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### Research Papers: Conduction

J. Heat Transfer. 2017;139(8):081301-081301-11. doi:10.1115/1.4036099.

The most popular methods used for solving transient heat conduction problems, like finite element method (FEM) and boundary element method (BEM), require discretization of the domain or the boundary. The discretization problem escalates for unsteady issues, because an iterative process is required to solve them. An alternative to avoid the mentioned problem is parametric integral equations systems (PIESs), which do not require classical discretization of the boundary and the domain, while being numerically solved. PIES have been previously used with success to solve steady-state problems. Moreover, they have been recently tested also with success for transient heat conduction problems, without internal heat sources. The purpose of this paper is to generalize PIES based on analytical modification of classical boundary integral equation (BIE) for transient heat conduction with internal heat source and nonuniform rational basis spline (NURBS) for boundary modeling. The obtained generalization of PIES is tested on examples, mostly with defined exact solution.

Commentary by Dr. Valentin Fuster

### Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2017;139(8):081501-081501-13. doi:10.1115/1.4036075.

Several simple ways of improving the accuracy of Spalding model predictions over common textbook conventions for air/water evaporation/condensation problems are illustrated using open-literature examples. First is the choice of thermodynamic reference state for enthalpy evaluation. The common practice of choosing the steam table reference point (0.01 °C) with water-vapor enthalpy of hfg (2501 kJ/kg) and air enthalpy of zero introduces an enthalpy mismatch between air and water vapor that unnecessarily compromises accuracy. Choosing the air/water interface temperature as the reference point and setting both air and water-vapor enthalpies at this point to the same numerical value gives the most accurate results of several methods tried. Second is judicious choice of the blowing factor in high-rate mass transfer situations. The laminar boundary layer blowing factor is more accurate than the common stagnant-film (Couette flow) blowing factor for flat-plate flow and may be more accurate for a cylinder in crossflow under laminar conditions, as illustrated by the example of air leak effect on steam condenser tube performance. Third is radiation modeling, often a problematic or ignored feature in this type of problem. Two common, but opposite, assumptions about radiation participation in water—transparent interface and opaque interface—are shown to be equivalent for most purposes. A methodology is introduced for modeling true interfacial absorption/emission associated with phase change if/when the amount of this effect becomes known well enough to justify its inclusion. The importance of including radiation is illustrated by several examples: cloud droplet evaporation–condensation, sweat cooling, and the wet-bulb psychrometer. Fourth is inaccuracy introduced by unnecessarily setting Lewis number to unity.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2017;139(8):082001-082001-12. doi:10.1115/1.4036041.

The paper deals with the research of temperature fields in the proximity of heated pipes arranged above each other in a natural air convection. The holographic interferometry method was used for the visualization of temperature fields. The experiments were made with pipes, diameter of 20 mm, length 200 mm, spacing two-dimensional (2D) at surface temperatures of 40 °C, 50 °C, and 60 °C, with the vertical arrangement of the pipes as well as with the horizontal shift of their centers by 1/4D and 1/2D (on a surface temperature of 50 °C). Temperature profiles were determined from the experimentally obtained images of temperature fields, and local parameters of heat transfer were calculated. Under the same marginal and geometric conditions, computational fluid dynamics (CFD) simulations of temperature fields were performed as well, while the results (temperature fields, local and mean parameters of heat transfer) were also calculated for various distances between the pipe centers (1D, 2D, and 3D). From the obtained experimental results and CFD simulation results, it is possible to observe the impact of the arrangement and spacing of pipes on heat transfer parameters. The achieved results imply the change in the spacing of the pipes has a greater impact on heat transfer parameters in the bundle of heated pipes located above each other than a moderate horizontal shift of their centers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):082002-082002-13. doi:10.1115/1.4036057.

Thermal analysis of fluid flow is always regarded as an important research issue within cavities in order to become familiar with the characteristics of fluid flow phenomenon in enclosures. This research paper investigates the fluid and heat transfer analysis of fluid flow inside a triangular cavity using natural element methodology (NEM). This Galerkin-based methodology has been introduced for a decade and almost demonstrated its efficiency in the numerical heat transfer analysis of problems in most engineering sciences. The fluid flow contains natural convection along with conduction and radiation heat transfer with medium's walls, which have absorbing, emitting, semitransparent, and nonscattering characteristics. The final results investigate the effects of radiative and natural convection heat transfer on the fluid flow pattern as expressed in Rayleigh number, stream function, strength of natural convection regime, etc., which are checked with other similar studies presented in the literature and shows how promising NEM can be as an efficient numerical approach to improve computational precision when dealing with fluid mechanic problems.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):082003-082003-10. doi:10.1115/1.4036092.

Multilayered piezoelectric structures have special applications for vibration control, and they often serve in a thermoelastic coupling environment. In this work, the fractional-order generalized thermoelasticity theory is used to investigate the dynamic thermal and elastic behavior of a bilayer piezoelectric–thermoelastic plate with temperature-dependent properties. The thermal contact resistance is implemented to describe the interfacial thermal wave propagation. The governing equations for the bilayer piezoelectric–thermoelastic plate with temperature-dependent properties are formulated and then solved by means of Laplace transformation and Riemann-sum approximation. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. According to the numerical results, the effects of the thermal contact resistance, the ratio of the material properties between different layers, the temperature-dependent properties, and the fractional-order parameters on the distributions of the considered quantities are revealed in different cases and some remarkable conclusions are obtained. The investigation helps gain insights into the optimal design of actuators, sensors, which are made of piezoelectric materials.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):082004-082004-12. doi:10.1115/1.4036153.

This article presents a new method of estimation of thermophysical parameters using the hybrid Monte Carlo (HMC) algorithm that synergistically combines the advantages of a Markov chain Monte Carlo (MCMC) method and molecular dynamics. The advantages of this technique over the conventional MCMC are elucidated by considering the multiparameter estimation in heat transfer. Four situations were analyzed. The first two involve a two- and a three-parameters estimation in a lumped capacitance model, third involves estimation in a distributed system, and the fourth involves estimation in a fin system. The goal is to establish the potency and usefulness of the HMC method for a wide class of engineering problems.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):082005-082005-7. doi:10.1115/1.4036279.

This article is concerned with the class of solutions of gas boundary layer containing uniform, spherical solid particles over the surface of rotating axisymmetric round-nosed body. By using the method of transformed coordinates, the boundary layer equations for two-phase flow are mapped into a regular and stationary computational domain and then solved numerically by using implicit finite difference method. In this study, a rotating hemisphere is used as a particular example to elucidate the heat transfer mechanism near the surface of round-nosed bodies. We will investigate whether the presence of dust particles in carrier fluid disturbs the flow characteristics associated with rotating hemisphere or not. A comprehensive parametric analysis is presented to show the influence of the particle loading, the buoyancy ratio parameter, and the surface of rotating hemisphere on the numerical findings. In the absence of dust particles, the results are graphically compared with existing data in the open literature, and an excellent agreement has been found. It is noted that the concentration of dust particles’ parameter, Dρ, strongly influences the heat transport rate near the leading edge.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Transfer in Manufacturing

J. Heat Transfer. 2017;139(8):082101-082101-12. doi:10.1115/1.4036100.

The rapid growth in the number of data centers combined with the high-density heat dissipation of computer and telecommunications equipment has made energy efficient thermal management of data centers a key research area. Localized hybrid air–water cooling is one approach to more effectively control the cooling when there is wide variation in the amount of dissipation in neighboring racks while the traditional air cooling approach requires overprovisioning. In a closed, hybrid air–water cooled server cabinet, the generated heat is removed by a self-contained system that does not interact with the room level air cooling system. Here, a hybrid-cooled enclosed cabinet and all its internal components were characterized experimentally in steady-state mode (e.g., experimentally determined heat-exchanger effectiveness and IT characterization). Also, a comprehensive numerical model of the cabinet was developed and validated using the experimental data. The computational model employs full numerical modeling of the cabinet geometry and compact models to represent the servers and the air/water heat exchanger. The compact models were developed based on experimental flow and thermal characterization of the internal components. The cabinet level model has been used to simulate a number of operating scenarios relevant to data center applications such as the effect of air leakage within the cabinet. The effect of the air side and the water side failure of the cooling system on the IT performance were investigated experimentally. A comparison was made of the amount of time required to exceed the operating temperature limit for the two scenarios.

Commentary by Dr. Valentin Fuster

### Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2017;139(8):082201-082201-11. doi:10.1115/1.4036090.

In conventional jet impingement array heat sinks, all the spent coolant is extracted from component edges, resulting in cross-flow interference and nonuniform heat transfer. Jet impingement arrays with interspersed fluid extraction ports can reduce cross-flow, improving heat transfer uniformity and reducing pumping loads. While this configuration offers technical advantages, limited pressure drop and heat transfer data are available. In this investigation, simulations are performed for laminar single-phase jet impingement arrays with interspersed fluid extraction ports over varying flow rates (Rej = 20–500), fluid transport properties (Pr = 1–100), and geometries (jet pitch to diameter ratios of 1.8–7.1 and jet diameter to gap height ratios of 0.1–4.0). The simulation approach is validated for isolated jet impingement, and grid sensitivity studies are performed to quantify numerical uncertainty. Over 1000 randomized cases are evaluated to develop new correlations for Nusselt number and pressure-drop k-factors. Conjugate heat transfer studies are performed to compare heat sinks (5 × 5 mm heated, 500 W m−2 heat flux) employing jet arrays with interspersed fluid extraction ports, microchannels, and jet arrays with edge fluid extraction. The design with jet arrays with interspersed fluid extraction ports yields lower average temperatures, improved temperature uniformity, and modest pressure drops. This study provides new data for jet impingement thermal management and highlights the technical potential of configurations with interspersed fluid extraction ports.

Commentary by Dr. Valentin Fuster

### Research Papers: Melting and Solidification

J. Heat Transfer. 2017;139(8):082301-082301-12. doi:10.1115/1.4036280.

Numerical simulations of metal alloy solidification are used to gain insight into physical phenomena that cannot be observed experimentally. These models produce results that are used to draw conclusions about a process or alloy and often compared to experimental results. However, uncertainty in model inputs cause uncertainty in model results, which have the potential to significantly affect conclusions drawn from their predictions. As a step toward understanding the effect of uncertain inputs on solidification modeling, uncertainty quantification (UQ) and sensitivity analysis are performed on a transient model of solidification of Al–4.5 wt % Cu in a rectangular cavity. The binary alloy considered has columnar solidification morphology, and this model solves equations for momentum, temperature, and species conservation. UQ and sensitivity analysis are performed for the degree of macrosegregation and solidification time. A Smolyak sparse grid algorithm is used to select input values to construct a polynomial response surface fit to model outputs. This polynomial is then used as a surrogate for the complete solidification model to determine the sensitivities and probability density functions (PDFs) of the model outputs. Uncertain model inputs of interest include the secondary dendrite arm spacing (SDAS), heat transfer coefficient, and material properties. The most influential input parameter for predicting the macrosegregation level is the dendrite arm spacing, which also strongly depends on the choice of permeability model. Additionally, the degree of uncertainty required to produce accurate predictions depends on the outputs of interest from the model.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2017;139(8):082401-082401-9. doi:10.1115/1.4036089.

In this paper, we show how the design of a microdevice manifold should be tapered for uniform flow rate distribution. The designs based on the tree-branching rule of Leonardo da Vinci and the Hess–Murray rule were considered in addition to the constructal design. Both da Vinci and Hess–Murray designs are insensitive to the inlet velocity, and they provide better flow uniformity than the base (not tapered) design. However, the results of this paper uncover that not only pressure drop but also velocity distribution in the microdevice play an integral role in the flow uniformity. Therefore, an iterative approach was adopted with five degrees-of-freedom (inclined wall positions) and one constraint (constant distribution channel thickness) in order to uncover the constructal design which conforms the uniform flow rate distribution. In addition, the effect of slenderness of the microchannels (Svelteness) and inlet velocity on the flow rate distribution to the microchannels has been documented. This paper also uncovers that the design of a manifold should be designed with not only the consideration of pressure distribution but also dynamic pressure distribution especially for non-Svelte microdevices.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):082402-082402-9. doi:10.1115/1.4036282.

The nanocapillarity phenomenon involves ultralow frictional flow of water molecules through nanoscale channels, and here we study this using exceptionally large number of nanochannels within graphene oxide (GO) laminates. The nanoconfined water molecules in GO nanochannels form square lattice (as in the ice bilayer), which melts and jumps across the channels, similar to slip flow, with mean speed of the order of 1 m/s. This ease of liquid spreading in GO laminate is used to delay the critical heat flux (CHF) phenomenon in water pool boiling, by preventing formation/growth of dry spots. The water nanocapillarity speed is derived based on the measured water penetration flux, and the CHF enhancement (up to 140%) is demonstrated on a 1-μm-thick GO laminate. The GO laminate offers efficient surface modifications for increased transport efficiency (and safety margin) of pool boiling heat transfer systems.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2017;139(8):082501-082501-7. doi:10.1115/1.4035968.

Entropy generation due to natural convection has been computed for a wide range of Rayleigh numbers based on fin spacing, RaS in the entire laminar range $5≤RaS≤108$, and diameter ratio 2 ≤ D/d ≤ 5 for an isothermal horizontal cylinder fitted with vertical annular fins. Entropy generation in the tube-fin system is predominantly due to heat transfer rather than fluid friction. The results demonstrate that the degree of irreversibility is higher in the case of the finned configuration when compared with the unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to show the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)finned/(I/Q)unfinned which gets its minimum value at optimum fin spacing where heat transfer is maximum. A detailed view of the entropy generation around the finned cylinder has been shown for various S/d (fin spacing to tube diameter ratio) at a particular D/d (fin to tube diameter ratio) and Rayleigh number, which explains the nature and reason of entropy production.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):082502-082502-8. doi:10.1115/1.4036088.

The validity of a parabolic model for simulating the developing buoyancy-assisted mixed convection flow in a vertical channel with spatially periodic wall temperature is verified by a full elliptic model of the momentum and energy equations. A detailed assessment of the effects of the grid resolution, the Richardson number, the Reynolds number, and the preheating zone is presented through extensive comparisons of the velocity and temperature fields and spatial variations of pressure and local heat fluxes at the walls yielded by both models. The parabolic model is capable of reproducing the flow modification into a pattern consisting of a recirculating zone with increasing Richardson number, capturing adequately the main trends of the flow and heat transfer results. For certain combinations of the relevant nondimensional parameters, the solutions of the parabolic model agree reasonably well with those of the elliptic model from a quantitative point of view. In all the cases examined here, the computational time needed by the parabolic model is significantly smaller than that of the elliptic model.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2017;139(8):084501-084501-7. doi:10.1115/1.4036040.

Enhancing of boiling heat transfer by combining the electrohydrodynamic (EHD) effect and surface wettability has been shown to remove the high heat fluxes from electrical devices such as laser diodes, light emitting diodes, and central processing units. However, this phenomenon is not well understood. Our previous studies on the critical heat flux (CHF) of pool boiling have shown that CHF greatly increases with the application of an electric field and that the wall temperature can be decreased to a level with the safe operation of the electrical devices by using a low contact angle with the boiling surface. To verify the earlier prediction model, CHF enhancement by changing the contact angle with the boiling surface and by the application of an electric field was investigated. A fluorinated dielectric liquid (Asahi Glass Co. Ltd, Tokyo, Japan, AE-3000) was selected as the working fluid. To allow the contact angle between the boiling surface and the dielectric liquid to be changed, several different materials (Cu, Cr, NiB, Sn) and a surface coated with a mixture of 1.5 and 5 μm diamond particles were used as boiling surfaces. The CHFs at different contact angles were 20.5–26.9 W/cm2, corresponding to 95–125% of that for a polished Cu surface (21.5 W/cm2). Upon application of a −5 kV/mm electric field to the microstructured surface (the mixture of 1.5 μm and 5 μm diamond particles), a CHF of 99 W/cm2 at a superheat of 33.5 K was obtained. Based on this experimental evidence, we normalized the CHF and contact angle using our previously developed hydrodynamic instability model and semi-empirical model derived from the interfacial area density close to the boiling surface. This procedure allowed us to develop a general model that predicted CHF well, including the CHF for the de-ionized (DI) water.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):084502-084502-5. doi:10.1115/1.4036081.

The fast and accurate modeling of phase change is of a significant importance in many processes from steel casting to latent heat thermal energy storage. The paper presents a numerical case study on the transient 3D heat diffusion problem with phase change. Three different approaches to modeling of the solid–liquid phase change in combination with four commonly used numerical schemes are compared for their efficiency, accuracy, applicability, simplicity of implementation, and robustness. The possibility of parallel decomposition of the approaches is also discussed. The results indicate that the best accuracy was achieved with the second-order implicit methods, and the best efficiency was reached with the simple explicit methods.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(8):084503-084503-2. doi:10.1115/1.4036087.

This paper formulates a modified thermal resistance model (MTRM) for dealing with heat transfer situations involving heat sources from chemical reactions or phase transition. The modified thermal resistance model describes the various heat transfer mechanisms by three common thermal resistors, radiation, convection, and conduction (in media with no internal mass diffusion), adding a new coupled thermal resistor that stands for conduction and enthalpy flow in the gas phase. Similarly to the classical thermal resistance approach, the present model is valid for one-dimensional, quasi-steady heat transfer problems, but it can also handle problems with an internal chemical heat generation source. The new thermal resistance approach can be a useful modular tool for solving relatively easily and quickly complex problems involving chemical reactions and phase transition, such as combustion problems.

Commentary by Dr. Valentin Fuster