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HEAT TRANSFER PHOTOGALLERY

J. Heat Transfer. 2004;126(4):493-506. doi:10.1115/1.1778411.
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Commentary by Dr. Valentin Fuster

PHOTOGALLERY

J. Heat Transfer. 1904;126(4):494. doi:10.1115/1.1811713.
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Abstract
Topics: Heat transfer
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1904;126(4):495. doi:10.1115/1.1811714.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1904;126(4):496. doi:10.1115/1.1811715.
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Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1904;126(4):499. doi:10.1115/1.1811718.
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Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1904;126(4):503. doi:10.1115/1.1811722.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1904;126(4):504. doi:10.1115/1.1811723.
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Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1904;126(4):505. doi:10.1115/1.1811724.
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Abstract
Topics: Nanoparticles
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

RESEARCH PAPER

J. Heat Transfer. 2004;126(4):507-517. doi:10.1115/1.1777579.

Scale deposition on the heat transfer surfaces from water containing dissolved salts considerably reduces fuel economy and performance of heat transfer equipment. This problem is more serious during nucleate boiling due to the mechanisms of bubble formation and detachment. Using a precision pool boiling test apparatus, the effects of heat flux and calcium sulfate concentration on heat transfer coefficient and formation and growth of deposits are investigated. The transient change in heat transfer is closely related to wick boiling, and the associated changes in bubble departure diameter and bubble site density. A physically sound prediction model was developed for the prediction of heat transfer coefficients as a function of time during deposition processes. Based on comparison with experimental data over a wide range of foulant concentrations and heat fluxes, the model is considered to be sufficiently accurate for practical application.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):518-526. doi:10.1115/1.1778187.

Microchannels are being considered in many advanced heat transfer applications including automotive and stationary fuel cells as well as electronics cooling. However, there are a number of fundamental issues from the heat transfer and fluid mechanics perspectives that still remain unresolved. The present work focuses on obtaining the fundamental heat transfer data and two-phase flow patterns present during flow boiling in microchannels. An experimental investigation is performed for flow boiling using water in six parallel, horizontal microchannels with a hydraulic diameter of 207 μm. The ranges of parameters are: mass flux from 157 to 1782 kg/m2 s, heat flux from 5 to 930 kW/m2 , inlet temperature of 22°C, quality from sub-cooled to 1.0, and atmospheric pressure at the exit. The corresponding single-phase, all-liquid flow Reynolds number range at the saturation conditions is from 116 to 1318. The measured single-phase, adiabatic pressure drop agreed with the conventional theory within the experimental error. The experimental single-phase Nusselt number was found to be between the constant heat flux and the constant wall temperature boundary conditions, corresponding to NuH and NuT respectively. The flow visualization demonstrates that the flow reversal condition in parallel flow channels is due to bubble nucleation followed by its rapid growth. In addition, the dry-out condition is observed, showing a change in the contact angles of the liquid-vapor interface. The local flow boiling heat transfer coefficient exhibits a decreasing trend with increasing quality. A comparison with the nucleate boiling dominant regime of a flow boiling correlation shows good agreement, except for the large peak in two-phase heat transfer coefficient observed at the onset of nucleate boiling.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):527-534. doi:10.1115/1.1778188.

The heat transfer rates that develop when ammonia water mixtures condense within a small, un-vented, horizontal, shell and tube condenser are examined. The vapor flow within the condenser was constrained by baffles and the condensate created formed a pool that flowed along the base of the condenser. During the test program the inlet ammonia vapor concentration to the condenser varied from 0 to 10 wt % and the maximum local vapor concentration measured was 26 wt %. The experimental results demonstrate that the condensation heat transfer rates generally decrease with increasing ammonia concentration, however at low ammonia concentrations (<2 wt %) the local and overall heat transfer rates for the condenser were enhanced. When the ammonia concentration was 0.9 wt %, the vapor heat transfer rate was 34 percent greater than that predicted by the Nusselt analysis for steam at the same conditions. This enhancement is attributed to the disturbed morphology of the condensate film, created by Marangoni instabilities.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):535-539. doi:10.1115/1.1773585.

The present paper addresses the measurement errors in temperature due to the effects of surface-mounted temperature sensors like thermocouples. Heat conduction into or from the installed thermocouple wires can alter the temperature at the thermocouple junction as well as in its immediate vicinity. As a result, the emf appearing at the thermocouple terminals does not correspond to the actual surface temperature. In this paper, we present a dual-scale computational method that can be used to calculate the transient temperatures at the multiple thermocouple junctions during heating or cooling of an object. The basis of the method is a thermocouple submodel embedded in a FEM model for the parent object. The numerical results of the dual-scale computational model are compared with that of the conventional FEM models as well as the analytical solutions available. This paper also discusses the characteristics of surface-mounted thermocouples in a range of configurations.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):540-545. doi:10.1115/1.1773586.

The present experimental work investigates the effect of a metallic porous matrix, inserted in a pipe, on the rate of heat transfer. The pipe is subjected to a constant and uniform heat flux. The effects of porosity and thickness of the porous matrix on the heat transfer rate and pressure drop are investigated. That is, the surface temperature distribution along a heated section of the pipe, the pressure drop over this section, as well as the inlet temperature of the air were continuously monitored with a data acquisition system and recorded when steady-sate conditions were attained. The results obtained for a range of Reynolds numbers 1000–4500, comprise both laminar and turbulent regime. Also, the results are compared with the clear flow case where no porous insert was used. It is shown that higher heat transfer rates are achieved when using porous inserts at the expense of a reasonable pressure drop, which depends on the permeability of the porous matrix.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):546-553. doi:10.1115/1.1777580.

A detailed investigation on the effect of squealer geometries on the blade tip leakage flow and associated heat transfer is presented for a scaled up high pressure turbine blade in a low-speed wind tunnel facility. The linear cascade is made of four blades with the two corner blades acting as guides. The tip profile of a first stage rotor blade is used to fabricate the two-dimensional blade. The wind tunnel accommodates an 116° turn for the blade cascade. The mainstream Reynolds number based on the axial chord length based on cascade exit velocity is 4.83×105. An upstream wake effect is simulated with a spoked wheel wake generator placed upstream of the cascade. A turbulence grid placed even farther upstream generates a free-stream turbulence of 4.8%. The center blade has a tip clearance gap of 1.56% with respect to the blade span. Static pressure measurements are obtained on the blade surface and the shroud. Results show that the presence of the squealer alters the tip gap flow field significantly and produces lower overall heat transfer coefficients. The effects of different squealer arrangements are basically to study the effect of squealer rim placement on tip leakage flow and associated heat transfer. Detailed heat transfer measurements are obtained using a steady state liquid crystal technique. The effect of periodic unsteady wake effect is also investigated by varying the wake Strouhal number from 0–0.4. Results show that suction side squealers may be favorable in terms of overall reduction in heat transfer coefficients over the tip surface. However, the presence of a full squealer is most beneficial in terms of reducing overall heat load on the tip surface. There is reasonable effect of wake induced periodicity on tip heat transfer.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2003;126(4):554-557. doi:10.1115/1.1777583.

The effects of nozzle diameter on heat transfer and fluid flow are investigated for a round turbulent jet impinging on a flat plate surface. The flow at the nozzle exit has a fully developed velocity profile. A uniform heat flux boundary is created at the plate surface by using gold film Intrex, and liquid crystals are used to measure the plate surface temperature. The experiments are performed for the jet Reynolds number (Re) of 23,000, with a dimensionless distance between the nozzle and plate surface (L/d) ranging from 2 to 14 and a nozzle diameter (d) ranging from 1.36 to 3.40 cm. The results show that the local Nusselt numbers increase with the increasing nozzle diameter in the stagnation point region corresponding to 0≤r/d≤0.5. This may be attributed to an increase in the jet momentum and turbulence intensity level with the larger nozzle diameter, which results in the heat transfer augmentation. In the mean time, the effect of the nozzle diameter on the local Nusselt numbers is negligibly small at the wall jet region corresponding to r/d>0.5.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2003;126(4):558-565. doi:10.1115/1.1773584.

The present study has been performed for obtaining the heat transfer enhancement characteristics of the plural microencapsulated solid-liquid phase change materials (PCM) slurry having different sizes, which flows in a straight tube heated under a constant wall heat flux condition. In the turbulent flow region, the friction factor of the plural PCM slurry was found to be lower than that of pure water flow due to the drag reducing effect of the PCM slurry. The heat transfer coefficient of the plural PCMs slurry flow in the tube was increased by both effects of latent heat evolved in phase change process and micro-convection around plural microcapsules with different diameters. The experimental results revealed that the average heat transfer coefficient of the plural PCMs slurry flow was about 2∼2.8 times greater than that of a single phase of water.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):566-576. doi:10.1115/1.1777581.

It is recently conceptualized that nano-scale machining might be achieved by coupling electron emission with radiation transfer. A laser may be used to heat a workpiece to a threshold temperature, and a nano-probe might then transfer additional energy via electron emission to remove a minute amount of material. To investigate this hypothesis, a detailed numerical study is presented. The electron-beam transport is modeled using a Monte Carlo approach, and a radiation transfer model that includes Fresnel reflections is adapted to simulate laser heating. The numerical study suggests that approximately 0.5 W from a single electron-beam is sufficient to initialize local evaporation from a gold film. With the use of a laser, the required power can be halved if the film is sufficiently thin. This paper describes the details of the numerical study and establishes guidelines for such nano-scale machining processes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):577-585. doi:10.1115/1.1777582.

The thermal conductivity of nanometric objects or nanostructured materials can be determined using nonequilibrium molecular dynamics (NEMD) simulations. The technique is simple in its principle, and resembles a numerical guarded hot plate experiment. The “sample” is placed between a hot source and a cold source consisting of thermostatted sets of atoms. The thermal conductivity is obtained from the heat flux crossing the sample and the temperature profile in the system. Simulation results, however, exhibit a strong dependence of the thermal conductivity on the sample size. In this paper, we discuss the physical origin of this size dependence, by comparing MD results with those obtained from simple models of thermal conductivity based on harmonic theory of solids. A model is proposed to explain the variation of the thermal conductivity with system size.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):586-599. doi:10.1115/1.1773588.

The three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow in a vertical cylinder with a partially heated sidewall is studied numerically. The central part of the sidewall is maintained at constant temperature, while its upper and lower parts are thermally insulated. The dependence of the critical Grashof number on the cylinder aspect ratio (A=height/radius) is obtained for a fixed value of the Prandtl number, Pr=0.021, and fixed length of the heated central region, equal to the cylinder radius. Three different modes of the most dangerous three-dimensional perturbations, which replace each other with the variation of the aspect ratio, are found. Comparison with experiment shows a good agreement at the aspect ratio A=8 and 12, while at A=4 a significant disagreement is observed. Possible reasons for this disagreement are discussed. At A=4, the dependence of the critical Grashof number on the Prandtl number is studied in the range 0<Pr<0.05, to rule out the possibility that the disagreement is due to uncertainty in values of fluid properties. The similarities and differences of instabilities in the cylindrical and rectangular geometries are examined. The computations are carried out using two independent numerical approaches, which cross-validate each other.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):600-610. doi:10.1115/1.1777578.

The heat transport in two-layer fluid systems has been investigated numerically for slice-type semicircular pools with internal heat sources. The fixed interface model has been applied to study natural convection in the system of the immiscible fluids. The double-diffusion model has been employed to describe the heat transfer and mixing for the miscible fluids. The numerical results are compared to data measured in the SIMECO experiments. Based on the numerical simulations, the effect of the ratio of the fluid properties has been quantified. The results are of interest for the corium melt coolability in a postulated severe accident scenario in a light water reactor.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):611-620. doi:10.1115/1.1773196.

A detailed, two-dimensional, laminar, flame spread model over a thin solid is solved in both a normal gravity downward spread configuration and in a microgravity quiescent atmosphere configuration. The radiation transfer equation is solved using discrete ordinates methods. While flame radiation plays only a secondary role in normal gravity spread, it is crucial in microgravity. By using the solid fuel total emittance and total absorptance as parameters, systematic computations have been performed to isolate the roles of flame radiative loss to the ambient, absorption of flame radiation by the solid and solid emission. Computations show that depending on the values of the solid radiation parameters, trend reversals in spread rate and extinction limits between flames in normal gravity and in microgravity can occur.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):621-627. doi:10.1115/1.1773587.

The Monte Carlo (MC) method has been widely used to solve radiative transfer problems due to its flexibility and simplicity in simulating the energy transport process in arbitrary geometries with complex boundary conditions. However, the major drawback of the conventional (or forward) Monte Carlo method is the long computational time for converged solution. Reverse or backward Monte Carlo (RMC) is considered as an alternative approach when solutions are only needed at certain locations and time. The reverse algorithm is similar to the conventional method, except that the energy bundle (photon ensemble) is tracked in a time-reversal manner. Its migration is recorded from the detector into the participating medium, rather than from the source to the detector as in the conventional MC. There is no need to keep track of the bundles that do not reach a particular detector. Thus, RMC method takes up much less computation time than the conventional MC method. On the other hand, RMC will generate less information about the transport process as only the information at the specified locations, e.g., detectors, is obtained. In the situation where detailed information of radiative transport across the media is needed the RMC may not be appropriate. RMC algorithm is most suitable for diagnostic applications where inverse analysis is required, e.g., optical imaging and remote sensing. In this study, the development of a reverse Monte Carlo method for transient radiative transfer is presented. The results of non-emitting, absorbing, and anisotropically scattering media subjected to an ultra short light pulse irradiation are compared with the forward Monte Carlo and discrete ordinates methods results.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):628-637. doi:10.1115/1.1773194.

Passive control of steady and unsteady thermal loads using effective thermal conductivity enhancers, such as metal foams, internal fins and metal filler particles, is being explored for a variety of electronics applications. The interstices are filled with air, phase change materials, or other fluids. Local thermal equilibrium between the solid filler and the matrix is not ensured in such systems since their thermal diffusivities are frequently very different. The use of a single volume-averaged energy equation for both the phases cannot be justified in such situations. A two-medium approach is used in the present work to account for the local thermal non-equilibrium. Separate energy equations are written for the solid and fluid respectively, and are closed using a steady-state interphase heat transfer coefficient between the two phases. A general momentum equation which includes the Brinkman-Forchheimer extension to Darcy flow is employed. The resulting equations are solved implicitly using a fully transient method on fixed orthogonal co-located finite volumes. Unsteady natural convection in a metal-foam filled cavity is computed. The influence of various parameters such as the ratios of solid-to-fluid thermal conductivities and heat capacities, Rayleigh number, Prandtl number and Darcy number on the thermal and flow fields is investigated. The results illustrate that local thermal equilibrium is not assured, either during the transient or at steady state for the range of parameters considered. Furthermore, even if the steady-state solid-to-fluid temperature differences are small, large temperature differences are seen during the unsteady response.

Commentary by Dr. Valentin Fuster

TECHNICAL NOTES

J. Heat Transfer. 2004;126(4):638-641. doi:10.1115/1.1778190.

Nucleate pool boiling heat transfer of water on the inside surface of a horizontal tube of 51 mm internal diameter has been studied experimentally at atmospheric pressure. Experiments were performed at four different azimuthal angles (0 deg, 45 deg, 120 deg, and 180 deg from the tube bottom) to investigate variations in local heat transfer coefficients along the tube periphery. The local coefficient changes much along the tube periphery and the minimum was observed at the tube bottom. It is found that heat transfer on the inside surface is strongly dependent on the intensity of the liquid agitation and the evaporative mechanism.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):642-647. doi:10.1115/1.1773195.

Three-dimensional conjugate heat transfer in a rectangular duct with two discrete flush-mounted heat sources has been studied numerically in the context of cooling of electronic equipments. The Grashof number is fixed as 106 and the working fluid is taken as air. The effects of the spatial arrangement of heat sources, the thermal conductivity ratio of the bottom plate material to air, and the Reynolds numbers on the overall and local heat transfer in the duct are evaluated. The magnitudes of the conduction and the convection transport are compared for different parametric combinations. Of particular interest are the transverse variation in the flow, temperature and heat transfer, the interaction between the heat sources, and the effects of conjugate transport.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):648-651. doi:10.1115/1.1773193.

Transient radiative heat transfer in a two-dimensional inhomogeneous rectangular medium is considered. The medium is gray, absorbing, emitting and strongly scattering, and bounded by cold, black walls. Inhomogeneous zones of various sizes are placed at different locations within the medium. The incident radiant energy due to a short laser pulse produces a highly transient and unique transmittance, which is investigated. The discrete wavelets method is used to solve the corresponding equation of transient radiative transfer. The time dependent transmittance for various inhomogeneous areas and the significance of the size and location of the inhomogeneous zones are computed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):652-655. doi:10.1115/1.1778189.

An analytical solution is proposed to calculate the thermal constriction resistance for an eccentric circular spot with uniform flux on a semi-infinite circular heat flux tube. This solution is developed using the finite cosine Fourier transform and the finite Hankel transform. It allows to calculate the stationary three-dimensional temperature distribution and the thermal constriction resistance. The results of proposed solution are in agreement with available theoretical and experimental studies. We show that the thermal constriction resistance for an eccentric contact is greater than the one of a centered contact (few tens percent), which is consistent with recent studies on random contacts. A simple correlation is also proposed to calculate the thermal constriction resistance as a function of the eccentricity and the relative contact size.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2004;126(4):656-659. doi:10.1115/1.1777585.

This paper uses the entropy generation minimization (EGM) method to optimize a single-phase, convective, fully developed flow with uniform and constant heat flux. For fixed mass flow rate and fixed total heat transfer rate, and the assumption of uniform and constant heat flux, an optimal Reynolds number for laminar and turbulent flow is obtained. The study also compares optimal Reynolds number and minimum entropy generation for cross sections: square, equilateral triangle, and rectangle with aspect ratios of two and eight. The rectangle with aspect ratio of eight had the smallest optimal Reynolds number, the smallest entropy generation number, and the smallest flow length.

Commentary by Dr. Valentin Fuster

DISCUSSION AND CLOSURE

J. Heat Transfer. 2004;126(4):660. doi:10.1115/1.1755247.
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Bejan,  A., 1996, “ Street Network Theory of Organization in Nature,” J. Adv. Transp., JATRDC30, pp. 85–107.9qiJATRDC0197-6729Bejan, A., 1997, Advanced Engineering Thermodynamics, 2ed, John Wiley and Sons, New York, NY.Bejan,  A., 1997, “ Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, IJHMAK40, pp. 799–816.ijhIJHMAK0017-9310Nelson, Jr., R. A., and Bejan, A., 1998, “Self-Organization of the Internal Flow Geometry in Convective Heat Transfer,” ASME HTD-Vol 356-3, pp. 149–161.Nelson,  R. A., and Bejan,  A., 1998, “ Constructal Optimization of Internal Flow Geometry in Convection,” ASME J. Heat Transfer, JHTRAO120, pp. 357–364.97lJHTRAO0022-1481Bejan,  A., and Tondeur,  D., 1998, “ Equipartition, Optimal Allocation, and the Constructal Approach to Predicting Optimization in Nature,” Rev. Gen. Therm., RGTHA737, pp. 165–180.rgtRGTHA70035-3159Bejan, A., 2000, Shape and Structure From Engineering to Nature, Cambridge University Press, Cambridge, UK.

J. Heat Transfer. 2004;126(4):660-661. doi:10.1115/1.1755248.
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Chai,  L. H., and Shoji,  M., 2002, “ Self-Organization and Self-Similarity in Boiling Systems,” ASME J. Heat Transfer, JHTRAO124(3), pp. 507–515.97lJHTRAO0022-1481Nelson,  A., and Bejan,  A., 1998, “ Constructal Optimization of Internal Flow Geometry in Convection,” ASME J. Heat Transfer, JHTRAO120(2), pp. 357–364.97lJHTRAO0022-1481Bejan, A., 1997, Advanced Engineering Thermodynamics, Wiley, New York, Chap. 13.Nelson,  A., and Bejan,  A., 1998, “ Self-Organization of the Internal Flow Geometry in Convective Heat Transfer,” ASME HTD,ZZZZZZ357(3), pp. 149–161.Bejan, A., 2000, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK.

J. Heat Transfer. 2004;126(4):661. doi:10.1115/1.1755249.
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J. Heat Transfer. 2004;126(4):661-662. doi:10.1115/1.1755250.
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Chai,  L. H., and Shoji,  M., 2002, “ Self-Organization and Self-Similarity in Boiling Systems,” ASME J. Heat Transfer, JHTRAO124, pp. 507–515.97lJHTRAO0022-1481Bejan,  A., 1997, “ Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, IJHMAK40, pp. 799–816.ijhIJHMAK0017-9310Heinrich,  B., 1981, “ The Mechanism and Energetics of Honeybee Swarm Temperature Regulation,” J. Exp. Biol., JEBIAM91, pp. 25–55.jewJEBIAM0022-0949Basak,  T., Rao,  K. K., and Bejan,  A., 1996, “ A Model for Heat Transfer in a Honey Bee Swarm,” Chem. Eng. Sci., CESCAC51, pp. 387–400.cerCESCAC0009-2509Bejan,  A., 2000, “ From Heat Transfer Principles to Shape and Structure in Nature: Constructal Theory,” ASME J. Heat Transfer, JHTRAO122, pp. 430–449.97lJHTRAO0022-1481

J. Heat Transfer. 2004;126(4):662. doi:10.1115/1.1755251.
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Chai,  L. H., and Shoji,  M., 2002, “ Self-Organization and Self-Similarity in Boiling Systems,” ASME J. Heat Transfer, JHTRAO124, pp. 507–515.97lJHTRAO0022-1481Bejan,  A., 1997, “ Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, IJHMAK40, pp. 799–816.ijhIJHMAK0017-9310Bejan, A., 2000, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge, UK.

J. Heat Transfer. 2004;126(4):662-663. doi:10.1115/1.1755252.
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Bejan,  A., 1997, “ Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, IJHMAK40(4), pp. 799–816.ijhIJHMAK0017-9310Bejan, A., 2000, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge.Cervantes-de Gortari,  J., 2002, “ Shape and Structure, from Engineering to Nature,” by A. Bejan, book review, Int. J. Heat Mass Transfer, IJHMAK45(7), p. 1583.ijhIJHMAK0017-9310

J. Heat Transfer. 2004;126(4):663-665. doi:10.1115/1.1755253.
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Chai,  L. H., and Shoji,  M., 2002, “ Self-Organization and Self-Similarity in Boiling Systems,” ASME J. Heat Transfer, JHTRAO124, pp. 507–515.97lJHTRAO0022-1481Chai, L. H., 1999, “Binary Mixtures Boiling Under Microgravity and Nonlinear Features of Boiling,” Ph.D. thesis, Tsinghua University, China.Chai,  L. H., Peng,  X. F., and Wang,  B. X., 2000, “ Nucleation Site Interaction During Boiling,” Int. J. Heat Mass Transfer, IJHMAK43, pp. 4249–4258.ijhIJHMAK0017-9310Klimontovich, Y. L., 1991, Turbulent Motion and the Structure of Chaos. A New Approach to the Statistical Theory of Open Systems, Kluwer Academic Publishers, Boston, London.Haken, H., 1977, Synergetics, Springer, Berlin.Prigogine, I., 1980, From Being to Becoming, W. H. Freeman, San Francisco.Nicolis, G., and Prigogine, I., 1977, Self-Organization in Nonequilibrium Systems, Wiley, New York.Stratonovich, R. L., 1992, Nonlinear Non-Equilibrium Thermodynamics I, Springer Verlag, Berlin.Lavenda, B. H., 1993, Thermodynamics of Irreversible Processes, Dover ed., Dover, New York.Gallagher,  R., and Appenzeller,  T., 1999, “ Beyond Reductionism,” Science, SCIEAS284, pp. 87–109.sciSCIEAS0036-8075Haken, H., 1983, Advanced Synergetics, Springer, Berlin.Toda, M., Kubo, R., and Saito, N., 1992, Statistical Physics 1, Springer, Berlin.Haken, H., 2000, Information and Self-Organization, Springer, Berlin.Mandelbrot, B., 1982, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, CA.Bejan, A., 1997, Advanced Engineering Thermodynamics, Wiley, New York, Chpt. 13.Takayasu, H., 1992, Fractals in the Physical Sciences, John Wiley & Sons.Waldrop, M. M., 1992, Complexity: The Emerging Science at the Edge of Order and Chaos, Simon & Schuster, New York.Davies,  K. G., 2000, “ Creative Tension—What Links Aristotle, William Blake, Darwin and GM Corps?” Nature (London), NATUAS407(6807), p. 135.natNATUAS0028-0836

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