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### Research Papers: Heat Exchangers

J. Heat Transfer. 2018;141(2):021801-021801-13. doi:10.1115/1.4041832.

Vortex generator as secondary flow enhancement technique has captured the attention of many researchers recently to augment the performance of the fin-and-tube heat exchanger (FTHE). There are various vortex generator parameters that influence the thermal and hydraulic performance in the FTHE such as the geometry and arrangement. In this study, the effect of different vortex generator geometries and arrangements was investigated using numerical simulation method. There are three vortex generator geometries studied including rectangular winglet (RWVG), delta winglet (DWVG), and trapezoidal winglet (TWVG). The vortex generators were placed behind tubes either in common flow down (CFD) or common flow up (CFU) arrangement. The introduction of vortex generators behind tubes resulted in heat transfer augmentation but comes together with higher pressure drop penalty. Further analysis on the thermal performance has found that TWVG in CFU arrangement almost obtained similar thermal performance factor with respect to the baseline case at Reynolds number 500 and 600. However, the thermal performance factor for TWVG in CFU arrangement decreases as the Reynolds number further increased. For other vortex generator cases, lesser thermal performance factor was found as compared to the baseline case.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):021802-021802-13. doi:10.1115/1.4042050.

In the present work, a numerical analysis of conjugate heat transfer and fluid flow in vortex generator (VG) enhanced double-fin and tube heat exchanger is carried out. The enhanced design aims to improve the heat transfer performance of a conventional double-fin and tube heat exchanger for waste heat recovery applications. A three-dimensional (3D) numerical model is developed using ANSYS cfx to simulate fluid flow and conjugate heat transfer process. Numerical simulations with rectangular winglet vortex generators (RWVGs) at five different angles of attack ($−20deg≤α≤20deg$) are performed for the Reynolds number range of $5000≤Re≤11,000$. Salient performance characteristics are analyzed in addition to the temperature distribution and flow fields. Based on the numerical results, it is concluded that the overall performance of the double-fin and tube heat exchanger can be improved by 27–91% by employing RWVGs at $α=−20deg$ for the range of Reynolds number investigated. The study provides useful design information and necessary performance data that can be adopted for the design development of the heat exchanger at a lower manufacturing cost.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2018;141(2):022001-022001-9. doi:10.1115/1.4041802.

The rate of heat conduction (or mass transfer by diffusion) from a cylindrical or a spherical particle confined between two walls is determined as a function of the position and the radius of the particle. It is shown that the appropriate Green's function can be determined using the method of images even when the resulting series is divergent with the help of Shanks transformation. Asymptotic expansions for small particle radius compared to the distance between the walls are combined with the expressions for the case in which the gap between the particle and one of the walls is small compared to the particle radius to provide formulas that are surprisingly accurate for estimating the rate of heat transfer for the entire range of parameters that include the radius and the position of the particle. Results are also presented for the thermal dipole induced by a spherical or a cylindrical particle placed between two walls with unequal temperatures and these are used to predict the effective thermal conductivity of thin composite films containing spherical or cylindrical particles.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022002-022002-9. doi:10.1115/1.4041951.

This study examines the effects of viscous and porous dissipation on entropy generation in the viscoelastic fluid flow induced by a linearly stretching surface. Analysis of mass transfer is also performed. Consideration of rheological characteristics of viscoelastic fluid in the energy conservation law and entropy generation number in terms of viscous dissipation makes a striking difference in the energy equation and entropy generation number for Newtonian and viscoelastic fluid. This important concern which is yet not properly attended is also be examined in the present study. The dimensional governing equations are reduced to a set of self-similar differential equations. The energy and concentration equations are solved exactly by employing the Laplace transform technique. The obtained exact solutions of reduced set of governing equations are utilized to compute the entropy generation number. To analyze the impacts of flow parameter on velocity profile, temperature distribution, concentration profile, and entropy generation number inside the boundary layer, graphs are plotted and discussed physically. The permeability and viscoelastic parameters have strong influence on the entropy generation in the vicinity of stretching surface.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022003-022003-6. doi:10.1115/1.4041959.

Stagnation-point flow toward a stretching sheet with slip effects has been investigated. Unlike most classical works, Cattaneo–Christov heat flux model is utilized for the formulation of the energy equation instead of Fourier's law of heat conduction. A similarity transformation technique is adopted to reduce partial differential equations into a system of nonlinear ordinary differential equations. Numerical solutions are obtained by using shooting method to explore the features of various parameters for the velocity and temperature distributions. The obtained results are graphically presented and analyzed. It is found that fluid temperature has a converse relationship with the thermal relaxation time. A comparison of Cattaneo–Christov heat flux model and Fourier's law is also presented.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022004-022004-8. doi:10.1115/1.4041955.

This paper discusses about the numerical prediction of forced convection heat transfer through high-porosity metal foams with discrete heat sources in a vertical channel. The physical geometry consists of a discrete heat source assembly placed at the center of the channel along with high thermal conductivity porous metal foams in order to enhance the heat transfer. The novelty of the present work is the use of combination of local thermal equilibrium (LTE) model and local thermal nonequilibrium (LTNE) model for the metal foam region to investigate the temperature distribution of the heat sources and to obtain an optimal heat distribution so as to achieve isothermal condition. Aluminum and copper metal foams of 10 PPI having a thickness of 20 mm are considered for the numerical simulations. The metal foam region is considered as homogeneous porous media and numerically modeled using Darcy Extended Forchheimer model. The proposed methodology is validated using the experimental results available in literature. The results of the present numerical solution indicate that the excess temperature of the bottom heat source reduces by 100 °C with the use of aluminum metal foam. The overall temperature of the vertical channel reduces based on the combination of LTE and LTNE models compared to only LTNE model. The results of excess temperature for both the empty and the metal foam filled vertical channels are presented in this work.

Commentary by Dr. Valentin Fuster

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

J. Heat Transfer. 2018;141(2):022201-022201-13. doi:10.1115/1.4041958.

In this paper, heat transfer and effectiveness of a turbulent slot jet impinging over a heated circular cylinder have been investigated numerically by varying the ratio of jet temperature to the ambient temperature, Θj = Tj/Tamp, from 0.7 to 1.2. In all cases, the ambient temperature (Tamb) is assumed to be constant (300 K). The Reynolds number defined based on the average nozzle exit velocity, the diameter of the cylindrical target (D), and properties at the nozzle exit temperature, $ReD=ρVD/μ$ is varied from 6000 to 20,000. The ratio of cylinder diameter to the slot width, D/S = 5.5, 8.5, and 17 are considered and the nondimensional distance from the nozzle exit to the cylinder, H/S is varied in the range of 2 ≤ H/S ≤ 12. The $v′2¯−f$ turbulence model was used for numerical simulations. Numerical results reveal that the local Nusselt number is found to be higher at the stagnation point in the case of cold jet impingement at Θj = 0.7. The local heat transfer at the rear side of the cylinder is 8–18% less as compared to that of Θj = 1.0 for ReD = 6000. The local effectiveness calculated over a circular cylinder strongly depends on H/S and D/S. Based on the parametric study, a correlation has been provided for the local effectiveness at the stagnation point.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022202-022202-7. doi:10.1115/1.4041954.

In this study, air jet impingement on flat, triangular-corrugated, and sinusoidal-corrugated surfaces was numerically investigated. Bottom surface was subjected to constant surface temperature. Air was the working fluid. The air exited from a rectangular shaped slot and impinged on the bottom surface. The Reynolds number was changed between 125 and 500. The continuity, momentum, and energy equations were solved using the finite volume method. The effect of the shape of bottom surface on heat and flow characteristics was investigated in detail. Average and local Nusselt number were calculated for each case. It was found out that Nusselt number increases by increasing the Reynolds number. The optimum conditions were established to get much more enhancement in terms of performance evaluation criterion (PEC). It was revealed that the shape of the cooling surface (bottom wall) influences the heat transfer substantially.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2018;141(2):022401-022401-13. doi:10.1115/1.4040415.

The present research aims to examine the micropolar nanofluid flow of Casson fluid between two parallel plates in a rotating system with effects of thermal radiation. The influence of Hall current on the micropolar nanofluids have been taken into account. The fundamental leading equations are transformed to a system of nonlinear differential equations using appropriate similarity variables. An optimal and numerical tactic is used to get the solution of the problem. The convergence and comparison have been shown numerically. The impact of the Hall current, Brownian movement, and thermophoresis phenomena of Casson nanofluid have been mostly concentrated in this investigation. It is found that amassed Hall impact decreases the operative conductivity which intends to increase the velocity field. The temperature field enhances with larger values of Brownian motion thermophoresis effect. The impacts of the Skin friction coefficient, heat flux, and mass flux have been deliberate. The skin friction coefficient is observed to be larger for $k=0$, as compared to the case of $k=0.5$. Furthermore, for conception and visual demonstration, the embedded parameters have been deliberated graphically.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022402-022402-9. doi:10.1115/1.4041971.

Combination of electric and magnetic forces on charged molecules of flowing fluid in the presence of a significant electromagnetic fields on surfaces with a nonuniform thickness (as in the case of upper pointed surface of an aircraft and bonnet of a car which are examples of upper horizontal surfaces of a paraboloid of revolution—uhspr) is inevitable. In this study, the influence of imposed magnetic field and Hall effects on the flow of 29 nm CuO–water nanofluid over such object is presented. Suitable similarity variables were employed to nondimensionalize and parameterize the dimensional governing equation. The numerical solutions of the corresponding boundary value problem were obtained using Runge–Kutta fourth-order integration scheme along with shooting technique. The domain of cross-flow velocity can be highly suppressed when the magnitude of imposed magnetic strength and that of Hall parameter are large. A significant increase in the cross-flow velocity gradient near an upper horizontal surface of the paraboloid of revolution is guaranteed with an increase in the Hall parameter. Enhancement of temperature distribution across the flow is apparent due to an increase in the volume fraction.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022403-022403-12. doi:10.1115/1.4042157.

We study hydrodynamics, heat transfer, and entropy generation in pressure-driven microchannel flow of a power-law fluid. Specifically, we address the effect of asymmetry in the slip boundary condition at the channel walls. Constant, uniform but unequal heat fluxes are imposed at the walls in this thermally developed flow. The effect of asymmetric slip on the velocity profile, on the wall shear stress, on the temperature distribution, on the Bejan number profiles, and on the average entropy generation and the Nusselt number are established through the numerical evaluation of exact analytical expressions derived. Specifically, due to asymmetric slip, the fluid momentum flux and thermal energy flux are enhanced along the wall with larger slip, which, in turn, shifts the location of the velocity's maximum to an off-center location closer to the said wall. Asymmetric slip is also shown to redistribute the peaks and plateaus of the Bejan number profile across the microchannel, showing a sharp transition between entropy generation due to heat transfer and due to fluid flow at an off-center-line location. In the presence of asymmetric slip, the difference in the imposed heat fluxes leads to starkly different Bejan number profiles depending on which wall is hotter, and whether the fluid is shear-thinning or shear-thickening. Overall, slip is shown to promote uniformity in both the velocity field and the temperature field, thereby reducing irreversibility in this flow.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022404-022404-12. doi:10.1115/1.4042148.

This experimental study on rhombic shaped microchannels was conducted to understand the effect of a low acute side angle on the Nusselt number and compare the results with the published numerical results for H1 (axially constant heat flux and circumferentially constant temperature) and H2 (constant axial and circumferential wall heat flux) boundary conditions. The hydraulic and heat transfer characteristics of the rhombic geometry with a side angle of 30 deg for different mass flow rates and heat flux inputs are obtained using a three-dimensional (3D) conjugate heat transfer model, which is validated with the experimental results. It is found that the average Nusselt number obtained from the experimental and numerical results can be approximated closely with that computed using the H1 boundary condition. The local Nusselt number of hydrodynamically and thermally developed regions obtained from the numerical analysis is compared with a correlation for the H1 boundary condition. These results will be useful in design and optimization of a rhombic shaped microchannel for electronic cooling applications.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2018;141(2):022501-022501-12. doi:10.1115/1.4039642.

Numerical simulations are carried out for fluid flow and natural convection heat transfer induced by a temperature difference between a hot inner cylinder with different geometries (i.e., circular; triangular; elliptic; rectangular; and rhombic) and a cold outer square enclosure filled with nanofluid superposed porous-nanofluid layers. The Darcy–Brinkman model is applied for the saturated porous layer with nanofluid. Moreover, the transport equations (mass, momentum, and energy) are solved numerically using the Galerkin weighted residual method by dividing the domain into two sets of equations for every layer with incorporating a nonuniform mesh size. The considered domains in this investigation are closely examined over a wide range of Rayleigh number (103 ≤ Ra ≤ 106), Darcy number (10−5 ≤ Da ≤ 10−1), the thickness of porous layer (0% ≤ Xp ≤ 100%), thermal conductivity ratio (1 ≤ Rk ≤ 20), and nanoparticle volume fraction (0 ≤ φ ≤ 0.1), respectively. The nanofluid is considered to be composed of Ag-nanoparticle and water as a base fluid. The results showed that the obtained total surfaces-averaged Nusselt numbers of the enclosure, in all cases, at the same operating conditions, the rate of heat transfer from the outer enclosure which the triangular cylinder is located inside is better. Also, as the thickness of the porous layer is increased from 20% to 80%, the free convection performance will decrease significantly (to about 50%) due to the hydrodynamic properties of the porous material.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022502-022502-12. doi:10.1115/1.4041797.

Convective heat transfer in a rotating two-pass square channel with 45 deg ribs is numerically investigated to simulate turbine blade cooling operation under extreme design cooling conditions (high rotation number, high density ratio, and high buoyancy number). Two channel orientations are examined β = 0 deg and β = 45 deg in order to determine the effects of passage orientation on flow and heat transfer. For a reference pressure of 10-atm and a Reynolds number of 25,000, the results show that at low buoyancy number and for both channel orientations, the combined effect of Coriolis and centrifugal buoyancy forces generates an important thermal gradient between low- and high-pressure surfaces of the first passage, while the second passage remains almost unchanged compared to the stationary cases. At high buoyancy number, and unlike low buoyancy number, the interaction of Coriolis-driven cells, rib-induced vortices, and buoyancy-driven cells are destructive, which degrade the heat transfer rate on trailing and leading surfaces in the first passage for β = 0 deg. In contrast, for β = 45 deg, this interaction is constructive, which enhances the heat transfer rate on co-trailing and co-leading surfaces. In the second passage, the interaction of rib-induced vortices and buoyancy-driven cells deteriorates significantly the heat transfer rate in case of β = 0 deg than in case of β = 45 deg compared to low buoyancy number. The computations are performed using the second-moment closure turbulence model and the numerical results are in fair agreement with available experimental data.

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2018;141(2):022601-022601-8. doi:10.1115/1.4041707.

In this paper, heat transfer modeling of a high-temperature porous-medium filled solar thermochemical reactor for hydrogen and synthesis gas production is investigated. The numerical simulation is performed using a three-dimensional (3D) numerical model and surface-to-surface radiation model coupled to Rosseland approximation for radiation heat transfer. The effects of operating conditions and the porous structural parameters on the reactor thermal performance were investigated significantly. It was found that large axial temperature gradient and high-temperature distribution throughout the reactor were strongly dependent on the operating conditions. The inlet gas temperature has remarkable effects on the temperature distribution. The thermal performance of porous-medium filled solar thermochemical reactor could be improved by preheating the inlet gas up to 393.15 K. Moreover, a correlation was established between the protective gas inlet velocity and the porosity of porous media. The temperature difference decreased with the increase in the porosity of the inner cavity of the reactor. In contrast to the front and back parts of the inner cavity of the reactor, higher temperature distribution could be obtained in the porous region by increasing the average cell diameters of porous media.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2018;141(2):022701-022701-8. doi:10.1115/1.4041803.

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):022702-022702-10. doi:10.1115/1.4041831.

The refractive index and absorption coefficient fields in participating media are reconstructed simultaneously in this work. In the direct model, the coupled radiation–conduction heat transfer in participating media exposed to a pulse laser irradiation is solved by finite volume method (FVM). In the inverse model, the sequential quadratic programming (SQP) algorithm combined with the generalized Gaussian Markov random field (GGMRF) model is employed to solve the reconstruction problem. It is found that the refractive index and absorption coefficient fields cannot be reconstructed simultaneously. A secondary reconstruction technique based on different regularization parameters is proposed to reconstruct the refractive index and absorption coefficient fields simultaneously. All the retrieval results indicate that the proposed secondary reconstruction technique performs accurately and effectively.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2018;141(2):024501-024501-6. doi:10.1115/1.4041801.

An investigation is made to study the Blasius flow of a nanofluid in the presence of homogeneous–heterogeneous chemical reactions. Here, the diffusion coefficients of the reactant and autocatalyst are considered to be in comparable sizes. The Buongiorno's mathematical model is applied in describing the behavior of nanofluids. Multiple solutions of the steady-state system of nonlinear ordinary differential equations are obtained. Results show that nanofluids significantly participate in the transport mechanism of the homogeneous–heterogeneous reactions, which play different roles in the procedures of homogeneous and heterogeneous reactions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):024502-024502-5. doi:10.1115/1.4041799.

In this paper, we briefly present the heat/momentum transfer analogies of Reynolds and the followers for turbulent flow. Next, we discuss differences between turbulent and laminar flow and turn to the Lévêque analogy for laminar flow. This enables heat transfer coefficients (Nusselt numbers) to be derived, based on the flow friction results that include only viscous friction. Some examples of Lévêque analogy applications, such as flow through packed beds, wire gauzes, short-channel structures (short monoliths), and structured catalyst carriers (tube inserts), are given. The Lévêque analogy gave satisfactory accuracy when compared to experiments with flow friction derived on the theoretical basis.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):024503-024503-5. doi:10.1115/1.4041956.

Theoretical understanding of phase change heat transfer problems is of much interest for multiple engineering applications. Exact solutions for phase change heat transfer problems are often not available, and approximate analytical methods are needed to be used. This paper presents a solution for a one-dimensional (1D) phase change problem with time-dependent heat flux boundary condition using the perturbation method. Two different expressions for propagation of the phase change front are derived. For the special case of constant heat flux, the present solution is shown to offer key advantages over past papers. Specifically, the present solution results in greater accuracy and does not diverge at large times unlike past results. The theoretical result is used for understanding the nature of phase change propagation for linear and periodic heat flux boundary conditions. In addition to improving the theoretical understanding of phase change heat transfer problems, these results may contribute toward design of phase change based thermal management for a variety of engineering applications, such as cooling of Li-ion batteries.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):024504-024504-5. doi:10.1115/1.4041957.

An analytical and numerical study was conducted for estimation of the effective thermal conductivities of curved metal frame core structures, which can replace metal foams, in views of their advantages over the metal foams for both load bearing and heat dissipation. The trajectory of the frame ligament and its cross-sectional area were allowed to vary arbitrarily in the three-dimensional (3D) space. The analytical formula obtained by extending the formula previously proposed by Bai et al. (2017, “A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures,” ASME J. Heat Transfer, 140(5), p. 052001) was examined by comparing it with the numerical results directly obtained from full 3D numerical computations. An air layer partially filled with a collection of coiled circular rods was treated both analytically and numerically. Furthermore, the effect of lattice nodes on the effective thermal conductivity was investigated by introducing an analytical model with the lattice ligaments merging together at one nodal point. The analytical expressions thus derived for the lattice structures with nodes were applied to tetrahedral structure and octet-truss structure to find their effective thermal conductivities, which are found to agree closely with the 3D numerical results. Thus, the present analytical expressions can be used to customize the structure to meet its desired thermal performance.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;141(2):024505-024505-7. doi:10.1115/1.4042156.

Numerical and thermodynamic analyses have been undertaken in this study to examine energy and exergy efficiencies of in-line tube banks for unsteady cross-flow. Pitch ratio (PR) and the number of in-line tubes are varied for Reynolds numbers of 500 and 10,000, and artificial heat leakages are modeled as a source term. Numerical results are compared with published values, and good agreements are obtained regarding Nusselt number and pressure drop. Whereas the energy efficiency varied between 72% and 99%, the exergy efficiency ranged from 40% to 70%. It was found that while viscous dissipation has a low effect on energy and exergy efficiencies for the lower Reynolds number, it has a significant effect for the higher Reynolds number. On the other hand, heat leakage had a greater effect on exergy efficiency compared to energy efficiency, especially for the lower Reynolds number case. Overall, this study verified how heat leakage could play a vital role on efficiency for low-inlet temperature heat recovery systems.

Commentary by Dr. Valentin Fuster