F d = inside tube diameter, in. G = mass velocity, Ib/sec/ft v = fluid velocity, ft/sec k = thermal conductivity, Btu/hr (ft )(°F/ft) n, = viscosity, lb/(hr)(ft) Cp = specific heat, Btu/(lb)(°F). (Used by permission Engineering Manual for Dowtherm Heat Transfer Fluids, 1991. The Dow Chemical Co.)...

Ya.B. ZeFdovich, FizGoreniyaVzryva 7 (4), 463-76 (1971) CA 77, 64194 (1972) The influence of turbulence and nonturbulence is examined relative to a proplnt burning in a gas flow. Equations indicate exptl methods for determining the magnitudes of the thermal conductivity and viscosity under turbulent flow, and permit a study of thermal flow distribution and temps in a gas wherein an exothermic chem reaction occurs. Equations for non turbulent conditions can be used to calculate the distance from the surface of the proplnt to the zone of intense chem reaction and establish the relation of bulk burning rate to the vol reaction rate. 

In most cases where convective heat transfer is taking place from a surface to a fluid, the circulating currents die out in the immediate vicinity of the surface and a film of fluid, free of turbulence, covers the surface. In this film, heat transfer is by thermal conduction and, as the thermal conductivity of most fluids is low, the main resistance to transfer lies there, Thus an increase in the velocity of the fluid over the surface gives rise to improved heat transfer mainly because the thickness of the film is reduced. As a guide, the film coefficient increases as (fluid velocity)", where 0.6 < n < 0.8, depending upon the geometry. 

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. 

With turbulent flow, the major temperature drop occurs across the thin layer of gas at the tube wall. The coefficient h depends on the viscosity 17, the thermal conductivity... 

In this equation S includes heat of chemical reaction, any interphase exchange of heat, and any other user-defined volumetric heat sources. At is defined as the thermal conductivity due to turbulent transport, and is obtained from the turbulent Prandtl number... 

With regard to turbulence, in some cases an additional complication may have to be considered in that the temperature may vary locally, and then thermal conduction is important. It is possible to vary the constraints on the systems you have studied (e.g., concentration) so that by variation of one or more of these constraints both hysteresis and no hysteresis (at different constraints) can be observed in the same system. This is important to make sure that the observed hysteresis is due to the nonlinear kinetics and not due to other reasons. 

The equation of motion and the equation of energy balance can also be time averaged according to the procedure indicated above (SI, pp. 336 et seq. G7, pp. 191 et seq. pp. 646 et seq.). In this averaging process there arises in the equation of motion an additional component to the stress tensor t(,) which may be written formally in terms of a turbulent (eddy) coefficient of viscosity m(I) and in the equation of energy balance there appears an additional contribution to the energy flux q(1), which may be written formally in terms of the turbulent (eddy) coefficient of thermal conductivity Hence for an incompressible fluid, the x components of the fluxes may be written... 

The increased understanding of turbulence and the extension of the analysis of potential flow have made possible the consideration of many thermal and material transfer problems which formerly were not susceptible to analysis. However, at present the application of such methods is hampered by the absence of adequate information concerning the thermal conductivities and diffusion coefficients of the components of petroleum. The diffusion coefficient in particular is markedly influenced by the state of the phase. For this reason much experimental effort will be required to obtain the requisite experimental background to permit the quantitative application of the recent advances in fluid mechanics and potential theory to dynamic transfer problems of practical interest. 

The transfer of heat and/or mass in turbulent flow occurs mainly by eddy activity, namely the motion of gross fluid elements that carry heat and/or mass. Transfer by heat conduction and/or molecular diffusion is much smaller compared to that by eddy activity. In contrast, heat and/or mass transfer across the laminar sublayer near a wall, in which no velocity component normal to the wall exists, occurs solely by conduction and/or molecular diffusion. A similar statement holds for momentum transfer. Figure 2.5 shows the temperature profile for the case of heat transfer from a metal wall to a fluid flowing along the wall in turbulent flow. The temperature gradient in the laminar sublayer is linear and steep, because heat transfer across the laminar sublayer is solely by conduction and the thermal conductivities of fluids are much smaller those of metals. The temperature gradient in the turbulent core is much smaller, as heat transfer occurs mainly by convection - that is, by... 

In this text we are concerned exclusively with laminar flows that is, we do not discuss turbulent flow. However, we are concerned with the complexities of multicomponent molecular transport of mass, momentum, and energy by diffusive processes, especially in gas mixtures. Accordingly we introduce the kinetic-theory formalism required to determine mixture viscosity and thermal conductivity, as well as multicomponent ordinary and thermal diffusion coefficients. Perhaps it should be noted in passing that certain laminar, strained, flames are developed and studied specifically because of the insight they offer for understanding turbulent flame environments. 

We imagine a distribution of a which is characterized by an amplitude o0 and a length scale L which exceeds the maximum scale of the turbulent pulsation, l. We denote the pulsating velocity by u the turbulent coefficient of diffusion, the coefficient of thermal conductivity and the effective turbulent kinematic viscosity are all expressed by the formula k = ul. For an initial uniform distribution of a, obviously,... 

We consider turbulent motion in a closed region of size L at whose boundaries vn = 0 (the index n is the normal to the surface S of the region) in the presence of external fields. It follows from (7) that the quantity ht = (grad a)n should be continuous at the boundary. From the analogy between (7) and turbulent heat conduction, noting that r plays the role of molecular thermal conductivity and considering the flow a as a heat flow, we find... 

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