Kinematic heating

Velocity and temperature gradients are confined to the surface layer defined by z < I-. Above L the wind velocity and potential temperature are virtually uniform with height. Venkatram (1978) has presented a method to estimate the value of the convective velocity scale w,. On the basis of this method, he showed that convective conditions in the planetary boundary layer are a common occurrence (Venkatram, 1980). In particular, the planetary boundary layer is convective during the daytime hours for a substantial fraction of each year ( 7 months). For example, for a wind speed of 5 m sec , a kinematic heat flux Qo as small as O.PC sec can drive the planetary boundary layer into a convective state. 

The heavy fuel should be heated systematically before use to improve its operation and atomization in the burner. The change in kinematic viscosity with temperature is indispensable information for calculating pressure drop and setting tbe preheating temperature. Table 5.20 gives examples of viscosity required for burners as a function of their technical design. 

For the refiner, the main problem is to meet the specifications for kinematic viscosity and sulfur content. Dilution by light streams such as home-heating oil and LCO, and selection of feedstocks coming from low-sulfur crude oils give him a measure of flexibility that will nevertheless lead gradually to future restrictions, most notably the new more severe antipollution rules imposing lower limits on sulfur and nitrogen contents. 

Rheology. PVP solubihty in water is limited only by the viscosity of the resulting solution. The heat of solution is — 16.61 kJ/mol (—3.97 kcal/mol) (79) aqueous solutions are slightly acidic (pH 4—5). Figure 2 illustrates the kinematic viscosity of PVP in aqueous solution. The kinematic viscosity of PVP K-30 in various organic solvents is given in Table 13. 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

Temperature rc) Humidity kg HjO/kg dry air) Water vapor partial pressure (kPa) Water v K>r partial density (kg/m ) Water vaporization heat M/kg) Mixture enthalpy (kj/kg dry air) Dry air partial density (lKinematic viscosity (I0< mJ/s) Specific heat (kJ/K kg) Heat conductivity (W/m K) Diffusion factor water air (1 O mJ/s) Temperature rc)... 

Here, D is the diffusion constant for heat or material and the kinematic viscosity of the liquid. A consequence of the existence of such a diffusive surface barrier is that the diffusion length = D/F is to be replaced by in all formulas, as soon as growth rate V the more important become the hydrodynamic convection effects. 

Similarity for scale up, 312, 313 Dynamic, 313 Geometric, 312, 313 Kinematic, 313 Turbulence, 323 Mixing heat transfer... 

It may be noted that many of these dimensionless groups are ratios. For example, the Nusselt group h/(k/l) is the ratio of the actual heat transfer to that by conduction over a thickness l, whilst the Prandtl group, (p/p)/(k/Cpp) is the ratio of the kinematic viscosity to the thermal diffusivity. 

It is thus seen that the kinematic viscosity, the thermal diffusivity, and the diffusivity for mass transfer are all proportional to the product of the mean free path and the root mean square velocity of the molecules, and that the expressions for the transfer of momentum, heat, and mass are of the same form. 

In the buffer zone the value of d +/dy+ is twice this value. Obtain an expression for the eddy kinematic viscosity E in terms of the kinematic viscosity (pt/p) and y+. On the assumption that the eddy thermal diffusivity Eh and the eddy kinematic viscosity E are equal, calculate the value of the temperature gradient in a liquid flowing over the surface at y =15 (which lies within the buffer layer) for a surface heat flux of 1000 W/m The liquid has a Prandtl number of 7 and a thermal conductivity of 0.62 W/m K. 

Section V, other quantum effects are indeed present in the theory and we will discuss how these contribute both to the deviation of the conductivity from the law and to the way the heat capacity differs from the strict linear dependence, both contributions being in the direction observed in experiment. Finally, when there is significant time dependence of cy, the kinematics of the thermal conductivity experiments are more complex and in need of attention. When the time-dependent effects are included, both phonons and two-level systems should ideally be treated by coupled kinetic equations. Such kinetic analysis, in the context of the time-dependent heat capacity, has been conducted before by other workers [102]. 

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

In summary, the rheological studies of PATE are consistent with a proposed molecular association model for PATE solutions. Kinematic viscosity evaluation shows that at concentrations of 15% to 20% solids, a gelatinous solution results. The apparent viscosity measurements illustrate that network formation can be overcome by heating indicating that the association is electrostatic in nature. 

Figure 3. Dependency of kinematic viscosity on time since removal of heat...

The kinematic viscosity of a typical No. 6 fuel oil declines from 5000 mmVs (0.054 ftVs) at 298 K (77°F) to about 700 mmVs (0.0075 ff/s) and 50 mmVs (0.000538 ftVs) on heating to 323 K (122°F) and 373 K (212°F), respectively. Viscosity of 1000 mmVs or less is required for manageable pumping. Proper boiler atomization requires a viscosity between 15 and 65 mmVs. 

Relaxing the restriction of low Reynolds number, Rimmer (1968,1969) used a matched asymptotic expansion technique to develop a solution in terms of Pe and the Schmidt number Sc (or Prandtl number Pr for heat transfer), where Sc = v/D.j and Pr = v/a in which v is the kinematic viscosity of the flowing fluid. His solution, valid for Pe < 1 and Sc = 0(1), is... 

---