Heat diffusion during thin-film composite membrane formation

Thin-film composite (TFC) membranes, the backbone of modern reverse osmosis and nanofiltration, combine the high separation performance of a thin selective layer with the robust mechanical support. Previous studies have shown that heat released during interfacial polymerization (IP) can have a significant impact on the physical and chemical structure of the selective layer. In this study, we develop a multilayer transient heat conduction model to analyze how the thermal properties of the materials used in TFC fabrication impact interfacial temperature, focusing on support-free (SFIP), conventional (CIP), and interlayer-modulated IP (IMIP). Using a combination of analytic solutions and computational models, we demonstrate that the thermal effusivities of fluid and material layers can have a significant effect on the temporal evolution of interfacial temperature during IP. In CIP, we show that the presence of a polymeric support adjacent to the reaction interface yields a 20% to 60% increase in interfacial temperature rise, lasting for ∼ 0.1 s. Furthermore, we demonstrate that inorganic or metallic interlayers, which have high thermal effusivities, can lead to short-lived order-of-magnitude reductions in interfacial temperature rise. Finally, we provide analytical approximations for transient heat conduction through multilayered systems, enabling rapid evaluation of the thermal impact of novel membrane support and interlayer materials and structures on interfacial temperature during TFC fabrication. Quantifying how the thermal properties of solvents, support layers, and interlayers affect interfacial temperature during IP is critical for the rational design of new TFC membranes.

A. Deshmukh, J.H. Lienhard, and M. Elimelech, “Heat Diffusion During Thin-Film Composite Membrane Formation,” J. Membrane Science, 696:122493, March 2024. Editor’s Choice Article for March 2024. There are still fun things to do with classical heat conduction!

Heat transfer in flat-plate boundary layers: a correlation for laminar, transitional, and turbulent flow

The laminar and turbulent regimes of a boundary layer on a flat plate are often represented with separate correlations under the assumption of a distinct “transition Reynolds number.” Average heat coefficients are then calculated by integrating across the “transition point.” Experimental data do not show an abrupt transition, but rather an extended transition region in which turbulence develops. The transition region may be as long as the laminar region. Although this transitional behavior has been known for many decades, few correlations have incorporated it. One attempt was made by Stuart Churchill in 1976. Churchill, however, based his curve fit on some doubtful assumptions about the data sets. In this paper, we develop different approximations through a detailed consideration of multiple data sets for 0.7 ⩽ Pr ⩽ 257, 4,000 ⩽ Rex ⩽ 4,300,000, and varying levels of free stream turbulence for smooth, sharp-edged plates at zero pressure gradient. The result we obtain is in good agreement with the available measurements and applies smoothly over the full range of Reynolds number for either a uniform wall temperature or a uniform heat flux boundary condition. Fully turbulent air data are correlated to ±11%. Like Churchill’s result, this correlation should be matched to the estimated transition condition of any particular flow. We also review the laminar analytical solutions for a uniform wall heat flux, and we point out limitations of the classical Colburn analogy.

J.H. Lienhard V, “Heat transfer in flat-plate boundary layers: a correlation for laminar, transitional, and turbulent flow,” J. Heat Transfer, online 31 March 2020, 142(6):061805, June 2020. (doi: Open access) (presentation) (one-page summary) (DSpace)

Accurate linearization of non-gray radiation heat exchange

The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external,” radiation fractional function and an “internal” radiation fractional function. The latter is used for linearization of net radiation from a nongray surface when the temperature of an effectively black environment is not far from the surface’s temperature, without calculating a separate total absorptivity. This paper examines the analytical approximation involved in the internal fractional function, with results given in terms of the incomplete zeta function. A rigorous upper bound on the difference between the external and internal emissivity is obtained. Calculations using the internal emissivity are compared to exact calculations for several models and materials. A new approach to calculating the internal emissivity is developed, yielding vastly improved accuracy over a wide range of temperature differences. The internal fractional function should be used for evaluating radiation thermal resistances, in particular.

J.H. Lienhard V, “Linearization of Non-gray Radiation Exchange: The Internal Fractional Function Reconsidered,” J. Heat Transfer, online 3 Dec. 2018, 141(5):052701, May 2019. (OPEN ACCESS) (preprint) (presentation)