Relative convection

Before leaving this discussion, it is important to note that other forms of Peclet numbers are also possible and may be more appropriate depending on the type of convective influence studied. For example, in the case of oscillatory flows (as in oscillatory viscometers), it is more useful to define the Peclet number as (Rfa/D), where co is the frequency of oscillation. Regardless of the particular definition, the general significance of the Peclet number remains the same, i.e., it compares the effect of convection relative to diffusion. 

There are two types of convection, free and forced (Holman, 2009 Incropera et al., 2007 Kreith and Bohn, 2007). Free (natural) convection occurs when the heat transferred from a leaf causes the air outside the unstirred layer to warm, expand, and thus to decrease in density this more buoyant warmer air then moves upward and thereby moves heat away from the leaf. Forced convection, caused by wind, can also remove the heated air outside the boundary layer. As the wind speed increases, more and more heat is dissipated by forced convection relative to free convection. However, even at a very low wind speed of 0.10 m s-1, forced convection dominates free convection as a means of heat loss from most leaves (0.10 m s-1 = 0.36 km hour-1 = 0.22 mile hour-1). We can therefore generally assume that heat is conducted across the boundary layer adjacent to a leaf and then is removed by forced convection in the surrounding turbulent air. In this section, we examine some general characteristics of wind, paying particular attention to the air boundary layers adjacent to plant parts, and introduce certain dimensionless numbers that can help indicate whether forced or free convection should dominate. We conclude with an estimate of the heat conduction/convection for a leaf. 

For a given fluid, it is observed that the parameter Gi/Re represents the importance of natural convection relative to forced convection. This is not surprising since the convection heat transfer coefficient is a strong function of the Reynolds number Re in forced convection and the Grashof number Gr in natural convection. 

Changes in microstructure of the suspension become important when the diffusion time fj becomes long compared to the characteristic time of the process, fp. This number hcis been discussed earlier as the De number. The importance of convection relative to diffusion is compared in the Peclet number Pe (in which u is the fluid velocity). The importance of convection forces relative to the dispersion force is compared in Nf just as the dispersion force compared to the Brownian force. The electrical force compared to the dispersion or Brownian force is given by N. The particle size compared to the range of the electrical force is compared in UK. 

The magnitude of the Peclet number indicates the importance of the convective relative to the diffuse process for solute transport. The solute concentration profiles for representative values of Pe are illustrated in Fig. 12.2 according to Bungay [7]. When diffusion is dominant (Pe 0) the concentration varies nearly linearly in z. For large absolute values of the Peclet number, diffusion is significant only in a thin zone adjacent to the low pressure face of the membrane in which the concentration profile is very steep. For micro- and ultrafiltration membranes, the solute concentration varies little from the value at high pressure face. For nanofiltration the Peclet number can vary considerably depending on membrane characteristic almost dense or porous membranes. 

Evaluate the heat loss by natural convection, forced convection, and radiation from a flat plate at a uniform temperature Tm to ambient air or water at a temperature Tm. The temperature difference between the wall and ambient is 100 K. The heat transfer coefficients for natural and forced convection in air are 10 and 200 W/mz-K, and in water are 500 and 10,000 W/m2 -K, respectively. Plot the various heat losses from the plate as a function of Tm/ TW - Tm) for To, = 0,400,800, and 1200 K. Note the effect of convection relative to radiation as a function of temperature. 

The coefficient Xi is a correlation function that describes the rate of increase of the effective thermal conductivity with flow velocity, Pe is the P6clet number, which describes the contribution of forced convection relative to hydrogen heat conduction, is the velocity at the centerline of the bed, ave is the average velocity, fir) describes the radial variation in dispersion, and... 

Fluidized heds (direct convection), relatively insensitive, solutions, crystals and melts. Inlet temp about 400-500 °C AT = 150-300 °C solids residence or drying time, 30-250 s. Mass air/mass water evaporated = 10-100 evaporation rate = 0.005-0.4 kg water evaporated/s m. Solids holdup 10-30 kg solids/m. ... 

The Peclet number provides a measure of the importance of thermal convection relative to thermal conduction. The Peclet number in polymer processing is often quite large, typically of the order of 10= to 10 This indicates that convective heat transport is often quite important in polymer melt flow. 

As discussed in Sect. 5.6, the Peclet number in the diffusion Pep denotes the ratio of the mass transported by convection relative to the mass transported by diffusion. In the HA for the pure smectitic bentonite, the normalized length L of (5.142) is... 

Eurther research on convective transport under low Reynolds number, quasicontinuum conditions is needed before the optimal design of such a micro heat exchanger is possible. The cooling heat exchanger is usually thermally linked to a relatively massive substrate. The effects of this linkage need to be explored and accurate methods of predicting the heat-transfer and pressure-drop performance need to be developed. 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

An estimate of the relative importance of convection and radiation can be obtained from the ratio of the radiation-to-convection transfer rates. This dimensionless number reduces to... 

The life persistency of a smoke cloud is deterrnined chiefly by wind and convection currents in the air. Ambient temperature also plays a part in the continuance or disappearance of fog oil smokes. Water vapor in the air has an important role in the formation of most chemically generated smokes, and high relative humidity improves the performance of these smokes. The water vapor not only exerts effects through hydrolysis, but it also assists the growth of hygroscopic (deliquescent) smoke particles to an effective size by a process of hydration. Smoke may be generated by mechanical, thermal, or chemical means, or by a combination of these processes (7). 

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

Convection is the transfer of heat from one point to another within a fluid, gas, or liquid by the mixing of one portion of the fluid with another. In natural convection, the motion of the flmd is entirely the result of differences in density resiilting from temperature differences in forced convection, the motion is produced by mechanical means. When the forced velocity is relatively low, it should be reahzed that Tree-convection factors, such as density and temperature difference, may have an important influence. 

Heat is transferred by radiation, condurtion, and convection. Radiation is the primaiy mode and can occur even in a vacuum. The amount of heat transferred for a given area is relative to the temperature differential and emissivity from the radiating to the absorbing surface. Conduction is due to molecular motion and occurs within... 

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