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The Linear Wave Equation and Fundamental Acoustical Quantities
Published in Lawrence J. Ziomek, Fundamentals of Acoustic Field Theory and Space-Time Signal Processing, 2020
where JX is assumed to be positive. Mass flow per unit cross-sectional area is also referred to as mass flux. Next, let us assume that there is a net influx of mass into the constant volume dV in the positive X direction, that is, more mass flows into the back side of dV than flows out of the front side. With the use of Eqs. (1.2-1) through (1.2-3), the net influx of mass into the constant volume dV in the positive X direction can be expressed as () (JXBK−JXF)dydz=−∂∂x(ρUX)dV,
Heat Transfer and Pressure Drop Characteristics of Forced Convective Evaporation in Deep Spirally Fluted Tubing
Published in John C. Chen, Yasunobu Fujita, Franz Mayinger, Ralph Nelson, Convective Flow Boiling, 2019
Scott M. MacBain, Arthur E. Bergles
Figures 6, 7, and 8 show the effect of mass flux on the heat transfer coefficient. They demonstrate that increasing mass flux has an inverse relationship with the transition quality for DNB. They also illustrate that increasing the mass flux increases the heat transfer coefficient in the convection-dominated regime. For mass fluxes of 250 and 400 kg/m2s, the data show that increasing mass flux has no appreciable affect on the heat transfer coefficient in the nucleate-boiling regime. This disagrees with the increase in heat transfer coefficient with increasing mass flux for smooth tubes over this range of quality predicted by the Kandlikar correlation (Figure 9). This seems to run counter to the notion that mass flux has little effect on established nucleate boiling; however, the correlation predicts that for this range of quality, established nucleate boiling has been suppressed, and a convection dominated regime exists. The data for the mass flux of 100 kg/m2s show a distinct decrease in the heat transfer from the 250 and 400 kg/m2s mass fluxes (Figure 8). A comparison with single-phase liquid data calculated from a similar tube studied by Marto et al. (1979), showed that the heat transfer coefficient for 100 kg/m2s was appreciably higher than that for single-phase liquid, indicating that it is still in the nucleate boiling regime. The explanation for the reduction in heat transfer coefficient at the lowest mass flux may lie with the location of these data on the boiling curve.
Transport Phenomena of Bioprocesses
Published in Debabrata Das, Debayan Das, Biochemical Engineering, 2019
This is the right point of the chapter to discuss, the most important entity associated with the mass transfer and that is mass transfer coefficient. This will be illustrated based on Fick’s second law. It states that the mass-transfer rate/area or the mass flux is directly proportional to the concentration difference. For a solute undergoing gas–liquid diffusion, one can write the mass flux of solute on the gas side as () NG=qGA∝(CG−CGi)
Electroosmosis modulated peristaltic transport of Carreau magneto-nanofluid with modified Darcy’s law
Published in Waves in Random and Complex Media, 2022
Yasir Akbar, Hammad Alotaibi, Umer Javed, Mehvish Naz, Mohammad M. Alam
Figure 8(a-d) delineate the consequences of Nt, Nb, M and We on concentration profile. There is a tendency toward a decrease in concentration with an increase in ‘Nt’ (see Figure 8(a)). The strength of thermophoretic effects increases gradually. This leads to more mass flux due to the concentration gradient. It lowers the concentration profile. However, the opposite behavior is noted for ‘Nb’ (see Figure 8(b)). Concentration enhances for larger ‘Nb’. Aggregation of nanomaterials offers better density with an increment in Brownian motion, which, in turn, enhances the concentration. Figure 8(b) exhibits that the concentration profile declines with an increment in ‘M’. Contrary to the previous case, concentration profile rises with a rise in ‘We’.
Modeling Of Heat Transfer Coefficients During Condensation At Low Mass Fluxes Inside Horizontal And Inclined Smooth Tubes
Published in Heat Transfer Engineering, 2021
Daniel Raphael Ejike Ewim, Mehdi Mehrabi, Josua Petrus Meyer
Details of previous experimental studies can be found in [1–22]. According to these studies, at high mass fluxes, the heat transfer coefficients are mass flux dependent. On the other hand, studies at low mass fluxes reveal that temperature differences between the condensing wall and saturation temperatures of the condensing fluids play a pivotal role in the overall heat transfer process. The challenge with experimental work is that it is usually expensive to carry out because of the nature of the equipment and instrumentation needed. Furthermore, it may be time consuming and challenging. On the other hand, computational fluid dynamics work [23,24] is also in the development phase and no study has yet coupled the effect of temperature difference and inclination on heat transfer at low mass fluxes.
Internal two-phase flow induced vibrations: A review
Published in Cogent Engineering, 2022
Samuel Gebremariam Haile, Elmar Woschke, Getachew Shunki Tibba, Vivek Pandey
The Mass Flux is defined as the mass flow rate of a phase per unit cross-sectional area occupied by that phase. It is denoted by G, where G = ρj, and ρ is the phase (liquid or gas) density. The total mass flux is given as G = GL + GG. Since G is the mass flow rate (in kg/s) divided by cross-sectional area (in m2), the SI units for G are kg-m−2s−1. The Volumetric Flux (or Superficial Velocity) for internal two-phase flow, is the volumetric flow rate per unit cross-sectional area of the pipe/conduit (compare this to the Mass Flux). It is denoted as jL or jG indicating the volumetric flux/superficial velocity of the liquid and gas phases, respectively. The measurement units for j are the same as the velocity, that is, m/s. The total superficial velocity is j = jL+ jG. The instantaneous, local velocities of the liquid and gas phases are denoted as uL and uG. The relative velocity between the phases is uL—uG. The Volume Fraction (Holdup) of a phase is the volume occupied by a phase to the total volume considered and is denoted by α. It follows that αL= 1 − αG. The Void Fraction is the volume of the gas phase for unit volume of the pipe. From the above definitions, it follows that the Volumetric Flux (or Superficial Velocity) of a phase has the following relation to its volume fraction, and its velocity. For example, for the gas phase, jG= αGuG. Therefore, the superficial velocity of a phase is the product of the phase volume fraction and the phase velocity. The Mass Fraction, xL, of the liquid phase is ρL α L/ρ. The Volumetric Quality of a phase is defined as the ratio of the Volumetric Flux of the phase (L or G) to the total volumetric flux. For the liquid phase, the Volumetric Quality for the liquid phase would be jL/j. The Mass Quality (or Quality), for the Liquid phase, χL, is the ratio of the liquid mass flux to the total mass flux, GL/G, or ρLjL/ρ j . The Drift Velocity, or Slip Velocity of a phase is defined as the velocity of that phase in a frame of reference moving at a velocity equal to the total volumetric flux, j. For example, the Drift Velocity for the Liquid phase (uLj) is written as uLj= uL−j.