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Research Papers: Conduction

J. Heat Transfer. 2017;139(7):071301-071301-10. doi:10.1115/1.4035713.

The finite difference (FD), finite element (FE), and finite volume (FV) methods are critically assessed by comparing the solutions produced by the three methods for a simple one-dimensional steady-state heat conduction problem with heat generation. Three issues are assessed: (1) accuracy of temperature, (2) accuracy of heat flux, and (3) satisfaction of global energy conservation. It is found that if the order of accuracy of the numerical discretization schemes is the same (central difference for FD and FV, linear basis functions for FE), the accuracy of the temperature produced by the three methods is similar, except close to the boundaries where the FV method outshines the other two methods. Consequently, the FV method is found to predict more accurate heat fluxes at the boundaries compared to the other two methods and is found to be the only method that guarantees both local and global conservation of energy irrespective of mesh size. The FD and FE methods both violate energy conservation, and the degree to which energy conservation is violated is found to be mesh size dependent. Furthermore, it is shown that in the case of prescribed heat flux (Neumann) and Newton cooling (Robin) boundary conditions, the accuracy of the FD method depends in large part on how the boundary condition is implemented. If the boundary condition and the governing equation are both satisfied at the boundary, the predicted temperatures are more accurate than in the case where only the boundary condition is satisfied.

Commentary by Dr. Valentin Fuster

Research Papers: Forced Convection

J. Heat Transfer. 2017;139(7):071701-071701-10. doi:10.1115/1.4035855.

The Chilton–Colburn analogy is very helpful for evaluating the heat transfer in internal forced flows. The Chilton–Colburn analogy between the Chilton–Colburn j-factor for heat transfer, jH (St·Pr2/3) and the Fanning friction factor (cf) is popularly considered to hold when St·Pr2/3 equals to cf/2, for constant fluid properties. The physical fluid properties, namely, viscosity and thermal conductivity, are generally a function of temperature for microconvective water flow due to a quite steep temperature gradient. Therefore, in present investigation, the validity of Chilton–Colburn analogy between St·Pr2/3 and cf is re-examined for laminar microconvective flow with variable thermophysical fluid properties. It is observed that the Chilton–Colburn analogy is valid only for that portion of the flow regime, where St·Pr2/3 decreases with decreasing cf. The validity of Chilton–Colburn analogy is also verified by the inverse dependence of Reynolds number (Re) with cf. Two modified nondimensional parameters “Π and ΠSk” are emerged from the nondimensional form of 2D, steady-state, incompressible, pure continuum-based, laminar conservation of momentum and energy equations, respectively. These modified nondimensional parameters show the significance of variable fluid properties in momentum transport and energy transport. Additionally, the role of Π and ΠSk in flow friction is also investigated. The higher values of Π and ΠSk indicate the stronger influence on microconvection due to large variations in fluid properties.

Commentary by Dr. Valentin Fuster

Research Papers: Heat Transfer Enhancement

J. Heat Transfer. 2017;139(7):071901-071901-8. doi:10.1115/1.4035712.

The present study aims at explaining why heat transfer is enhanced in turbulent ribbed-pipe flow, based on our previous large eddy simulation (LES) database (Kang and Yang, 2016, “Characterization of Turbulent Heat Transfer in Ribbed Pipe Flow,” ASME J. Heat Transfer, 138(4), p. 041901) obtained for Re = 24,000, Pr = 0.71, pitch ratio (PR) = 2, 4, 6, 8, 10, and 18, and blockage ratio (BR) = 0.0625. Here, the bulk velocity and the pipe diameter were used as the velocity and length scales, respectively. The ribs were implemented in the cylindrical coordinate system by means of an immersed boundary method. In particular, we focus on the cases of PR ≥ 4 for which heat transfer turns out to be significantly enhanced. Instantaneous flow fields reveal that the vortices shed from the ribs are entrained into the main recirculating region behind the ribs, inducing velocity fluctuations in the vicinity of the pipe wall. In order to identify the turbulence structures responsible for heat transfer enhancement in turbulent ribbed-pipe flow, various correlations among the fluctuations of temperature and velocity components have been computed and analyzed. The cross-correlation coefficient and joint probability density distributions of velocity and temperature fluctuations, obtained for PR = 10, confirm that temperature fluctuation is highly correlated with velocity-component fluctuation, but which component depends upon the axial location of interest between two neighboring ribs. Furthermore, it was found via the octant analysis performed for the same PR that at the axial point of the maximum heat transfer rate, O3 (cold wallward interaction) and O5 (hot outward interaction) events most contribute to turbulent heat flux and most frequently occur.

Commentary by Dr. Valentin Fuster

Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2017;139(7):072001-072001-12. doi:10.1115/1.4035714.

Considerable recent research has focused on the ability of microstructured fibers to exhibit diverse optical functionalities. However, accurately preserving the structure imposed at the preform stage after drawing it down to fiber, while avoiding Rayleigh–Plateau style instabilities, has proven to be a major fabrication challenge. This modeling/analytical study was carried out in support of an experimental program into possible fabrication options for various microstructured optical fibers and considers the generic case of the nonisothermal drawing of a capillary preform to fiber. Model development was carried out in two stages. Initially, a fully conjugate multiphase model, which includes all heat transfer modes within an operational fiber drawing furnace, was validated against available experimental data. To evaluate the external radiative heat flux using the net-radiation method, a Monte Carlo ray-tracing (MC-RT) method was coupled to the commercial polyflow package to obtain all view factors between the various furnace walls and the deforming preform/fiber. A simplified model was also developed (to shorten simulation run times) by explicitly calculating the convective heat transfer between the air within the furnace and the preform/fiber surface using a heat transfer coefficient determined by matching predicted results with those obtained from the multiphase model.

Commentary by Dr. Valentin Fuster

Research Papers: Heat Transfer in Manufacturing

J. Heat Transfer. 2017;139(7):072101-072101-10. doi:10.1115/1.4035889.

A major challenge in maintaining quality and reliability in today's microelectronics chips comes from the ever increasing levels of integration in the device fabrication, as well as from the high current densities. Transient Joule heating in the on-chip interconnect metal lines with characteristic sizes of tens of nanometer, can lead to thermomechanical fatigue and failure due to the thermal expansion coefficient mismatch between different materials. Full-field simulations of nearly a billion interconnects in a modern microprocessor are infeasible due to the grid size requirements. To prevent premature device failures, a rapid predictive capability for the thermal response of on-chip interconnects is essential. This work develops a two-dimensional (2D) transient heat conduction framework to analyze inhomogeneous domains, using a reduced-order modeling approach based on proper orthogonal decomposition (POD) and Galerkin projection. POD modes are generated by using a representative step function as the heat source. The model rapidly predicted the transient thermal behavior of the system for several cases, without generating any new observations, and using just a few POD modes.

Commentary by Dr. Valentin Fuster

Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2017;139(7):072201-072201-13. doi:10.1115/1.4035651.

This paper describes the experimental investigations of film-cooling effectiveness on a highly loaded low-pressure turbine blade under steady and unsteady wake flow conditions. The cascade facility in Turbomachinery Performance and Flow Research Lab (TPFL) at the Texas A&M University was used to simulate the periodic flow condition inside gas turbine engines. Moving wakes, originated from upstream stator blades, are simulated inside the cascade facility by moving rods in front of the blades. The flow coefficient is maintained at 0.8 and the incoming wakes have a reduced frequency of 3.18. A total of 617 holes on the blade are distributed along 13 different rows. Six rows cover the suction side, six other rows cover the pressure side, and one last row feeds the leading edge. Each row has a twin row on the other side of the blade with exact same number of holes and arrangement (except for leading edge). They both are connected to the same cavity. Coolant is injected from either sides of the blade through cavities to form a uniform distribution along the span of the blade. Film-cooling effectiveness under periodic unsteady flow condition was studied using pressure-sensitive paint. Experiments were performed at Reynolds number of 150,000 and blowing ratio of one, based on equal mass flux distribution. Experimental investigations were performed to determine the effect of flow separation and pressure gradient on film-cooling effectiveness. Moreover, the effect of impinging wakes on the overall film coverage of blade surfaces was studied. It was found that heat transfer coefficient (HTC) and film-cooling effectiveness (FCE) in majority of regions behave in opposite ways. This can be justified from turbulence intensity and velocity fluctuation point of view. Also, unsteady wakes imposed on top of film injection have opposite effects on suction and pressure side of the blade. This is more clearly seen in region near leading edge.

Commentary by Dr. Valentin Fuster

Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2017;139(7):072401-072401-12. doi:10.1115/1.4035890.

Improvement of the effectiveness of heat exchanger is the demand of compact and efficient cooling devices. In that respect, a numerical study of fluid flow and heat transfer has been conducted with different arrangements of simple vortex generator (VG) in a rectangular microchannel Reynolds number (Re) in the range between 200 and 1100. The combined effect of spanwise and pitchwise distance of VG on heat transfer is investigated rigorously to observe the dependence of heat transfer on both. By processing the numerical predictions through gene expression programing and genetic algorithm optimization, the output variations in heat transfer, or Nusselt number, and friction factor with Re and locations of VGs in the channel are predicted in the form of explicit equations. The predicted monotonic increase of the outputs with Re shows heat transfer enhancement of 40–135% at the cost of increased pressure drop by 62–186.7% with respect to channels without VGs.

Commentary by Dr. Valentin Fuster

Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2017;139(7):072501-072501-13. doi:10.1115/1.4035919.

Numerical simulations have been conducted to study natural convection heat transfer from solid or hollow cylinders in the laminar range of Ra spanning from 104 to 108 for L/D in the range of 0.05(L/D)20. Interesting flow structures around the thin hollow cylinder have been observed for small and large L/D. It has been found that the average Nu for solid or hollow horizontal cylinders in air is marginally higher than when they are on ground for the entire range of L/D and Ra limited up to 107. Up to a Ra of 107 Nu for a solid cylinder in air is higher than that of Nu for a hollow cylinder in air but when Ra exceeds 107 Nu for a hollow cylinder is marginally higher than that of the solid cylinder until an L/D of 0.2. When, L/D rises beyond 0.2 the situation reveres causing Nu for a solid cylinder to be again higher than that of the hollow cylinder when suspended in air. A solid cylinder on ground has higher Nu compared to that of a hollow cylinder on ground up to a Ra of 106. However, for higher Ra of 108 a hollow cylinder on ground has higher Nu compared to that of a solid cylinder on ground until an L/D of 5 and after that the situation reverses again.

Topics: Cylinders
Commentary by Dr. Valentin Fuster

Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2017;139(7):072701-072701-6. doi:10.1115/1.4035732.

Turbine blade temperature measurements are important for monitoring the turbine engine performance to protect the hot components from damage due to excess temperatures. However, the reflected radiation from the blades and the surrounding environment complicate the blade temperature measurements by optical pyrometers. This study characterizes the effect of the reflected radiation on the effective spectral emissivity of a three-dimensional turbine blade in a confined turbine space for optical pyrometry temperature measurements. The effective spectral emissivity distribution on a three-dimensional blade was numerically determined for various wavelengths (0.8–15.0 μm) and actual blade surface emissivities for a specified turbine blade model. When the actual spectral emissivity of the blade surface is assumed to be 0.5, the effective spectral emissivity varies from 0.5 to 0.538 at the longer wavelength of 10.0 μm and further increases from 0.5 to 1.396 at the shorter wavelength of 0.9 μm. The results show that the effective emissivity distributions at shorter wavelengths differ greatly from those at longer wavelengths. There are also obvious differences between the effective spectral emissivity and the actual surface emissivity at shorter wavelengths. The effect of the effective emissivity on the temperature measurement accuracy, when using the optical pyrometry, was also investigated for various wavelengths (0.8–15.0 μm). The results show that the radiation reflected from the blades has less effect on the temperature measurements than on the effective emissivity, especially at the shorter wavelengths of 0.8–3.0 μm. However, the temperature measurements still need to be corrected using the effective spectral emissivity to improve the temperature calculation accuracy. This analysis provides guidelines for choosing the optimum measurement wavelengths for optical pyrometry in turbine engines.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Heat Transfer. 2017;139(7):074501-074501-10. doi:10.1115/1.4035805.

Modeling subcooled boiling flows in vertical channels has relied heavily on the utilization of empirical correlations for the active nucleation site density, bubble departure diameter, and bubble departure frequency. Following the development and application of mechanistic modeling at low pressures, the capability of the model to resolve flow conditions at elevated pressure up to 10 bar is thoroughly assessed and compared with selected empirical models. Predictions of the mechanistic and selected empirical models are validated against two experimental data at low to elevated pressures. The results demonstrate that the mechanistic model is capable of predicting the heat and mass transfer processes. In spite of some drawbacks of the currently adopted force balance model, the results still point to the great potential of the mechanistic model to predict a wide range of flow conditions in subcooled boiling flows.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2017;139(7):074502-074502-5. doi:10.1115/1.4036005.

This paper presents research for a class of recombination reaction and diffusion problems in which the Cattaneo relaxation, n-diffusion flux, and p-Fisher–Kolmogorov–Petrovsky–Piscounov (KPP) reaction are considered. Approximate analytical solutions are obtained by Adomian decomposition method (ADM) and shown graphically. Some interesting results for spatial variable and temporal variable evolution are obtained. For specified spatial variable, the temperature profiles decrease with respect to the increase of relaxation parameter and power-law index n but decrease with respect to Fisher–KPP reaction parameter p. For specified temporal variable, the temperature profiles are seem oscillating with values of the relaxation parameter and power-law index n.

Commentary by Dr. Valentin Fuster

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