Thermal diffusivity units

This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

Grady and Asay [49] estimate the actual local heating that may occur in shocked 6061-T6 Al. In the work of Hayes and Grady [50], slip planes are assumed to be separated by the characteristic distance d. Plastic deformation in the shock front is assumed to dissipate heat (per unit area) at a constant rate S.QdJt, where AQ is the dissipative component of internal energy change and is the shock risetime. The local slip-band temperature behind the shock front, 7), is obtained as a solution to the heat conduction equation with y as the thermal diffusivity... 

The term (CppO) represents the heat content per unit volume of fluid and therefore the flow of heat is proportional to the gradient in the K-direction of the heat content per unit volume, The proportionality constant k/Crp is called the thermal diffusivity Du ... 

Equation 1.70 shows that the molar diffusional flux of component A in the y-direction is proportional to the concentration gradient of that component. The constant of proportionality is the molecular diffusivity 2. Similarly, equation 1.69 shows that the heat flux is proportional to the gradient of the quantity pCpT, which represents the. concentration of thermal energy. The constant of proportionality klpCp, which is often denoted by a, is the thermal diffusivity and this, like 2, has the units m2/s. 

The minns sign in Eq. (4.2) arises dne to the fact that in order for there to be heat flow in the +y direction, the temperatnre gradient in that direction must be negative—that is, lower temperature in the direction of heat flow. If the temperature gradient is expressed in units of K/m, and the heat flux is in J/m - s, then the thermal conductivity has units of J/K m s, or W/m K. A related quantity is the thermal diffusivity, which is often represented by the lowercase Greek letter alpha, a. Thermal diffusivity is defined as k/pCp, where k is the thermal conductivity, p is the density, and Cp is the heat capacity at constant pressure per unit mass. We will see in a moment why the term diffusivity is used to describe this parameter. We will generally confine our descriptions in this chapter to thermal conductivity. 

The proportionality constant for mass transport is called the molecular diffusivity of A in B, and it has cgs units of cm /s when concentration is mol/cm and distance is in centimeters. As a result, the molar flux has units of mol/cm s. You should now recognize why the term thermal diffusivity is used in certain versions of Eq. (4.2). 

Recall from the beginning of the chapter that a related quantity to the thermal conductivity is the thermal diffusivity, a, which is defined as k/pCp, where k is the thermal conductivity, p is the density and Cp is the heat capacity at constant pressure per unit mass, or specific heat. Below are these thermal properties for polycarbonate. 

In this equation the kinematic viscosity is v = fi/p, the thermal diffusivity is a = X/p-cp, and cp is the specific heat (per unit mass) at constant pressure. The Prandtl number is related to the Eucken factor as... 

Profiles of measured temperatures (°C) and silane density (in units of 1016 molecules / cm3) versus height above the surface (measured at this axial position) are found in the file silaneprofiles550C.csv. Plot measured and calculated gas-phase temperatures (at this axial position). Plot measured and calculated silane density profiles (with and without thermal diffusion). 

For thermal conductivity, the SI units are W/(m K). In laminar flow, the thermal conductivity, A, and the diffiisivity, D, are constant with respect to their respective gradients. Eqn. (3.4-3) indicates that the diffusion flux of solute [mol A/(m2 s)] is proportional to the transverse concentration gradient, with D as the proportionality constant. The dimensions of D are length2/ time, and its units are m2/s in the SI. Eqn. (3.4-2) states that the heat flux [in J/ (m2.s) = W/m2] is proportional to the temperature gradient, with a constant a = A/(p cp) that is called the thermal diffusivity. Its dimensions are length2/time and its SI units are m2/s. Thus, it is not unexpected that the coefficient v = p/p has the same dimensions and units, m2/s. The coefficient v is called the kinematic viscosity, and it clearly has a more fundamental significance than the dynamic viscosity. The usual unit for kinematic viscosity is the Stokes (St) and submultiples such as the centistokes (cSt). In many viscometers, readings... 

Equality of the thermal diffusivity (the ratio of thermal conductivity to heat capacity per unit volume) and the diffusion coefficients of the substances. 

The supersaturation in condensers arises for two reasons. First, the condensable vapor is generally of higher molecular weight than the noncondensable gas. This means that the molecular diffusivity of the vapor will be much less than the thermal diffusivity of the gas. Restated, the ratio of NSc/Npr is greater than 1. The result is that a condenser yields more heat-transfer units dTg/(Tg — Tt) than mass-transfer units dYg/(Yg — Yt). Second, both transfer processes derive their driving force from the temperature difference between the gas Tg and the interface Tt. Each incremental decrease in interface temperature... 

Fig. 3 Mass and thermal diffusion coefficients D and Z>r as functions of reduced temperature . Literature PCS data for D taken from Meier [8] and Sato [92] (scattering angle 60° (open diamond) and 130° (open square)). See text for a discussion of the fit functions. Also shown Dj (upper curve, right y-axis) for the same temperature range together with fit function containing only thermal activation (dotted line). Open diamonds data with unclear error bars due to very long equilibration times. Note the different units of the two y-axes...

Figure 8 Analysis of the appropriate characteristic dimensions for specific heat transfer surface requirements in a chemical reactor exhibiting typical reaction rates. Da = Damkoehler number, NTU = number of thermal transfer units, Nu = Nusselt number, a = thermal diffusivity. (From Ref. 9.)... 

Technical solutions relating to selection of the thermal conversion unit design mainly depend on the results of analysis of various accident modes of the selected design, and estimates of diffusion flows (hydrogen flow to primary circuit and tritium flow to process circuit), i.e. on those problems which are connected with validation of possible failure as a result of intermediate circuit application. 

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