Dimensionless temperature

Domain Furnace or combustor type Dimensionless sink temperature Dimensionless firing density... 

Viscosity 11, r/R p. Density p Slip radius V, Momentum diffusivity 9, Dimensionless temperature Dimensionless axial coordinate... 

The following dimensionless quantities, i.e., dimensionless temperature, dimensionless heat flux, and dimensionless time and space variables are introduced as... 

Ratio of moles of solute to the total number of moles of all species in a mixture Independent of temperature -> Dimensionless quantity... 

Dimensionless group Dimensionless group Dimensionless concentration Peclet number for mass transfer Peclet number for heat transfer Dimensionless temperature Dimensionless length Activation energy group Dimensionless time... 

The temperature at which B changes sign is called the Boyle temperature Tg it occurs at roughly two-thirds of the critical temperature, Tg/T 2/3. The Boyle temperature is used in Figure 4.10 to make the plotted temperature dimensionless. To make B and C dimensionless, we use the Boyle volume which is defined by [20]... 

Schmidt number Sherwood number dimensionless time dimensionless fluid temperature initial dimensionless temperature distribution dimensionless soUd phase temperature dimensionless volume-averaged solid temperature scale for temperature change, K dimensionless external temperature rise dimensionless inlet temperature maximum dimensionless temperature in the solid maximum dimensionless internal temperature rise... 

The above equation is valid at low pressures where the assumptions hold. However, at typical reservoir temperatures and pressures, the assumptions are no longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the ideal gas law. In practice, it is convenient to represent the behaviour of these real gases by introducing a correction factor known as the gas deviation factor, (also called the dimensionless compressibility factor, or z-factor) into the ideal gas law ... 

Density is the most commonly measured property of a gas, and is obtained experimentally by measuring the specific gravity of the gas (density of the gas relative to air = 1). As pressure increases, so does gas density, but the relationship is non-linear since the dimensionless gas compressibility (z-factor) also varies with pressure. The gas density (pg) can be calculated at any pressure and temperature using the real gas law ... 

Figure A2.2.1. Heat capacity of a two-state system as a function of the dimensionless temperature, lc T/([iH). From the partition fimction, one also finds the Helmholtz free energy as...

The upper limit of the dimensionless variable Vp, is typically written in tenns of the Debye temperature 9, as... 

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Figure A2.5.4. Themiodynamic fimctions (i, n, and C as a fimction of temperature T at eonstant pressure and eomposition x = 1/2) for the two-eomponent system shown in figure A2.5.3. Note the diflferenee between these and those shown for the one-eomponent system shown in figure A2.5.2. The fiinetions shown are dimensionless as in figure A2.5.2. The dashed lines represent metastable extensions (superheating or supereooling) of the one-phase systems.

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. 

The physical properties of argon, krypton, and xenon are frequendy selected as standard substances to which the properties of other substances are compared. Examples are the dipole moments, nonspherical shapes, quantum mechanical effects, etc. The principle of corresponding states asserts that the reduced properties of all substances are similar. The reduced properties are dimensionless ratios such as the ratio of a material s temperature to its critical... 

F, Factor, ratio of temperature difference across tube-side film to overall mean temperature difference Dimensionless Dimensionless... 

Since each ratio is dimensionless, any consistent units may be employed in any ratio. The significance of the symbols is as follows t = temperature of the surroundings tb = initial uniform temperature of the body t = temperature at a given point in the body at the time 0 measured from the start of the heating or coohng operations k = uniform thermal conductivity of the body p = uniform density of the boc c = specific heat of the body hf = coefficient of total heat transfer between the surroundings and the surface of the body expressed as heat transferred per unit time per unit area of the surface per unit difference in temperature between surroundings and surface r = distance, in the direction of heat conduction, from the midpoint or midplane of the body to the point under consideration / = radius of... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

The dimensional equations are usually expansions of the dimensionless expressions in which the terms are in more convenient units and in which all numerical factors are grouped together into a single numerical constant. In some instances, the combined physical properties are represented as a linear function of temperature, and the dimension equation resolves into an equation containing only one or two variables. 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

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