bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical Prediction of Flow and Heat Transfer in a Parallel Plate Channel With Staggered Fins
Authors: Kelkar K. M. , Patankar S. V.
Published: October 2009

Fluid flow and heat transfer in two-dimensional finned passages were analyzed for constant property laminar flow. The passage is formed by two parallel plates to which fins are attached in a staggered fashion. Both the plates are maintained at a constant temperature. Streamwise periodic variation of the cross-sectional area causes the flow and temperature fields to repeat periodically after a certain developing length. Computations were performed for different values of the Reynolds number, the Prandtl number, geometric parameters, and the fin-conductance parameter. The fins were found to cause the flow to deflect significantly and impinge upon the opposite wall so as to increase the heat transfer significantly. However, the associated increase in pressure drop was an order of magnitude higher than the increase in heat transfer. Streamline patterns and local heat transfer results are presented in addition to the overall results.
Heat Transfer Downstream of an Abrupt Expansion in the Transition Reynolds Number Regime
Authors: Baughn J. W. , Hoffman M. A. , Takahashi R. K. , Lee Daehee
Published: October 2009

The heat transfer downstream of an axisymmetric abrupt expansion in a pipe in the transition Reynolds number regime has been investigated experimentally. In these experiments the wall of the downstream pipe was heated to give a constant heat flux into the air flow. The ratio of the upstream to downstream pipe diameters was 0.8 and the downstream Reynolds number ranged from 1420 to 8060. Within a narrow range of Reynolds numbers, around 5000, the position of the maximum Nusselt number was found to shift considerably. This interesting behavior may be associated with the flow instabilities in sudden expansions which have been observed by others.
Local Heat Transfer Measurements in Turbulent Flow Around a 180-deg Pipe Bend
Authors: Baughn J. W. , Iacovides H. , Jackson D. C. , Launder B. E.
Published: October 2009

The paper reports extensive connective heat transfer data for turbulent flow of air around a U-bend with a ratio of bend radius:pipe diameter of 3.375:1. Experiments cover Reynolds numbers from 2 × 104 to 1.1 × 105. Measurements of local heat transfer coefficient are made at six stations and at five circumferential positions at each station. At Re = 6 × 104 a detailed mapping of the temperature field within the air is made at the same stations. The experiment duplicates the flow configuration for which Azzola and Humphrey [3] have recently reported laser-Doppler measurements of the mean and turbulent velocity field. The measurements show a strong augmentation of heat transfer coefficient on the outside of the bend and relatively low levels on the inside associated with the combined effects of secondary flow and the amplification/suppression of turbulent mixing by streamline curvature. The peak level of Nu occurs halfway around the bend at which position the heat transfer coefficient on the outside is about three times that on the inside. Another feature of interest is that a strongly nonuniform Nu persists six diameters downstream of the bend even though secondary flow and streamline curvature are negligible there. At the entry to the bend there are signs of partial laminarization on the inside of the bend, an effect that is more pronounced at lower Reynolds numbers.
Turbulent Heat Transfer in Corrugated-Wall Channels With and Without Fins
Authors: Amano R. S. , Bagherlee A. , Smith R. J. , Niess T. G.
Published: October 2009

A numerical study is performed examining flow and heat transfer characteristics in a channel with periodically corrugated walls. The complexity of the flow in this type of channel is demonstrated by such phenomena as flow impingement on the walls, separation at the bend corners, flow reattachment, and flow recirculation. Because of the strong nonisotropic nature of the turbulent flow in the channel, the full Reynolds-stress model was employed for the evaluation of turbulence quantities. Computations are made for several different corrugation periods and for different Reynolds numbers. The results computed by using the present model show excellent agreement with experimental data for mean velocities, the Reynolds stresses, and average Nusselt numbers. The study was further extended to a channel flow where fins are inserted at bends in the channel. It was observed that the insertion of fins in the flow passage has a visible effect on flow patterns and skin friction along the channel wall.
Secondary Flow Effects in High Tip Speed Free Convection
Authors: Eckels P. W. , Parker J. H. , Patterson A.
Published: October 2009

Experimental analyses of the effects of secondary flows on heat transfer in high tip speed rotating apparatus are not readily available. This paper provides data on the heat transfer within two different test modules which were rotated at high speed with the heat transfer surfaces perpendicular and parallel to the Coriolis acceleration. One module contained a heated wall and another a parallel plate free convection experiment. Uniform heat fluxes were maintained. Rayleigh numbers in excess of 1015 were achieved with liquid helium as the transfer medium. Some of the findings are that secondary flows can reduce heat transfer by as much as 60 percent in single-phase heat transfer, the transitions to fully turbulent flow are in agreement with existing prediction methods, the critical heat flux in two-phase flow boiling is significantly increased, forced convection correlations underpredict single-phase thermosyphon performance, and the usual nondimensional parameters of free convection establish similitude between various fluids and speeds. These results suggest that techniques used to enhance heat transfer in the rotating frame should be verified by tests in the rotating frame.
Two-Dimensional Transient Solutions for Crossflow Heat Exchangers With Neither Gas Mixed
Authors: Spiga G. , Spiga M.
Published: October 2009

The two-dimensional transient behavior of gas-to-gas crossflow heat exchangers is investigated, solving by analytical methods the thermal balance equations in order to determine the transient distribution of temperatures in the core wall and in both the unmixed gases. Assuming large wall capacitance, the general solutions are deduced by the Laplace transform method and are presented as integrals of modified Bessel functions on space and time, for a transient response with any arbitrary initial and inlet conditions, in terms of the number of transfer units, capacity rate and conductance ratio. Specializing the entrance temperature and assuming constant initial conditions, the most meaningful transient conditions (such as step, ramp, and exponential responses) have been simulated and the relevant solutions, expressed by means of either integrals or series, have been accurately computed with extremely low computational time. The temperature responses are then presented in graphic form for a wide range of the number of transfer units.
Forced Convection Cooling Across Rectangular Blocks
Authors: Davalath J. , Bayazitoglu Y.
Published: October 2009

Conjugate heat transfer for two-dimensional, developing flow over an array of rectangular blocks, representing finite heat sources on parallel plates, is considered. Incompressible flow over multiple blocks is modeled using the fully elliptic form of the Navier–Stokes equations. A control-volume-based finite difference procedure with appropriate averaging for the diffusion coefficients is used to solve the coupling between the solid and fluid regions. The heat transfer characteristics resulting from recirculating zones around the blocks are presented. The analysis is extended to study the optimum spacing between heat sources for a fixed heat input and a desired maximum temperature at the heat source.
Boundary-Layer Treatment of Forced Convection Heat Transfer From a Semi-infinite Flat Plate Embedded in Porous Media
Authors: Kaviany M.
Published: October 2009

The effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate is studied using the integral method. The closed-form solutions found are in good agreement with the available numerical results and also with the results obtained using a finite difference approximation and the expansion method. For large values of the flow resistance (due to the presence of the solid matrix), the asymptotic value for the heat transfer rate shows a Prandtl number dependency of 1/2 power, while the results for the intermediate values of the resistances show a 1/3 power dependency. The effect of the presence of the solid matrix on the heat transfer rate is shown through a regime diagram marking the boundaries of the regime of no significant alteration, the non-Darcian regime, and the Darcian regime.
Instabilities of Steady, Periodic, and Quasi-Periodic Modes of Convection in Porous Media
Authors: Kimura S. , Schubert G. , Straus J. M.
Published: October 2009

Instabilities of steady and time-dependent thermal convection in a fluid-saturated porous medium heated from below have been studied using linear perturbation theory. The stability of steady-state solutions of the governing equations (obtained numerically) has been analyzed by evaluating the eigenvalues of the linearized system of equations describing the temporal behavior of infinitesimal perturbations. Using this procedure, we have found that time-dependent convection in a square cell sets in at Rayleigh number Ra=390. The temporal frequency of the simply periodic (P(1)) convection at Rayleigh numbers exceeding this value is given by the imaginary part of the complex eigenvalue. The stability of this (P(1)) state has also been studied; transition to quasi-periodic convection (QP2) occurs at Ra ≈ 510. A reverse transition to a simply periodic state (P(2)) occurs at Ra ≈ 560; a slight jump in the frequency of the P(2) state occurs at Ra between 625 and 640. The jump coincides with a second narrow (in terms of Ra) region of quasi-periodicity.
Natural Convection Along a Finite Vertical Plate
Authors: Yang R. , Yao L. S.
Published: October 2009

The discrepancy between the measured mean heat flux for natural convection on a finite vertical plate and the solution of Pohlhausen, Schmidt, and Beckmann has been known for a long time; no theoretical explanation has ever been provided. In this paper, a double-deck structure is introduced to account for the trailing-edge effect. This solution shows that the flow accelerates near the training edge due to the geometric discontinuity which leads to a decreased flow constraint. An inward normal flow is induced by the local flow acceleration and generates a change in the displacement of the thin viscous layer near the plate. Consequently a pressure disturbance is developed and transmits information upstream. The heat flux and wall shear stress both increase due to this flow acceleration. Even though the effect on the total heat flux is small, the local heat flux is modified substantially. Thus the smaller effects due to the leading edge, the displacement, and the wake cannot be the reason for the discrepancy.
An Experimental Study of High Rayleigh Number Mixed Convection in a Rectangular Enclosure With Restricted Inlet and Outlet Openings
Authors: Neiswanger L. , Johnson G. A. , Carey V. P.
Published: October 2009

Measured local heat transfer data and the results of flow visualization studies are reported for cross-flow mixed convection in a rectangular enclosure with restricted inlet and outlet openings at high Rayleigh number. In this study, experiments using water as the test fluid were conducted in a small-scale test section with uniformly heated vertical side walls and an adiabatic top and bottom. As the flow rate through the enclosure increased, the enhancement of heat transfer, above that for natural convection alone, also increased. The variation of the local heat transfer coefficient over the heated surface was found to be strongly affected by the recirculation of portions of the forced flow within the enclosure. Mean heat transfer coefficients are also presented which were calculated by averaging the measured local values over the heated surface. A correlation for the mean heat transfer coefficient is also proposed which agrees very well with the experimentally determined values. A method of predicting the flow regime in this geometry for specified heating and flow conditions is also discussed.
Integral Solution of Diffusion Equation: Part 2—Boundary Conditions of Second and Third Kinds
Authors: Haji-Sheikh A. , Lakshminarayanan R.
Published: October 2009

An analytical solution of the diffusion equation using the Galerkin method to calculate the eigenvalues is currently available for boundary conditions of the first kind. This paper includes algebraic techniques to accommodate boundary conditions of the second and third kinds. Several case studies are presented to illustrate the utility and accuracy of the procedure. Selected examples either have no exact solutions or their exact solutions have not been cited because of the mathematical or numerical complexity. The illustrations include transient conduction in hemielliptical solids with either external convective surfaces or convective bases, and buried pipe in a square enclosure. Whenever possible, symbolic programming is used to carry out the differentiations and integrations. In some cases, however, the integrations must be strictly numerical. It is also demonstrated that a Green’s function can be defined to accommodate many geometries with nonorthogonal boundaries subject to more complex boundary conditions for which an exact Green’s function does not exist.
Effect of the Thermal Capacitance of Contained Fluid on Performance of Symmetric Regenerators
Authors: Romie F. E.
Published: October 2009

The operation of the symmetric counterflow regenerative heat exchanger is described for conditions under which the thermal capacitance of the contained fluid cannot, as is the usual case, be set equal to zero. The solution of the system equations is found by use of the Laplace transform method. The thermal effectiveness is presented for a range of parameters believed to cover most applications of the symmetric regenerator.
Sealing Strips in Tubular Heat Exchangers
Authors: Taylor C. E. , Currie I. G.
Published: October 2009

This paper presents design data relating to sealing strips for tubular heat exchangers. Sealing strip shapes, locations, and gap widths (the distance between the sealing strip and the nearest tube) are evaluated as to the pressure drop they create and, more importantly, as to their heat transfer characteristics. Velocity data were collected using a laser-Doppler anemometry system for which the fluid within the test model flow loop was refractive index matched with the pyrex rods that made up the tube bundle. A normalized heat transfer coefficient for each test has been inferred from the local velocity field. Unexpected trends were found in the heat transfer and pressure drop results of the gap width tests. It was concluded that the rectangular sealing strip located at the seventh row with a gap equal to the difference between the tube pitch and the tube diameter was the most effective. The successful application of LDA in the test program introduces a powerful measuring technique for the flow field in and around tube banks. From the measurements, pressure drops and heat transfer coefficients may be deduced. In addition, the technique will prove to be of great value in the field of flow-induced vibrations where detailed velocity data are required.
Turbulent Heat and Momentum Transports in an Infinite Rod Array
Authors: Yang An-Shik , Chieng Ching-Chang
Published: October 2009

An anisotropic factor is carefully selected from eleven distributions and adopted to the k–ε two-equation model of turbulence to obtain detailed velocity and temperature fields for steady-state, fully developed turbulent flow through infinite triangular/square rod array. The present study covers the ranges of pitch-to-diameter ratio from 1.123 to 1.5, and Reynolds number from 2.4 × 104 to 106. Velocity and wall shear stress are calculated and compared to experimental data. Normalized fluid temperature, friction factor, and heat transfer coefficient are also computed. The correlations of friction factor and heat transfer coefficients for flow inside circular pipe and flow through finite rod arrays are compared with the results for flow through infinite rod arrays.
Transition Boiling Heat Transfer and the Film Transition Regime
Authors: Ramilison J. M. , Lienhard J. H.
Published: October 2009

The “Berenson” flat-plate transition-boiling experiment has been re-created with a reduced thermal resistance in the heater, and an improved access to those portions of the transition boiling regime that have a steep negative slope. Tests have been made in Freon-113, acetone, benzene, and n-pentane boiling on horizontal flat copper heaters that have been mirror-polished, “roughened,” or teflon-coated. The resulting data reproduce and clarify certain features observed by Berenson: the modest surface finish dependence of boiling burnout, and the influence of surface chemistry on both the minimum heat flux and the mode of transition boiling, for example. A rational scheme of correlation yields a prediction of the heat flux in what Witte and Lienhard previously identified as the “film-transition boiling” region. It is also shown how to calculate the heat flux at the boundary between the pure-film, and the film-transition, boiling regimes, as a function of the advancing contact angle.
Crevice Boiling in Steam Generators
Authors: Tieszen S. , Merte H. , Arpaci V. S. , Selamoglu S.
Published: October 2009

Experimental results are presented on the influence of confinement (normal to heated surface) on nucleate boiling in forced flow. The forced flow conditions and confinement geometry studied are similar to those found for boiling between a primary-fluid tube and a tube-support plate in steam generators of pressurized-water-reactor nuclear power plants. Visual observations of the boiling process within the confined region (crevice) between the tube and its support plate, obtained by high-speed photography, are related to simultaneous two-dimensional temperature maps of the hot primary-fluid-tube surface. The results demonstrate the existence of three confinement-dependent boiling regimes in forced flow conditions that are similar to those found in pool boiling conditions. These regimes are shown to be associated with the Weber number.
A Stefan Problem With Contact Resistance
Authors: Barry G. W. , Goodling J. S.
Published: October 2009

A Stefan problem in which a semi-infinite molten material at the fusion temperature solidifies as a result of imperfect thermal contact with a cooler semi-infinite solid is considered. The contact resistance, due to surface roughness, is modeled by a convective boundary condition. Biot’s variational principle is used to reduce the coupled partial differential equations to a pair of coupled ordinary differential equations that are solved numerically. The position of the moving boundary as a function of time is given for both bismuth and aluminum solidifying on stainless steel.
Integral Equation Solution for Internal Flow Subjected to a Variable Heat Transfer Coefficient
Authors: Vick B. , Beale J. H. , Frankel J. I.
Published: October 2009

A solution methodology based on integral equations is presented for the problem of heat transfer to laminar duct flow subjected to an axial variation of the external heat transfer coefficient. The technique offers an efficient and accurate calculation procedure which combines standard analytical methods with a simple numerical integration. In order to examine the effect of external finning, results are calculated for the cases of a stepwise periodic and a harmonic variation of the heat transfer coefficient for both fully developed laminar flow and slug flow. The general procedure is applicable to a wide class of problems in heat and mass transfer involving variable boundary condition parameters.
Impingement Heat Transfer Within Arrays of Circular Jets: Part 1—Effects of Minimum, Intermediate, and Complete Crossflow for Small and Large Spacings
Authors: Obot N. T. , Trabold T. A.
Published: October 2009

An experimental study of the effects of three jet-induced crossflow schemes on impingement heat transfer was made. The schemes, referred to as minimum, intermediate, and maximum crossflow correspond, successively, to unrestricted flow of spent air away from the target surface, restriction of the flow to leave through two opposite sides, and through one side of a rectangular impingement surface. The study covered jet Reynolds number, jet-to-surface spacing, and open area of 1000–21,000, 2–16 jet hole diameters, and 1–4 percent, respectively. The best heat transfer performance is obtained with the minimum scheme, intermediate and complete crossflow being associated with varying degrees of degradation. For a given blower power, heat transfer can be enhanced markedly by having greater number of jets over a fixed target area; notably when working with the minimum scheme at narrow jet-to-target spacings.
Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries
Authors: Winters K. H.
Published: October 2009

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.
Prediction of the Natural Convective Heat Transfer From a Horizontal Heated Disk
Authors: Robinson S. B. , Liburdy J. A.
Published: October 2009

A thin-layer approximation is applied to the laminar momentum and energy equations governing the natural convection above an isothermal heated disk in air. Using the Boussinesq assumption the equations are nondimensionalized in terms of a stream function, pressure and temperature difference. The variables are expanded in a series solution and the resulting set of equations are solved numerically. The solution is cast in terms of the nondimensional radial position and the disk Grashof number. These two parameters are shown to define the outer boundary conditions which are uniquely determined from a point source solution. The outer velocity boundary condition is shown to decrease in relative magnitude as the disk Rayleigh number increases. Beyond a Rayleigh number of approximately 106 the outer flow may be ignored in calculating the disk heat transfer rate. The radial variation of the outer flow is to the – 1/5 power measured inward from the leading edge. This is a result of the scaling difference of the thin layer flow, and the outer, plume entrainment flow. The local heat transfer rate is increased by including the entrainment effects on the outer flow and varies as the Grashof number to the power (1/5–ε), where ε is a decreasing function of inward radial distance.
Development of Convective Heat Transfer Near Suddenly Heated, Vertically Aligned Horizontal Wires
Authors: Parsons J. R. , Arey M. L.
Published: October 2009

Experiments have been performed which describe the transient development of natural convective flow from both a single and two vertically aligned horizontal cylindrical heat sources. The temperature of the wire heat sources was monitored with a resistance bridge arrangement while the development of the flow field was observed optically with a Mach–Zehnder interferometer. Results for the single wire show that after an initial regime where the wire temperature follows pure conductive response to a motionless fluid, two types of fluid motion will begin. The first is characterized as a local buoyancy, wherein the heated fluid adjacent to the wire begins to rise. The second is the onset of global convective motion, this being governed by the thermal stability of the fluid layer immediately above the cylinder. The interaction of these two motions is dependent on the heating rate and relative heat capacities of the cylinder and fluid, and governs whether the temperature response will exceed the steady value during the transient (overshoot). The two heat source experiments show that the merging of the two developing temperature fields is hydrodynamically stabilizing and thermally insulating. For small spacing-to-diameter ratios, the development of convective motion is delayed and the heat transfer coefficients degraded by the proximity of another heat source. For larger spacings, the transient behavior approaches that of a single isolated cylinder.
Enhanced Heat Transfer Due to Secondary Flows in Mixed Turbulent Convection
Authors: Swanson L. W. , Catton I.
Published: October 2009

An experimental study of the fluid flow and heat transfer phenomena associated with opposing mixed turbulent convection in vertical ducts has been conducted. The duct considered had vertical and horizontal aspect ratios of 24.4 and 9.7, respectively. The working fluid was Freon-113, providing a Prandtl number of approximately 6.5. The results showed that a number of flow bifurcations occurred as GrDh/ReDh2 was increased. The first bifurcation observed was from parallel turbulent mean flow to a large single flow cell in the x−z plane. This occurred in the neighborhood of GrDh/ReDh2 = 2. Further bifurcations to multiple cells and eventually pure large-scale chaos were also observed. A correlation for the enhanced heat transfer was found to be NuDh/NuDh,0 = 1.0 + 0.9[ln(GrDh/ReDh2 + 1)]1.39, where NuDh,0 is the Petukhov–Virillov correlation for pure forced turbulent convection.
A Study of Ice-Formation Phenomena on Freezing of Flowing Water in a Pipe
Authors: Hirata T. , Matsuzawa H.
Published: October 2009

Ice-formation phenomena in a water pipe whose wall is kept at a uniform temperature lower than the freezing temperature of water are examined under the conditions of an unstable ice-water interface. The onset conditions for a step or smooth change in ice thickness occurring with flow transition from laminar to turbulent are found to be correlated with ice thickness at the contraction region of the ice band and are expressed as a function of a pipe Reynolds number ReD, and a cooling temperature ratio θ. It is shown that the transient freezing process depends strongly on flow as well as temperature conditions and that the typical ice shapes at steady-state conditions can be classified on a θ-ReD coordinate system.
Melting Powder Particles in a Low-Pressure Plasma Jet
Authors: Wei D. Y. C. , Farouk B. , Apelian D.
Published: October 2009

A numerical model has been developed to predict the temperature history of metal particles injected in a low-pressure (supersonic) d-c plasma jet. The temperature and velocity fields of the plasma jet are predicted by solving the parabolized compressible Navier–Stokes equations using a spatial marching scheme. Particle trajectories and heat transfer characteristics are calculated using the predicted plasma jet temperature and velocity fields. Correction factors have been introduced to take into account the noncontinuum effects encountered in the low-pressure environment. The plasma jet profiles as well as the particle/plasma interactions under different jet pressure ratios (from underexpanded to overexpanded cases) have been investigated.
Transient Radiative Cooling of a Layer Filled With Solidifying Drops
Authors: Siegel R.
Published: October 2009

An analysis is carried out for radiative cooling of a plane layer initially filled with liquid drops that solidify and then continue to cool by loss of sensible heat. This is in connection with a proposed lightweight radiator system for heat dissipation in space. Hot liquid drops would be ejected and then cooled by direct exposure in space; they would then pass into a collector for reuse. The cooling analysis contains three transient zones. In the first, the drops cool by losing latent heat until the outermost drops become solid. Then the cooling continues by loss of both latent and sensible heat. Finally, all of the drops are solid, and they continue to cool by loss of sensible heat. A similarity behavior is eventually achieved in which the transient emittance of the layer depends only on the optical thickness.
Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature
Authors: Lee H. R. , Chen T. S. , Armaly B. F.
Published: October 2009

Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature Tw(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of Tw(x) = T∞ + axn, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.
Heat Transfer by Natural Convection of Helium Between Horizontal Isothermal Concentric Cylinders at Cryogenic Temperature
Authors: Bishop E. H.
Published: October 2009

An experimental study was performed of the heat transfer by natural convection of helium between horizontal isothermal concentric cylinders at cryogenic temperatures. Time-averaged temperature profiles at various locations in the annulus and overall heat transfer rates were measured as the Rayleigh number was varied from 6 × 106 to 2 × 109 and the expansion number from 0.20 to 1.0 for a constant Prandtl number of 0.688 and diameter ratio of 3.36. It was found that the heat transfer rate depends on the magnitude of the expansion number as well as on the magnitude of the Rayleigh number. With gas properties evaluated at a volume-weighted reference temperature, a correlation equation is presented that correlates the heat transfer data with maximum deviations of −8.2 and +8.5 percent. The results of this study are compared with previously published studies of other investigators.
Measurement of Total Hemispherical Emissivities of Metal Wires by Using Transient Calorimetric Technique
Authors: Masuda H. , Higano M.
Published: October 2009

An application of the transient calorimetric technique was studied for measuring total hemispherical emissivities of metal wires. A unique idea of using guard wires, which have a function similar to usual guard heaters, was incorporated into the emissivity apparatus to reduce conduction heat losses through thermocouple leads suspending a specimen. Emissivity measurements were performed by using a copper wire as a specimen. The heat losses through the leads were analyzed in considering radiation heat transfer from the leads, and the effect of the guard wires on the heat losses was clarified. Temperature distributions in the specimen were also obtained analytically. From these results, it was found that an improved transient calorimetric technique in this work is applicable to the emissivity measurement on metal wires, and that the accuracy in the measurements is adequate.
Structure of the Stabilizing Region of a Laminar Jet Diffusion Flame
Authors: Takahashi F. , Mizomoto M. , Ikai S.
Published: October 2009

Velocity, temperature, and composition of major species were measured in the base region of a two-dimensional, laminar methane jet diffusion flame in unconfined still air under a low-velocity jetting condition. The velocity data showed acceleration near the flame zone caused primarily by thermal expansion and buoyancy. The heat flux vectors showed substantial heat flow from the flame base to both downstream and the burner wall. The premixed zone was formed in the dark space by convective penetration of oxygen and back-diffusion of methane. The molar flux vectors of methane and oxygen at the base pointed to the opposite directions, typical of diffusion flames.
Dynamics of Droplets Impacting on Thin Heated Strips
Authors: Yao S. C. , Hochreiter L. E. , Cai K. Y.
Published: October 2009

Experiments were conducted with water droplets impacting on the edge of thin steel strips that were heated to beyond the Leidenfrost temperature. High-speed movies were taken and analyzed and showed that the shattered droplets were generally bimodal in size distribution. The volume ratio of these two size groups of generated droplets, the mean diameter of droplets, and the ejection angles and velocities of shattered droplets are shown as a function of incoming droplet Weber number, the ratio of incoming droplet diameter to strip thickness, and the offset of the droplet relative to the strip. The data are presented in nondimensional form and correlations are provided for the mean diameter of the shattered droplets. The theoretical limiting conditions of a droplet impacting normally to a large plate and cutting by a strip of zero thickness are analyzed. The present results are compared with those of the limiting conditions. The application to a nuclear reactor spacer grid behavior during two-phase dispersed flow is discussed.
Thermal Contact Conductance of Packed Beds in Contact With a Flat Surface
Authors: Peterson G. P. , Fletcher L. S.
Published: October 2009

An experimental investigation was conducted to determine the thermal contact conductance of packed beds of spherical particles in contact with flat surfaces. Beds comprised of four materials, Aluminum 2017-T4, Yellow Brass, Stainless Steel 304, and Chromium Alloy AISI 52100, all in contact with flat Stainless Steel 304, surfaces were evaluated in a vacuum environment, at a mean interface temperature of 66°C. In addition to the experimental program, an analytical expression was developed by combining previous work performed by other investigators. The results of the experimental investigation are compared with the analytical expression and indicate that an accurate method of predicting the thermal contact conductance at the interface between beds of spherical particles and nominally flat surfaces has been identified.
Transient Temperature Fields in Crossflow Heat Exchangers With Finite Wall Capacitance
Authors: Spiga M. , Spiga G.
Published: October 2009

Solutions are provided in nondimensional form for the transient analysis of direct-transfer crossflow heat exchangers, with both fluids unmixed and finite wall heat capacity. The two-dimensional transient temperature distributions of core wall and both fluids are determined by analytical methods for any externally applied variation of the primary fluid inlet temperature. The general solutions are derived by the local energy balance equations, and are presented as simple integrals of the Green’s functions, which represent the pulse response following a deltalike perturbation in the inlet temperature of the primary fluid, and are deduced using the Laplace transform method. The Green’s functions are expressed as integrals of modified Bessel functions, in terms of the heat capacity ratios, number of transfer units, heat transfer resistance and flow capacitance ratios.
Thermal Effectiveness of Multiple Shell and Tube Pass TEMA E Heat Exchangers
Authors: Pignotti A. , Tamborenea P. I.
Published: October 2009

The thermal effectiveness of a TEMA E shell-and-tube heat exchanger, with one shell pass and an arbitrary number of tube passes, is determined under the usual symplifying assumptions of perfect transverse mixing of the shell fluid, no phase change, and temperature independence of the heat capacity rates and the heat transfer coefficient. A purely algebraic solution is obtained for the effectiveness as a function of the heat capacity rate ratio and the number of heat transfer units. The case with M shell passes and N tube passes is easily expressed in terms of the single-shell-pass case.
Heat Transfer From a Flat Surface to an Oblique Impinging Jet
Authors: Goldstein R. J. , Franchett M. E.
Published: October 2009

Experiments are conducted to determine the heat transfer to a jet impinging at different oblique angles to a plane surface. The main portion of the test plate contains a composite sheet of temperature-sensitive liquid crystal, which is sandwiched between a thin metallic-foil heater and a specially designed liquid bath. The results indicate a displacement of the peak heat transfer from the geometric center of the jet origin, the displacement being a function primarily of impingement angle. Contours of constant heat transfer coefficient are obtained and correlated with an empirical equation that permits determination of average Nusselt numbers over areas of interest.
Natural Convection From a Vertical Heat-Generating Fin—A Conjugate Problem
Authors: Sarma P. K. , Subrahmanyam T. , Dharma Rao V.
Published: October 2009

The problem of natural convection from a vertical heat-generating fin is solved by coupling the equation of thermal diffusion in the fin to the constitutive equations of the ambient medium under laminar flow conditions. The analysis is accomplished by employing an integral method. For the range of values of the fin parameter and the strength of the heat source considered in the analysis, the numerical results are rendered into a correlation equation for the average Nusselt number as a function of the fin parameter and the strength of the heat source.
Experimental Investigation of Heat Transfer in Coiled Annular Ducts
Authors: Garimella S. , Richards D. E. , Christensen R. N.
Published: October 2009

Forced convection heat transfer in coiled annular ducts was investigated experimentally. Average heat transfer coefficients were obtained for both laminar and transition flows. Two coiling diameters and two annulus radius ratios were used in the study. The data were correlated with Dean number and Reynolds number separately and compared with the available studies of coiled circular tubes and straight annular ducts. It was found that coiling augments the heat transfer coefficients above the values for a straight annulus especially in the laminar region. However, the augmentation is less than would be expected for a coiled circular tube. The augmentation decreases as the flow enters the transition region.
Analysis of Combined Buoyancy Effects of Thermal and Mass Diffusion on Laminar Forced Convection Heat Transfer in a Vertical Tube
Authors: Lin T. F. , Chang C. J. , Yan W. M.
Published: October 2009

This study investigates the role of vaporization of a thin liquid film on the tube wall in laminar mixed convection flows under the combined buoyancy effects of thermal and mass diffusion. Major nondimensional groups identified are GrT, GrM, Re, Pr, Sc, and φ. Results are specifically presented for an air–water system under various conditions. The effects of the liquid film temperature, the Reynolds number, and the relative humidity of the moist air in the ambient on the momentum, heat, and mass transfer in the flow are examined in great detail.
A Diffusion Flame Adjacent to a Partially Saturated Porous Slab: Funicular State
Authors: Kaviany M. , Tao Y.
Published: October 2009

The burning on the surface of a porous slab initially fully saturated with liquid fuel, and during the period where the liquid phase is continuous, is studied in order to determine the effects of the surface saturation, relative permeability, and vapor flow rate on the critical time. The critical time is defined as the time at which for the first time the surface saturation becomes zero, i.e., the first dry patches appear. The experimental and predicted results are in good agreement. The results show that unlike forced convection drying, the surface saturation does not influence the mass transfer rate significantly. Also, for the range of absolute permeabilities considered, the critical time is proportional to the absolute permeability.
A Continuous Exchange Factor Method for Radiative Exchange in Enclosures With Participating Media
Authors: Naraghi M. H. N. , Chung B. T. F. , Litkouhi B.
Published: October 2009

A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two types of exchange function are defined: the direct exchange function and the total exchange function. Certain integral equations relating total exchange functions to direct exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exchange factors.
Buoyancy Effects on Forced Convection Heat Transfer in the Transition Regime of a Horizontal Boundary Layer Heated From Below
Authors: Cheng K. C. , Obata T. , Gilpin R. R.
Published: October 2009

Convective instability and buoyancy effects on forced convection heat transfer in horizontal boundary layers heated from below by a constant temperature plate are studied experimentally for flow regimes with Rex = 2.5×104 ∼ 2.2×106 and Grx = 2×108 ∼ 1.5×1012. Heat transfer results obtained by heat flux gages and temperature measurements are studied using convective instability parameters, Grx/Rex1.5 for laminar flow and Grx/Rex2.7 for turbulent flow, with emphasis on flow in the transition regime. Buoyancy effects on heat transfer are also studied by comparison with predictions from the Pohlhausen solution and the von Ka´rma´n analogy. Convective instability data, velocity and temperature profiles, and flow visualization photographs (obtained by the hydrogen bubble method) and the wall temperature field (obtained by liquid crystal visualization) are presented. Flow visualization photographs reveal the spanwise periodic vortical motion, and the fluctuating velocity and temperature fields near the wall.
An Experimental Study of Natural Convection in a Vertical Cavity With Discrete Heat Sources
Authors: Keyhani M. , Prasad V. , Cox R.
Published: October 2009

Natural convection heat transfer in a tall vertical cavity (aspect ratio = 16.5), with one isothermal vertical cold wall, and eleven alternately unheated and flush-heated sections of equal height on the opposing vertical wall, is experimentally investigated. The flow visualization pictures for the ethylene glycol–filled cavity reveal a flow pattern consisting of primary, secondary, and tertiary flows. The heat transfer data and the flow visualization photographs indicate that the stratification is the primary factor influencing the temperature of the heated sections. This behavior persists for all the runs where the secondary flow cells cover a large vertical extend of the cavity. Based on the analysis of the photographs it is suggested that the turbulent flow should be expected when the local modified Rayleigh number is in the range of 9.3×1011 to 1.9×1012. It is found that discrete flush-mounted heating in the enclosure results in local Nusselt numbers that are nearly the same as those reported for a wide flush-mounted heater on a vertical plate. This is believed to be due to the fact that the present problem is inherently unstable, and the smallest temperature difference between a heated section and the cold wall results in the onset of convection motion.
An Effective Equation Governing Convective Transport in Porous Media
Authors: Georgiadis J. G. , Catton I.
Published: October 2009

The fine structure of disordered porous media (e.g., fully saturated randomly packed beds) causes microscopic velocity fluctuations. The effect of the spatial and temporal randomness of the interstitial velocity field on the convective transport of a scalar (heat or mass) is investigated analytically. For a uniform mean velocity profile, the effective heat transport equation is obtained as the equation governing the transport of the ensemble average of the scalar under conditions of steady or unsteady random fields (with given statistics). In both cases, it is shown that the effective transport coefficient is enhanced by a hydrodynamic dispersive component, which is an explicit function of the mean filtration velocity. The agreement with experiments is encouraging. The effective transport equation is then generalized to three-dimensional mean velocity fields for isotropic media.
Natural Convection Around a Heated Cylinder in a Saturated Porous Medium
Authors: Farouk B. , Shayer H.
Published: October 2009

Numerical solutions are presented for the natural convection heat transfer from a heated cylinder buried in a semi-infinite liquid-saturated porous medium. The governing equations are expressed in the stream function–temperature formulation and finite difference equations are obtained by integrating the governing equations over finite cells. The heat transfer characteristics of the heated cylinder are studied as functions of the Rayleigh number and the vertical depth of the cylinder center from a permeable surface. The numerical scheme involves the use of a cylindrical network of nodes in the vicinity of the cylinder with a Cartesian mesh covering the remainder of the flow domain. The results are of use in the design of underground electrical cables, power plant steam, and water distribution lines, among others.
Measurements of the Spectral and Directional Emission From Microgrooved Silicon Surfaces
Authors: Hesketh P. J. , Gebhart B. , Zemel J. N.
Published: October 2009

This paper reports measurements of both the spectral and specular thermal radiation emission characteristics of very regularly microconfigured grooved surfaces in a silicon substrate at 300 and 400°C. The resulting surfaces were phosphorus-doped, to assure the dominance of the emission from the material near the sample surface. The samples had groove depths H of zero for a reference, to 42 μm, and widths L = 12.6 to 14 μm. The geometry repeat distance was 22 μm, or 455 grooves per cm. The grooves correspond directly in size to the band of principle emission wavelengths λ that arises at these temperature levels. The measurements show strong spectral effects for normal emission, including highly favored frequencies, for H > λ. This suggests a cavity “organ pipe” mode of emission. Similar, though modified, effects were found in directional emission, away from the normal. There also were strong polarization effects, with the cross-groove polarization mode dominant. The spectral and specular measurements are compared with calculations of the classical kind, which tacitly assume that λ < < H = 0(L).