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

J. Heat Transfer. 2008;130(5):051501-051501-9. doi:10.1115/1.2887858.

A mathematical model predicting the heat transport capability in a miniature flat heat pipe (FHP) with a wired wick structure was developed to analytically determine its maximum heat transport rate including the capillary limit. The effects of gravity on the profile of the thin-film-evaporation region and the distribution of the heat flux along a curved surface were investigated. The heat transfer characteristics of the thin-film evaporation on the curved surface were also analyzed and compared with that on a flat surface. Combining the analysis on the thin-film-condensation heat transfer in the condenser, the model can be used to predict the total temperature drop between the evaporator and condenser in the FHP. In order to verify the model, an experimental investigation was conducted. The theoretical results predicted by the model agree well with the experimental data for the heat transfer process occurring in the FHP with the wired wick structure. Results of the investigation will assist in the optimum design of the curved-surface wicks to enlarge the thin-film-evaporation region and a better understanding of heat transfer mechanisms in heat pipes.

### Research Papers: Forced Convection

J. Heat Transfer. 2008;130(5):051701-051701-8. doi:10.1115/1.2885182.

The motion of a two-dimensional vortex pair moving toward a wall is studied numerically. The case for which the wall is heated is analyzed. The equations of momentum and energy conservation are solved using a finite volume scheme. In this manner, the instantaneous heat transfer from the wall is obtained and is related to the dynamics of the fluid vortex interacting with the wall. It was found that, as expected, when the fluid vortex approaches the wall, the heat transfer increases significantly. The heat transfer changes in a nonmonotonic manner as a function of time: When the vortex first reaches the wall, a volume of heated fluid is convected from the wall; this fluid volume circulates in the vicinity of the wall, causing the rate of heat transfer to decrease slightly, to then increase again. A wide range of Prandtl and Reynolds numbers were tested. A measure of the effective heat transfer coefficient, or Nusselt number, is proposed.

J. Heat Transfer. 2008;130(5):051702-051702-8. doi:10.1115/1.2884184.

This paper investigates the inverse heat transfer problem of laminar forced convection within a circular pipe. The performances of two classical algorithms used in the whole domain function specification method (WDFSM) to obtain simultaneous estimates of the time-varying inlet temperature and outer-wall heat flux are compared. Additionally, this study proposes a modification to the linear assumption employed in the conventional WDFSM to improve its estimation performance. The WDFSM solution procedure is based on future temperature measurements at two different locations within the pipe flow. In the modified algorithm, the variations of the estimations at all time steps for various values of the future-time parameter are investigated, and if large variations in the slope of the function are detected at some time steps, the originally linear assumption for the variation of the unknowns is replaced with the assumption of a constant function at these time steps. Otherwise, the estimates at the other time steps are calculated using the linear assumption. The numerical results confirm that the proposed algorithm yields slightly more accurate estimates of the unknowns than the two classic algorithms.

J. Heat Transfer. 2008;130(5):051703-051703-20. doi:10.1115/1.2885156.

This paper attempts to provide a detailed insight into the heat transfer and aerodynamic behavior of a separation zone that is generated as a result of boundary layer development along the suction surface of a highly loaded low pressure turbine blade. This paper experimentally investigates the individual and combined effects of periodic unsteady wake flows and freestream turbulence intensity (Tu) on heat transfer and aerodynamic behavior of the separation zone. Heat transfer experiments were carried out at Reynolds numbers of 110,000, 150,000, and 250,000 based on the suction surface length and the cascade exit velocity. Aerodynamic experiments were performed at $Re=110,000$. For the above Re numbers, the experimental matrix includes Tu’s of 1.9%, 3.0%, 8.0%, and 13.0% and three different unsteady wake frequencies with the steady inlet flow as the reference configuration. Detailed heat transfer and boundary layer measurements are performed with particular attention paid to the heat transfer and aerodynamic behavior of the separation zone at different Tu’s at steady and periodic unsteady flow conditions. The objectives of the research are (a) to quantify the effect of Tu on the aerothermal behavior of the separation bubble at steady inlet flow conditions, (b) to investigate the combined effects of Tu and the unsteady wake flow on the aerothermal behavior of the separation bubble, and (c) to provide a complete set of heat transfer and aerodynamic data for numerical simulation that incorporates Navier–Stokes and energy equations. The experimental investigations were performed in a large-scale, subsonic, unsteady turbine cascade research facility at the Turbomachinery Performance and Flow Research Laboratory of Texas A&M University.

### Research Papers: Heat Exchangers

J. Heat Transfer. 2008;130(5):051801-051801-9. doi:10.1115/1.2885153.

Transient analysis helps us to predict the behavior of heat exchangers subjected to various operational disturbances due to sudden change in temperature or flow rates of the working fluids. The present experimental analysis deals with the effect of flow distribution on the transient temperature response for $U$-type and $Z$-type plate heat exchangers. The experiments have been carried out with uniform and nonuniform flow distributions for various flow rates. The temperature responses are analyzed for various transient characteristics, such as initial delay and time constant. It is also possible to observe the steady state characteristics after the responses reach asymptotic values. The experimental observations indicate that the $Z$-type flow configuration is more strongly affected by flow maldistribution compared to the $U$-type in both transient and steady state regimes. The comparison of the experimental results with numerical solution indicates that it is necessary to treat the flow maldistribution separately from axial thermal dispersion during modeling of plate heat exchanger dynamics.

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2008;130(5):052401-052401-9. doi:10.1115/1.2885159.

Owing to their high thermal conductivities, carbon nanotubes (CNTs) are promising for use in advanced thermal interface materials. While there has been much previous research on the properties of isolated CNTs, there are few thermal data for aligned films of single wall nanotubes. Furthermore, such data for nanotube films do not separate volume from interface thermal resistances. This paper uses a thermoreflectance technique to measure the volumetric heat capacity and thermal interface resistance and to place a lower bound on the internal volume resistance of a vertically aligned single wall CNT array capped with an aluminum film and palladium adhesion layer. The total thermal resistance of the structure, including volume and interface contributions, is $12m2KMW−1$. The data show that the top and bottom interfaces of the CNT array strongly reduce its effective vertical thermal conductivity. A low measured value for the effective volumetric heat capacity of the CNT array shows that only a small volume fraction of the CNTs participate in thermal transport by bridging the two interfaces. A thermal model of transport in the array exploits the volumetric heat capacity to extract an individual CNT-metal contact resistance of $10m2K1GW−1$ (based on the annular area $Aa=πdb$), which is equivalent to the volume resistance of $14nm$ of thermal $SiO2$. This work strongly indicates that increasing the fraction of CNT-metal contacts can reduce the total thermal resistance below $1m2KMW−1$.

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2008;130(5):052501-052501-11. doi:10.1115/1.2780183.

Steady laminar free convection in air from a pair of misaligned, parallel horizontal cylinders, i.e., a pair of parallel cylinders with their axes set in a plane inclined with respect to the gravity vector, is studied numerically. A specifically developed computer code based on the SIMPLE-C algorithm is used for the solution of the dimensionless mass, momentum, and energy transfer governing equations. Results are presented for different values of the center-to-center cylinder spacing from 1.4 up to 10 diameters, the tilting angle of the two-cylinder array from $0degto90deg$, and the Rayleigh number based on the cylinder diameter in the range between $103$ and $107$. It is found that the heat transfer rates at both cylinder surfaces may in principle be traced back to the combined contributions of the so-called plume effect and chimney effect, which are the mutual interactions occurring in the vertical and horizontal alignments, respectively. In addition, at any misalignment angle, an optimum spacing between the cylinders for the maximum heat transfer rate, which decreases with increasing the Rayleigh number, does exist. Heat transfer dimensionless correlating equations are proposed for any individual cylinder and for the pair of cylinders as a whole.

J. Heat Transfer. 2008;130(5):052502-052502-9. doi:10.1115/1.2885166.

A computational study of steady, laminar, natural convective fluid flow in a partially open square enclosure with a highly conductive thin fin of arbitrary length attached to the hot wall at various levels is considered. The horizontal walls and the partially open vertical wall are adiabatic while the vertical wall facing the partial opening is isothermally hot. The current work investigates the flow modification due to the (a) attachment of a highly conductive thin fin of length equal to 20%, 35%, or 50% of the enclosure width, attached to the hot wall at different heights, and (b) variation of the size and height of the aperture located on the vertical wall facing the hot wall. Furthermore, the study examines the impact of Rayleigh number $(104⩽Ra⩽107)$ and inclination of the enclosure. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. The results show that the presence of the fin has counteracting effects on flow and temperature fields. These effects are dependent, in a complex way, on the fin level and length, aperture altitude and size, cavity inclination angle, and Rayleigh number. In general, Nusselt number is directly related to aperture altitude and size. However, after reaching a peak Nusselt number, Nusselt number may decrease slightly if the aperture’s size increases further. The impact of aperture altitude diminishes for large aperture sizes because the geometrical differences decrease. Furthermore, a longer fin causes higher rate of heat transfer to the fluid, although the equivalent finless cavity may have higher heat transfer rate. In general, the volumetric flow rate and the rate of heat loss from the hot surfaces are interrelated and are increasing functions of Rayleigh number. The relationship between Nusselt number and the inclination angle is nonlinear.

### Research Papers: Porous Media

J. Heat Transfer. 2008;130(5):052601-052601-9. doi:10.1115/1.2885871.

The effect of temperature modulation on the onset of thermal convection in an electrically conducting fluid-saturated-porous medium, heated from below, has been studied using linear stability analysis. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. The porous medium is confined between two horizontal walls and subjected to a vertical magnetic field; flow in porous medium is characterized by Brinkman–Darcy model. Considering only infinitesimal disturbances, and using perturbation procedure, the combined effect of temperature modulation and vertical magnetic field on thermal instability has been studied. The correction in the critical Rayleigh number is calculated as a function of frequency of modulation, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number, and the nondimensional group number $χ$. The influence of the magnetic field is found to be stabilizing. Furthermore, it is also found that the onset of convection can be advanced or delayed by proper tuning of the frequency of modulation. The results of the present model have been compared with that of Darcy model.

### Technical Briefs

J. Heat Transfer. 2008;130(5):054501-054501-4. doi:10.1115/1.2885162.

This technical brief addresses an elementary analytic procedure for solving approximately the quasi-1D heat conduction equation (a generalized Airy equation) governing the annular fin of hyperbolic profile. The importance of this fin configuration stems from the fact that its geometrical shape and heat transfer performance are reminiscent of the annular fin of convex parabolic profile, the so-called optimal annular fin. To avoid the disturbing variable coefficient in the quasi-1D heat conduction equation, usage of the mean value theorem for integration is made. Thereafter, invoking a coordinate transformation, the product is a differential equation, which is equivalent to the quasi-1D heat conduction equation for the simple straight fin of uniform profile. The nearly exact analytic temperature distribution is conveniently written in terms of the two controlling parameters: the normalized radii ratio $c$ and the dimensionless thermogeometric parameter $M2$, also called the enlarged Biot number. For engineering analysis and design, the estimates of temperatures and heat transfer rates for annular fins of hyperbolic profile owing realistic combinations of $c$ and $M2$ give evidence of good quality.

J. Heat Transfer. 2008;130(5):054502-054502-5. doi:10.1115/1.2885173.

Similarity solution of unaxisymmetric heat transfer of an unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder with simultaneous axial and rotational movement along with transpiration $Uo$ is investigated when the angular velocity, axial velocity, and wall temperature or wall heat flux vary arbitrarily with time. The impinging free stream is steady and with a strain rate of $k¯$. The results presented are found by numerical integration. The local coefficient of heat transfer (Nusselt number) is found to be independent of time and place, though the cylinder wall temperature or wall heat flux are functions of both time and place.

J. Heat Transfer. 2008;130(5):054503-054503-9. doi:10.1115/1.2887850.

The transient critical heat fluxes (CHFs) of the subcooled water flow boiling for the flow velocities $(u=4.0–13.3m∕s)$, the inlet subcoolings $(ΔTsub,in=68.08–161.12K)$, the inlet pressures $(Pin=718.31–1314.62kPa)$, the dissolved oxygen concentrations ($O2=2.94ppm$ to the saturated one), and the exponentially increasing heat inputs ($Q0exp(t∕τ)$, $τ=16.82msto15.52s$) are systematically measured with an experimental water loop comprised of a pressurizer. The SUS304 tubes of the inner diameters ($d=3mm$, $6mm$, $9mm$, and $12mm$), heated lengths $(L=33.15–132.9mm)$, $L∕d=5.48–11.08$, and wall thickness ($δ=0.3mm$ and $0.5mm$) with the rough finished inner surface (surface roughness, $Ra=3.18μm$) are used in this work. The transient CHF data $(qcr,sub=6.91–60MW∕m2)$ are compared with the values calculated by the steady state CHF correlations against inlet and outlet subcoolings. The transient CHF correlations against inlet and outlet subcoolings are derived based on the experimental data. The dominant mechanisms of the subcooled flow boiling CHF for a high heating rate are discussed.

J. Heat Transfer. 2008;130(5):054504-054504-4. doi:10.1115/1.2884183.

Two small horizontal surfaces, heated to temperatures up to $220°C$, were cooled by small (50–300 mm diameter) room-temperature droplets at 1 atmosphere pressure. One surface was a 10×10 mm thin-film nichrome heater that was used to measure heat fluxes below 100 W/$cm2$. The other surface, used for fluxes in excess of 100 W/$cm2$, was a solid copper heater with an 8×8 mm exposed surface. A continuous jet droplet generator coupled with two mutually perpendicular deflection plates was used to manipulate the path of constant diameter water droplets so that the impact of the drops could be precisely located on the heated surfaces. The droplet generator and the deflection plates were employed so that the effect of the impact frequency, droplet diameter, droplet velocity and spacing on the resulting heat transfer rates could be studied under controlled conditions. Optimal droplet spacing between 0.75 and 1.5 times the droplet diameter increased the critical heat flux approximately 30 percent above the value that was achieved when the drops were deposited in one location. For area-averaged mass flow rates less than about 0.08 g/($cm2$s), there was no trend in the critical heat flux with the Weber number. However, for larger mass flux rates, the critical heat flux increased with an increasing Weber number. The measured critical heat flux values were roughly twice the heat flux of traditional pool boiling for identical superheat temperatures. Two droplet cooling dimensionless critical heat flux correlations are proposed as a function of Weber and Strouhal numbers; one for a single stream of drops and the other for drops that are spaced across the heated surface. The correlation for the spaced droplets is a function of a dimensionless droplet spacing on the heater.