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Research Papers: Heat Exchangers

# An Effectiveness–Number of Transfer Units Relationship for Evaporators With Non-negligible Boiling Point Elevation Increases

[+] Author and Article Information
Gregory P. Thiel

Mem. ASME
Rohsenow Kendall Heat and
Mass Transfer Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: gpthiel@alum.mit.edu

John H. Lienhard, V

Fellow ASME
Professor
Rohsenow Kendall Heat and
Mass Transfer Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: lienhard@mit.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 10, 2015; final manuscript received June 20, 2016; published online August 2, 2016. Assoc. Editor: Amitabh Narain.

J. Heat Transfer 138(12), 121801 (Aug 02, 2016) (8 pages) Paper No: HT-15-1721; doi: 10.1115/1.4034055 History: Received November 10, 2015; Revised June 20, 2016

## Abstract

An effectiveness number of transfer units (ε–NTU) model is developed for use in evaporators where the evaporating stream: (1) comprises a volatile solvent and nonvolatile solute(s) and (2) undergoes a significant, but linear change in boiling point elevation (BPE) with increasing solute molality. The model is applicable to evaporators driven by an isothermal stream (e.g., steam-driven or refrigerant-driven) in parallel flow, counterflow, and crossflow configurations where the evaporating stream is mixed. The model is of use in a variety of process engineering applications as well as the sizing and rating of evaporators in high-salinity desalination systems.

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## References

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## Figures

Fig. 1

The BPE for some common aqueous mixtures is linear over a wide range of concentrations; the data are adapted from Refs. [3032] and are at atmospheric pressure except for urea, which is at 3.17 kPa

Fig. 2

Differential control volume of an evaporating stream: the solution enters at position x, pure solvent is vaporized at a rate jv′ dx, and the concentrated solution leaves the control volume at position x + dx. The evaporation is driven by a heat transfer rate q′ dx.

Fig. 3

ε–NTU curves for saline evaporators: at low max recoveries (as γ approaches one), the evaporator behaves like a single stream heat exchanger; at lower γ, the temperature distribution is more nonlinear

Fig. 4

A schematic of the mass diffusion and heat transfer processes occurring in the film: a temperature difference (Tw−Ts(x)) drives solvent evaporation jv′ at the vapor–liquid interface, increasing the local (nonvolatile) solute concentration ωδ and driving a diffusive flux of solute jB′ back toward the film bulk

Fig. 5

Ratio of Nu with BPE effects and zero mass transfer resistance (Eq. (34)) to the classical Nusselt solution for an NaCl-like solution with ΔT°=10 K, hfgμ/4k=7.42×105, and Kb=17.1 K: the BPE effects are more pronounced at higher inlet concentrations and higher concentration factors, or higher Re0−ReL. The dashed green line, w0=0.035, represents seawater salinity.

Fig. 6

Ratio of Nu with BPE effects and finite mass transfer resistance (Eq. (47)) to the classical Nusselt solution for an NaCl-like solution with ΔT°=10 K, hfgμ/4k=7.42·105, Kb=17.1 K, and D=2×10−9 m/s: the BPE effects are again more pronounced at higher solute feed concentrations and higher concentration factors, or higher Re0−ReL. The dashed green line, w0=0.035, represents seawater salinity.

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