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Research Papers: Conduction

J. Heat Transfer. 2017;139(12):121301-121301-10. doi:10.1115/1.4037081.

Estimation of thermal properties or diffusion properties from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Bodies of infinite extent are a particular challenge from this perspective. Even for exact analytical solutions, because the solution often has the form of an improper integral that must be evaluated numerically, lengthy computer-evaluation time is a challenge. The subject of this paper is improving the computer evaluation time for exact solutions for infinite and semi-infinite bodies in the cylindrical coordinate system. The motivating applications for the present work include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. In this paper, the computer evaluation time is improved by replacing the integral-containing solution by a suitable finite-body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized, by a suitable choice of the extent of the finite body. The key finding of this paper is that the resulting series may be accurately evaluated with a fixed number of terms at any value of time, which removes a long-standing difficulty with series solution in general. The method is demonstrated for the one-dimensional case of a large body with a cylindrical hole and is extended to two-dimensional geometries of practical interest. The computer-evaluation time for the finite-body solutions are shown to be hundreds or thousands of time faster than the infinite-body solutions, depending on the geometry.

Commentary by Dr. Valentin Fuster

Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2017;139(12):121501-121501-11. doi:10.1115/1.4037062.

Characterization of wavy film heat and mass transfer is essential for numerous energy-intensive chemical and industrial applications. While surface tension is the underlying cause of film waviness, widely used correlations for falling-film heat transfer do not account for surface tension magnitude as a governing parameter. Furthermore, although the effect of Prandtl number on wavy falling-film heat transfer has been highlighted in some studies, it is not included in most published Nusselt number correlations. Contradictory trends for Nusselt number variation with Prandtl number are found in correlations that do account for such effects. A systematic simulation-based parametric study is performed here to determine the individual effects of Reynolds, Prandtl, capillary, and Jakob numbers on heat transfer in laminar-wavy falling-films. First-principles based volume-of-fluid (VOF) simulations are performed for wavy falling condensation with varying fluid properties and flow rates. A sharp surface tension volumetric force model is employed to predict wavy interface behavior. The numerical model is first validated for smooth falling-film condensation heat transfer and wavy falling-film thickness. The simulation approach is applied to identify Nusselt number trends with Reynolds, Prandtl, capillary, and Jakob numbers. Finally, based on the collected simulation data, a new Nusselt number correlation for laminar-wavy falling-film condensation is proposed.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2017;139(12):121701-121701-15. doi:10.1115/1.4037080.

To find the reasons of heat transfer enhancement of a laminar convective heat transfer process in a channel at a uniform heat flux boundary when a pair of longitudinal vortex generators (VGs) is mounted on the bottom wall, the laminar convective heat transfer process in the channel is investigated numerically in a frame built up by the convective transport equation of the heat flux. The results show that longitudinal vortices greatly increase the local convection contribution terms that determine the local intensity of the convective transport of the heat flux component in the span direction, and that the increased local contribution terms intensify the local convective transport of the heat flux component in the same direction. This process increases the convection contribution terms that determine the convective transports of the heat flux components in the main stream direction and in the normal direction of the channel walls. The increase in these convection contribution terms results in an enhancement of the convective heat transfer ability on the channel walls, and then, the heat transfer is enhanced by longitudinal vortices. When the span-averaged characteristic is numerically counted, longitudinal vortices are found to have no contribution on the span-averaged convective transport of the heat flux in the span direction.

Commentary by Dr. Valentin Fuster

Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2017;139(12):122001-122001-10. doi:10.1115/1.4036871.

The influence of airflow shear on the free surface deformation and the flow structure for large Prandtl number fluid (Pr = 111.67) has been analyzed numerically as the parallel airflow shear is induced into the surrounding of liquid bridge from the lower disk or the upper disk. Contrasted with former studies, an improved level set method is adopted to track any tiny deformation of free surface, where the area compensation is carried out to compensate the nonconservation of mass. Present results indicate that the airflow shear can excite flow cells in the isothermal liquid bridge. The airflow shear induced from the upper disk impulses the convex region of free interface as the airflow shear intensity is increased, which may exceed the breaking limit of liquid bridge. The free surface is transformed from the “S”-shape into the “M”-shape as the airflow shear is induced from the lower disk. For the nonisothermal liquid bridge, the flow cell is dominated by the thermocapillary convection at the hot corner if the airflow shear comes from the hot disk, and another reversed flow cell near the cold disk appears. While the shape of free surface depends on the competition between the thermocapillary force and the shear force when the airflow is induced from the cold disk.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(12):122002-122002-8. doi:10.1115/1.4036872.

This paper investigates the effects of thermocapillarity on the flow and heat transfer in power-law liquid film over an unsteady stretching sheet. The surface tension is assumed to vary linearly with temperature, and the thermal conductivity of the fluid is assumed power-law-dependent on the velocity gradient with modified Fourier's law. The local similarity solutions are obtained numerically, and some interesting new phenomena are found. Results indicate that the thermally induced surface tension provides an opposite force in the direction of the stretching sheet which may cause the fluid adjacent to the free surface to flow in the opposite directions. The effect of thermocapillarity tends to decrease the thin film thickness and results in a smaller temperature distribution. With the increasing unsteadiness parameter, the thin film thickness has a local maximum, and thermal boundary layer is confined to the lower part of the thin film for bigger Prandtl number, while the temperature in the thin film remains equal to the slit temperature with Prandtl number close to 0.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(12):122003-122003-8. doi:10.1115/1.4036735.

Conventional first-principle approaches for studying nonequilibrium processes depend on the mechanics of individual particles or quantum states and as a result require many details of the mechanical features of the system to arrive at a macroscopic property. In contrast, thermodynamics, which has been successful in the stable equilibrium realm, provides an approach for determining macroscopic properties without the mechanical details. Nonetheless, this phenomenological approach is not generally applicable to a nonequilibrium process except in the near-equilibrium realm and under the local equilibrium and continuum assumptions, both of which limit its ability to describe nonequilibrium phenomena. Furthermore, predicting the thermodynamic features of a nonequilibrium process (of entropy generation) across all scales is difficult. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides a first-principle thermodynamic-ensemble based approach applicable to the entire nonequilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics, which crosses all temporal and spatial scales. Based on prior developments by the authors, SEAQT is used here to study the heat and mass diffusion of indistinguishable particles. The study focuses on the thermodynamic features of far-from-equilibrium state evolution, which is separated from the specific mechanics of individual particle interactions. Results for nonequilibrium size (volume) and concentration effects on the evolutionary state trajectory are presented for the case of high temperature and low particle concentration, which, however, do not impact the generality of the theory and will in future studies be relaxed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(12):122004-122004-7. doi:10.1115/1.4036982.

Presented here are the results of an experimental investigation of two ultrathin miniature loop heat pipes (mLHPs) with different internal wicking structures: one with a primary wicking structure in the evaporator and a secondary wicking structure in the liquid line, and the other only with the same primary wicking structure in the evaporator, but no secondary wick. The systematic experimental investigation was conducted using natural convection as the cooling mechanism in order to study the heat transfer performance of the two mLHPs and fully examine the effects of the secondary wick. The results indicated that both of the test articles could effectively dissipate 12 W at all test orientations with a minimum total thermal resistances of 6.38 °C/W and 6.39 °C/W, respectively. However, the results indicated that the presence of the secondary wicking structure in the liquid line at low power loads resulted in more stable startup characteristics and a weaker dependence on the different orientations. Moreover, it was demonstrated that the steady-state evaporator temperatures of the test article with the secondary wicking structure in the liquid line were much lower than those observed for a 1-mm thick copper plate with the same geometric dimensions for all heat loads in the horizontal orientation, showing a higher thermal performance.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(12):122005-122005-10. doi:10.1115/1.4036981.

A dynamic, partially permeable crack model for orthotropic materials is established with the crack full of thermal medium. Besides external thermal and elastic loadings, the heat flux generated by the crack interior full of a medium also contributes to the crack boundary conditions, which is dependent on the crack opening displacement. Thus, the heat conduction is dependent on elastic field. First, the heat conduction equation is solved exactly in terms of unknown heat flux of the crack interior. Then, the elastic field is presented for real or complex eigenvalue cases on the basis of the operator theory. Finally, the thermal and elastic fields are presented analytically, and the heat flux of the crack interior is determined explicitly. Numerical results are offered to show the influences of the thermal conductivity coefficient, normal and shear loadings and crack velocity on the distributions of the heat flux, temperature difference across the crack surfaces, and thermal stress intensity factor. Figures illustrate that increasing the crack velocity leads to a more thermally impermeable crack and produces a bigger temperature difference across the crack surfaces.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(12):122006-122006-10. doi:10.1115/1.4036600.

We develop a one-dimensional model for transient diffusion of gas between ridges into a quiescent liquid suspended in the Cassie state above them. In the first case study, we assume that the liquid and gas are initially at the same pressure and that the liquid column is sealed at the top. In the second one, we assume that the gas initially undergoes isothermal compression and that the liquid column is exposed to gas at the top. Our model provides a framework to compute the transient gas concentration field in the liquid, the time when the triple contact line begins to move down the ridges, and the time when menisci reach the bottom of the substrate compromising the Cassie state. At illustrative conditions, we show the effects of geometry, hydrostatic pressure, and initial gas concentration on the Cassie to Wenzel state transition.

Commentary by Dr. Valentin Fuster

Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2017;139(12):122501-122501-13. doi:10.1115/1.4036689.

A key subject of interest for technologies that involve flows of fluids at the supercritical thermodynamic state is the development of prediction methods that capture the fluid dynamics and convection heat transfer at this state. Due to the elevated temperatures and pressures associated with certain working fluids at this thermodynamic state, surrogate fluids are often used as substitutes for performing experiments during the design stages of prototype development. The success of this approach depends on the development of similarity criteria or fluid-to-fluid models. Similarity criteria for mixed-convection heat transfer in supercritical fluids are proposed based on a set of nondimensional dynamic similarity parameters and state-space parameters developed through our current understanding of the physical mechanisms that affect heat transfer in fluids at this state. The proposed similarity criteria are successfully validated using data from ducted flows of supercritical fluids with configurations having upstream, downstream, or wall-normal-oriented gravitational acceleration.

Commentary by Dr. Valentin Fuster

Research Papers: Two-Phase Flow and Heat Transfer

J. Heat Transfer. 2017;139(12):122901-122901-7. doi:10.1115/1.4037079.

An inorganic aqueous solution, known as IAS, has shown its compatibility with aluminum phase-change heat transfer devices. When using IAS in aluminum devices, aluminum prefers to react with the two oxidizers, permanganate and chromate, rather than water to generate a thin and compact layer of aluminum oxide, which protects the aluminum surface and prevents further reactions. In addition, an electrochemical theory of aluminum passivation is introduced, and the existence of an electrochemical cycle is demonstrated by an aluminum thermosiphon test. The electrochemistry cycle, built up by liquid back flow and tube wall, allows the oxidizers to passivate the aluminum surface inside the device without being directly in contact with it. However, failure was detected while using IAS in thermosiphons with air natural convection cooling. The importance of a continuous liquid back flow to aluminum passivation in phase-change heat transfer devices is pointed out, and a vertical thermosiphon test with natural convection cooling is used to demonstrate that a discontinuous liquid back flow is the main reason of the failures.

Commentary by Dr. Valentin Fuster

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