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### Research Papers: Forced Convection

J. Heat Transfer. 2008;130(3):031701-031701-10. doi:10.1115/1.2804945.

The properties of the mean momentum and thermal balance in fully developed turbulent channel flow on transitional rough surface have been explored by method of matched asymptotic expansions. Available high quality data support a dynamically relevant three-layer description that is a departure from two-layer traditional description of turbulent wall flows. The scaling properties of the intermediate layer are determined. The analysis shows the existence of an intermediate layer, with its own characteristic of mesolayer scaling, between the traditional inner and outer layers. Our predictions of the peak values of the Reynolds shear stress and Reynolds heat flux and their locations in the intermediate layer are well supported by the experimental and direct numerical simulation (DNS) data. The inflectional surface roughness data in a turbulent channel flow provide strong support to our proposed universal log law in the intermediate layer, that is, explicitly independent transitional surface roughness. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional type roughness, Colebrook–Moody monotonic roughness, etc. In traditional variables, the roughness scale for inflectional roughness is supported very well by experimental and DNS data. The higher order effects are also presented, which show the implications of the low Reynolds-number flows, where the intermediate layer provides the uniformly valid solutions in terms of generalized logarithmic laws for the velocity and the temperature distributions.

Commentary by Dr. Valentin Fuster

### Research Papers: Melting and Solidification

J. Heat Transfer. 2008;130(3):032301-032301-12. doi:10.1115/1.2804943.

One, two, and three needle cryoprobes, $1.47mm$ outside diameter, simultaneously and uniformly operated by high pressure argon gas, were tested in a gel simulating the thermal properties of biological tissues. The probes were inserted into the same depth in the gel through two parallel templates with holes drilled on a $5×5mm2$ mesh. The temperature of the active segment of the probe was monitored by a single soldered thermocouple (TC). Temperatures in the gel were monitored by K-type TC strings in the radial, and in the downward and upward axial directions. The phase-change problem in the gel was solved by ANSYS7.0 , based on the enthalpy method. Calculated and measured results compared reasonably well with the most deviations observed in the upward axial direction. Results of this study may be summarized as follows: (a) Due to the cylindrical structure of the probe, the advancement of the frozen fronts was more pronounced in the upward axial and the radial directions than in the downward direction. (b) The farthest placement of the two probes $(10mm)$ yielded the largest volumes enclosed by the isothermal contours. (c) In the tightest two placement configurations of the three probes, the $−40°C$ fronts of all frozen lumps have joined together even after $1min$ of operation, while in the less tight configurations, joining occurred later. (d) In multiprobe applications and for a given duration of application, there exists a certain placement configuration that will produce the maximal volume of any temperature-specific frozen lump. The computational tool presented in this study could assist the surgeon in the preplanning of cryosurgical procedures and thus reduce uncertainties and enhance its success rate.

Topics: Probes , Temperature
Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2008;130(3):032501-032501-10. doi:10.1115/1.2804934.

A penalty finite element analysis with biquadratic elements has been carried out to investigate natural convection flows within an isosceles triangular enclosure with an aspect ratio of 0.5. Two cases of thermal boundary conditions are considered with uniform and nonuniform heating of bottom wall. The numerical solution of the problem is illustrated for Rayleigh numbers (Ra), $103⩽Ra⩽105$ and Prandtl numbers (Pr), 0.026$⩽Pr⩽$1000. In general, the intensity of circulation is found to be larger for nonuniform heating at a specific Pr and Ra. Multiple circulation cells are found to occur at the central and corner regimes of the bottom wall for a small Prandtl number regime (Pr=0.026−0.07). As a result, the oscillatory distribution of the local Nusselt number or heat transfer rate is seen. In contrast, the intensity of primary circulation is found to be stronger, and secondary circulation is completely absent for a high Prandtl number regime (Pr=0.7–1000). Based on overall heat transfer rates, it is found that the average Nusselt number for the bottom wall is $2$ times that of the inclined wall, which is well, matched in two cases, verifying the thermal equilibrium of the system. The correlations are proposed for the average Nusselt number in terms of the Rayleigh number for a convection dominant region with higher Prandtl numbers (Pr=0.7 and 10).

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):032502-032502-17. doi:10.1115/1.2804935.

A fast and efficient method based on the proper orthogonal decomposition (POD) technique for predicting fluid flow and heat transfer problems is proposed in this paper. POD is first applied to an ensemble of numerical simulation results at design parameters to obtain the empirical coefficients and eigenfunctions, and then the fluid and temperature fields in the range of design parameters are resolved by a linear combination of empirical coefficients and eigenfunctions. The empirical coefficients at off-design parameters are obtained by a cubic spline interpolation method for steady problems and a Galerkin projection method for transient problems. Finally, the efficiency and accuracy of the algorithm are examined by three examples. The POD based algorithm can predict both the velocity and temperature fields in the range of design parameters accurately at a price of a large number of precomputed cases (snapshots). It also brings significant computational time savings for the new cases within the parameter range presimulated compared with the finite volume method with SIMPLE -like algorithm.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):032503-032503-11. doi:10.1115/1.2804938.

The analytical solution for a vertical heated plate subjected to conjugate heat transfer due to natural convection at the surface and conduction below is presented. The heated surface is split into two regions; the uniform heat flux region toward upstream and remaining fraction as the uniform wall temperature region. The fractional areas under the two regions are considered variable. Adopting thermally thin wall regime approximation, the possible solutions were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in the transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The ranges for Rayleigh number and heat conduction parameter $(α)$ during various test conditions were $2×108–6×108$, and 0.001–1, respectively. The limiting solutions for stipulated conditions are analyzed and compared with experimental data. Reasonable agreement is observed between the experimental and analytical results.

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2008;130(3):032601-032601-5. doi:10.1115/1.2804947.

This article aims to study the effect of pressure drop on the thermal behavior of porous burners. Since the reticulated ceramics are used in the burners’ construction, in the previous researches pressure drop arising from flow velocity was ignored. This research has showed that due to the increase of speed resulting from combustion, the consequence pressure drop creates considerable effects on the thermal performance of porous burners. To study this subject, the temperature of a point on the burner axis has been taken to be constant. The burned gas and exit surface temperature were obtained almost the same for two conditions, one with the pressure held constant and the other with a pressure drop. Results show that the firing rate was decreased up to 18%, compared to the constant pressure case. The thermal radiative efficiency of radiant porous burners, in which the pressure drop has been considered, was increased about 3–5% for the studied equivalence ratio of methane-air combustion.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):032602-032602-10. doi:10.1115/1.2804932.

The effective thermal conductivity of reticulate porous ceramics (RPCs) is determined based on the 3D digital representation of their pore-level geometry obtained by high-resolution multiscale computer tomography. Separation of scales is identified by tomographic scans at $30μm$ digital resolution for the macroscopic reticulate structure and at $1μm$ digital resolution for the microscopic strut structure. Finite volume discretization and successive over-relaxation on increasingly refined grids are applied to solve numerically the pore-scale conduction heat transfer for several subsets of the tomographic data with a ratio of fluid-to-solid thermal conductivity ranging from $10−4$ to 1. The effective thermal conductivities of the macroscopic reticulate structure and of the microscopic strut structure are then numerically calculated and compared with effective conductivity model predictions with optimized parameters. For the macroscale reticulate structure, the models by Dul’nev, Miller, Bhattachary and Boomsma and Poulikakos, yield satisfactory agreement. For the microscale strut structure, the classical porosity-based correlations such as Maxwell’s upper bound and Loeb’s models are suitable. Macroscopic and microscopic effective thermal conductivities are superimposed to yield the overall effective thermal conductivity of the composite RPC material. Results are limited to pure conduction and stagnant fluids or to situations where the solid phase dominates conduction heat transfer.

Commentary by Dr. Valentin Fuster

### Research Papers: Thermal Systems

J. Heat Transfer. 2008;130(3):032801-032801-6. doi:10.1115/1.2804949.

Heat transfer during compression and expansion of gas is investigated to obtain a correlation that is easy to use in the design of the reciprocating energy conversion machines. We carried out experiments to measure the heat transfer characteristics to̸from gas during compression and expansion to obtain the correlation. These measurements were performed using a piston-cylinder assembly over a range of volume ratios, frequencies, mean pressures, gases, and internal extended surface areas. The heat transfer was estimated thermodynamically from experimental pressure-volume data. Dimensionless groups for heat transfer are discussed in order to correlate the data. The product of the dimensionless heat transfer and specific heat ratio was found to be optimal and was correlated with only the Peclet number for a wide range of conditions, even for gases having different specific heat ratios. The temperature amplitude of the center of the test space was obtained, and it is found that the penetration depth reached the center when the Peclet number is in the range from 20 to 30.

Commentary by Dr. Valentin Fuster

### Research Papers: Two-Phase Flow and Heat Transfer

J. Heat Transfer. 2008;130(3):032901-032901-10. doi:10.1115/1.2804937.

A three-dimensional mathematical model is presented that models bubble deformation of a dielectric fluid due to the presence of a nonuniform electric field and calculates the net dielectrophoretic force that is exerted by the electric field on the bubble. The study includes the development of a method of predicting the shape of a bubble based on the arbitrary distribution of stresses over its surface without requiring an axisymmetric configuration. The reciprocal effect of the bubble’s presence on the electric field is also incorporated into the model, and dimensional analysis is used to obtain a single key parameter that governs the bubble deformation phenomenon. Numerical implementation of the mathematical model shows that the bubble deformation can be significant. Furthermore, bubble deformation and electric field distortion can have significant effects on the dielectrophoretic behavior of bubbles in nonuniform fields, especially within small-scale devices where the bubble size and electrode spacing are similar in magnitude.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Heat Transfer. 2008;130(3):034501-034501-6. doi:10.1115/1.2804941.

Forced convection heat transfer in high porosity metal foam, either attached to an isothermal surface or confined between two isothermal plates, has been analyzed, assuming a repetitive simple cubic structure for the foam matrix. The model, in the microscopic level takes account of the forced convective heat transfer coupled with heat conduction through the foam fibers. Analytical expressions have been derived for the gas-solid temperature difference, total heat transfer through the foam, and efficiency of foam as an extended surface. The resulting expressions have strong resemblance with those of the conventional finned surface. The effect of porosity and foam density on the heat transfer in metallic foam has been established through parametric studies. Significant heat-transfer augmentation due to cross connections in metal struts has been noticed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):034502-034502-5. doi:10.1115/1.2804933.

The aim of this work is to present a critical examination of both the available experimental data and the performance of the available heat transfer correlations for oil-free ammonia horizontal in-tube boiling at fin-and-tube-type air-to-refrigerant liquid overfeed evaporation conditions. First, a selection and comparison of the experimental database found in the open literature at the mentioned working conditions is presented. Subsequently, after a short description of the most relevant heat transfer correlations, and in accordance with the selected data, a detailed analysis of the performance of each correlation is carried out. Results show an important divergence between the experimental data sets and conclude that the presently available correlations show considerable discrepancies in heat transfer coefficients within the selected conditions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):034503-034503-5. doi:10.1115/1.2804936.

The present work is aimed toward understanding the effect of flow boiling stability on critical heat flux (CHF) with Refrigerant 123 (R-123) and water in microchannel passages. Experimental data and theoretical model to predict the CHF are the focus of this work. The experimental test section has six parallel microchannels, with each having a cross-sectional area of $1054×157μm2$. The effect of flow instabilities in microchannels is investigated using flow restrictors at the inlet of each microchannel to stabilize the flow boiling process and avoid the backflow phenomena. This technique resulted in successfully stabilizing the flow boiling process. The present experimental CHF results are found to correlate best with existing correlations to overall mean absolute errors (MAEs) of 33.9% and 14.3% with R-123 and water, respectively, when using a macroscale rectangular equation by Katto (1981, “General Features of CHF of Forced Convection Boiling in Uniformly Heated Rectangular Channels  ,” Int. J. Heat Mass Transfer, 24, pp. 1413–1419). A theoretical analysis of flow boiling phenomena revealed that the ratio of evaporation momentum to surface tension forces is an important parameter. A theoretical CHF model is proposed using these underlying forces to represent CHF mechanism in microchannels, and its correlation agrees with the experimental data with MAE of 2.5%.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):034504-034504-4. doi:10.1115/1.2804946.

An experimental apparatus was designed and fabricated to measure the effective thermal conductivities and simulate the temperature and pressure history of reentry of a launch vehicle into a planetary atmosphere with a maximum temperature of $1600°C$. An improved testing method was used to test the thermal conductivities of an alumina fibrous insulation at environmental pressures from $0.03Pato105Pa$ with the average temperature of the sample increased to $864°C$ and its density being $128kg∕m3$. A method based on temperature difference is used to compute the in-plane effective thermal conductivity, and the result shows that the in-plane thermal conductivity along the $y$ axis is 1.47 times that along the $x$ axis. The influences of temperature and pressure on the contribution of three heat transfer mechanisms to the effective thermal conductivities were compared.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2008;130(3):034505-034505-4. doi:10.1115/1.2804948.

This paper deals with phase change material (PCM), used in conjunction with thermal conductivity enhancer (TCE), as a means of thermal management of electronic systems. Eicosane is used as PCM, while aluminium pin or plate fins are used as TCE. The test section considered in all cases is a $42×42mm2$ base with a TCE height of $25mm$. An electrical heater at the heat sink base is used to simulate the heat generation in electronic chips. Various volumetric fractions of TCE in the conglomerate of PCM and TCE are considered. The case with 8% TCE volume fraction was found to have the best thermal performance. With this volume fraction of TCE, the effects of fin dimension and fin shape are also investigated. It is found that a large number of small cross-sectional area fins is preferable. A numerical model is also developed to enable an interpretation of experimental results.

Commentary by Dr. Valentin Fuster