Fluid properties variation with temperature

Other experimental studies for polymer solutions involved the work of Bassett and Welty [97], Popovska and Wilkinson [99], and Joshi and Bergles [103]. The first of these dealt with the thermal entry region and a constant wall flux. Popovska and Wilkinson used a numerical solution of the energy equation to test experimental data over Graetz numbers that ranged from 80 to 1600. Joshi and Bergles used a constant wall flux and correlated for power law fluids the effect of fluid property variation with temperature. 

As mentioned above, because of the large temperature variations that often exist in flows in whiA viscous dissipation is important, there can be large variations in the fluid properties across such flows.Tn dealing with external flows in which the effects of viscous dissipation are not important, fluid property variations can usually bead-... 

Nonuniform Surface Temperature. Nonuniform surface temperatures affect the convective heat transfer in a turbulent boundary layer similarly as in a laminar case except that the turbulent boundary layer responds in shorter downstream distances The heat transfer to surfaces with arbitrary temperature variations is obtained by superposition of solutions for convective heating to a uniform-temperature surface preceded by a surface at the recovery temperature of the fluid (Eq. 6.65). For the superposition to be valid, it is necessary that the energy equation be linear in T or i, which imposes restrictions on the types of fluid property variations that are permitted. In the turbulent boundary layer, it is generally required that the fluid properties remain constant however, under the assumption that boundary layer velocity distributions are expressible in terms of the local stream function rather than y for ideal gases, the energy equation is also linear in T [%]. 

Finally, it is important to highlight that the results presented here are valid under the hypothesis of thermophysical properties being independent of temperature. On the contrary the variation with temperature, especially for the fluid viscosity, cannot be ignored in particular for low Reynolds numbers when, for a prescribed wall heat flux, there is a strong temperature rise between the inlet and the outlet of the microchannel. Since the viscosity tends to decrease when the temperature increases, the viscous dissipation effects calculated by using the proposed constant properties model could be overestimated. 

The fluid viscosity and thermal conductivity experience the largest variation with temperature. Compared with the density and the specific heat variation, their influence on heat transfer is significantly higher, e.g. in the case of water. Therefore, density and thermal conductivity can in most cases be considered to be constant The fluid property variation becomes more important with decreasing diameter, where the axial variation is more pronounced than the variation over the cross-section of the channel. In contrast to the viscous dissipation, the significance of property variations increases with decreasing Br [53]. 

Table 7.12 Variations with temperature of wash and feed fluid properties.

This chapter discusses the electrolytic-solution properties of low-di-electric-constant nematic solvents. Dissolved substances, if electrolytes, can contribute only a fraction of their ions to the conductance because of equilibrium between the free ions and ion pairs. If the solute forms ions through intermediate charge-transfer reactions, additional equilibria must be considered. For nematics, the solvent fluidity is anisotropic, and the conductance depends on the direction of current flow with respect to the orientation of the fluid. The variation of the conductance with temperature is directly related to the variation with temperature of both the ionic equilibrium and the fluidity. 

Taking the fluid properties at 310 K and assuming that fully developed flow exists, an approximate solution will be obtained neglecting the variation of properties with temperature. 

An even more useful property of supercritical fluids involves the near temperature-independence of the solvent viscosity and, consequently, of the line-widths of quadrupolar nuclei. In conventional solvents the line-widths of e. g. Co decrease with increasing temperature, due to the strong temperature-dependence of the viscosity of the liquid. These line-width variations often obscure chemical exchange processes. In supercritical fluids, chemical exchange processes are easily identified and measured [249]. As an example. Figure 1.45 shows Co line-widths of Co2(CO)g in SCCO2 for different temperatures. Above 160 °C, the line-broadening due to the dissociation of Co2(CO)g to Co(CO)4 can be easily discerned [249]. 

The Reynolds analogy assumes no mixing with adjacent fluid and that turbulence persists right up to the surface. Further it is assumed that thermal and kinematic equilibria are reached when an element of fluid comes into contact with a solid surface. No allowance is made for variations in physical properties of the fluid with temperature. 

The present book is concerned with methods of predicting heat transfer rates. These methods basically utilize the continuity and momentum equations to obtain the velocity field which is then used with the energy equation to obtain the temperature field from which the heat transfer rate can then be deduced. If the variation of fluid properties with temperature is significant, the continuity and momentum equations... 

We now turn attention to a completely different kind of supercritical fluid supercritical water (SCW). Supercritical states of water provide environments with special properties where many reactive processes with important technological applications take place. Two key aspects combine to make chemical reactivity under these conditions so peculiar the solvent high compressibility, which allows for large density variations with relatively minor changes in the applied pressure and the drastic reduction of bulk polarity, clearly manifested in the drop of the macroscopic dielectric constant from e 80 at room temperature to approximately 6 at near-critical conditions. From a microscopic perspective, the unique features of supercritical fluids as reaction media are associated with density inhomogeneities present in these systems [1,4],... 

The high compressibility of sc-fluids allows continuous variation of their densities and related properties from gaseous to liquid-like values with comparatively small variations in temperature and/or pressure. In this way, the positions of equilibria and the rates of chemical reactions can be continuously changed ( reaction tuning ), as shown by the following two examples. 

The fluid temperature in the thermal boundary layer varies from T, at the surface to about 7V, at the outer edge of the boundary. The fluid properties also vary with temperature, and thus with position across the boundary layer. In order to account for the variation of the properties with temperature, the fluid properties are usually evaluated at the so-callcd film temperature, defined as... 

In heat transfer studies, the primary variable is temperature, and it is desirable to express the net buoyancy force (Eq. 9-2) in terms of temperature differences. But this requires expressing the density difference in terms of a temperature difference, which requires a knowledge of a property that represents the variation of the density of a fluid with temperature atconstant pressure. The property that provides that information is the volume expansion coefficient /3, defined as (Fig. 9-4)... 

Silver iodide exhibits an unusual property. In addition to a y-(blende) form and a -(wurtzite) form it has an a-form stable between 146° and 552° (the m.p.). In this the iodide ions are arranged in a body-centred cubic lattice but the Ag+ ions form what may be called an interstitial fluid, being apparently free to move through the rigid network of 1 ions. The variation of conductance with temperature in silver iodide (Table 23) is particularly interesting. 

Finally, the properties of the fluid—viscosity, thermal conductivity, specific heat, and density—are important parameters in heat transfer. Each of these, especially viscosity, is temperature dependent. Since the temperature varies from point to point in a flowing stream undergoing heat transfer, a problem appears in the choice of temperature at which the properties should be evaluated. For small temperature differences between fluid and wall and for fluids with weak dependence of viscosity on temperature, the problem is not acute, but for highly viscous fluids such as heavy petroleum oils or where the temperature difference between the tube wall and the fluid is large, the variations in fluid properties within the stream become large, and the difficulty of calculating the heat-transfer rate is increased. 

Ideal Gases at High Temperature. Three fundamentally different approaches have been applied to the treatment of the turbulent boundary layer with variable fluid properties all are restricted to air behaving as an ideal, calorically perfect gas. First, the Couette flow solutions have been extended to permit variations in viscosity and density. Second, mathematical transformations, analogous to Eq. 6.36 for a laminar boundary layer, have been used to transform the variable-property turbulent boundary layer differential equations into constant-property equations in order to provide a direct link between the low-speed boundary layer and its high-speed counterpart. Third, empirical correlations have been found that directly relate the variable-property results to incompressible skin friction and Stanton number relationships. Examples of the latter are reference temperature or enthalpy methods analogous to those used for the laminar boundary layer, and the method of Spalding and Chi [104]. 

With a thermal resistance heat flux sensor, the presence of the instrument in the environment will disturb the temperature field somewhat and introduce an error in the measurement. Wall-heating systems require a heat source (or sink) and an appropriate heat balance equation to determine the heat flux. The temperature-transient types require a measurement of the temperature variation with time. The energy input or output types require good control or measurement of the temperature of the heat flux instrument. For the fourth type, the properties of the fluid are required. A brief discussion of different types of heat flux sensors is given below. 

Fig. 5. Variations with time and temperature of dynamic (mean square displacement) (a), (b), and thermodynamic (enthalpy) (c),(d) properties of simple dense fluids evaluated by MD runs of Umited time duration, showing partial failure to equilibrate at 7, and frozen or glassy-state behavior at 7 and 7. Note the change in heat capacity from liquidlike to solidlike values implied by the change of slope of H versus T in (d). 

Industrial analysers can control physical or chemical parameters. Physical parameter analysers (conductimeters, viscometers, refractometers, pressure and temperature meters) frequently measure and control only one property of the fluid, the variation of which generally depends on a single component that is controlled In an indirect fashion. Chemical parameter analysers directly measure the concentration of one or more species In a fluid. They can be specific for a given species (e.g. pH-meters, potentiometers with Ion-selective electrodes, oxygen meters) or control several species simultaneously (e.g. gas or liquid chromatographs) or successively (photometers) with minimum alterations. 

It must be remembered, however, that the above methods for calculating cellular flow patterns are valid only for infinitesimal amplitudes, because linear theory (which requires that disturbance flows grow exponentially without limit) cannot by itself predict the final steady flows which are established. On the other hand, flows of macroscopic amplitudes would require consideration of the nonlinear terms in the equations of motion and perhaps the variation of fluid properties with temperature. Still, researchers have persisted in... 

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