Heat-transfer coefficients special cases

A sufficient condition that the RI be determined by a vertex critical point is that the feasible region R be convex. (Of course, a special case of this is when all the feasibility constraints are linear see Section III,B.) Unfortunately, when flow rates or heat transfer coefficients are included in the uncertainty range, the feasible region can be nonconvex (see Examples 1 and 2 and Section III,C,3). Thus, current algorithms for calculating the RI are limited to temperature uncertainties only. 

A special case is that of a cyclone reactor in which the reacting particles flow against its heated walls. The heat transfer coefficient hjj, is estimated close to 2700 W m K" [31] and hence ... 

Here aB is the heat transfer coefficient for nucleate boiling from section 4.2.6, and ac is that for forced, single phase flow, sections 3.7.4 and 3.9.3 The special case of S = F = 1 in saturated boiling heat transfer is included in the equations above. The factors S (suppression factor) and F (enhancement factor) are yielded from... 

Certain heat-transfer processes, notably nucleate boiling, do not follow the proportionality described above. Nevertheless, the concept of a film heat-transfer coefficient is so convenient for practical computation that it is often used in these cases. Special care is required to ensure that the heat flux, the temperature difference, and the coefficient are consistent. 

The heat transfer coefficient defined by Eq. 1.12 is sensitive to the geometry, to the physical properties of the fluid, and to the fluid velocity. However, there are some special situations in which h can depend on the temperature difference NT = T - Tf. For example, if the surface is hot enough to boil a liquid surrounding it, h will typically vary as AT2 or in the case of natural convection, h varies as some weak power of AT— typically as AT1 4 or AT1 3. It is important to note that Eq. 1.12 as a definition of h is valid in these cases too, although its usefulness may well be reduced. 

This jacket is considered a special case of a helical coil if certain factors are incorporated into equations for calculating outside-film coefficients. In the equations at left and below, the equivalent heat transfer diameter D. for a rectangular cross-section IS equal to four times the width of the annular space, w and IS the mean or centerline diameter of the coil helix. Velocities are calculated from the actual cross-section of the flow area. pw. where p IS the pitch of the spiral baffle, and from the effective mass flowrate. W. through the passage. The leakage around spiral baffles is considerable, amounting to 35-50% of the total mass flowrate. The effective mass flowrate is about 60% of the total mass flowrate to the jacket W =... 

Whenever the kinetics of a chemical transformation can be represented by a single reaction, it is sufficient to consider the conversion of just a single reactant. The concentration change of the remaining reactants and products is then related to the conversion of the selected key species by stoichiometry, and the rates of production or consumption of the various species differ only by their stoichiometric coefficients. In this special case, the combined influence of heat and mass transfer on the effective reaction rate can be reduced to a single number, termed the catalyst efficiency or effectiveness factor rj. From the pioneering work of Thiele [98] on this subject, the expressions pore-efficiency concept and Thiele concept have been coined. 

The forced convection heat transfer problem [Eq. (9-7) plus boundary conditions] is linear in 6, but it still cannot be solved exactly (except for special cases) for Pe > 0(1) because of the complexity of the coefficient u. What may appear surprising at first is that simplifications arise in the limit Pe 1, which allow an approximate solution even though no analytic solutions (exact or approximate) are possible for intermediate values of Pe. This is surprising because the importance of the troublesome convection term, which is... 

On the left-hand side is the heat flux Cht, liie surface coefficient of heat transfer, is an empirical constant that depends very much on the nature of the heat transport as well as on the surface structure, in case of two solid bodies on the contact pressure, and on the presence and nature of a fluid medium (gas or liquid) between the two bodies. This is of importance in calorimeters in which the tested substance is put into special containers (crucibles) that are then placed inside the calorimeter. If no measures are taken to ensure well-defined, reproducible heat transfer, the temperature difference involved in the heat exchange between the measuring system and the sample (or respectively, the crucible) may differ from one measurement to another, so variations will occur in the temperature as shown by the sensor relative to the actual temperature of the sample. As a consequence, the measured heat quantity may also differ, leading to an uncertainty of the result. 

Furthermore, Figures 5.12 and 5.13 can also be used to show the dimensionless concentration as a function of dimensionless time and position for the case in which there is resistance to mass transfer at the interface between a solid and a fluid —Bab (9Ca/9z) = kc (Ca, — Caoo), where kc is the convective mass transfer coefficient (Section 4.4), Ca, is the concentration of species A at the interface in the fluid side, and Caoo is the concentration of species A in the fluid far away from the interface. Note that the constant concentration boundary condition referred to in the previous paragraph could be considered as a special case of the convective-type boundary condition for a Sherwood number, Sh (or Nusselt number for diffusion), equal to oo. Also, in Figures 5.12 and 5.13, the Biot (or Nusselt) number for heat transfer should be replaced by kcb/BAB) (l/ ) = (Sh/AT) = Sh, where K is the ratio of the equilibrium concentration in the solid to the... 

---