Dimensionless Heat Transfer Coefficient Research Articles

Estimation of heat transfer coefficients in oscillating flows: The thermoacoustic case

The classical linear thermoacoustic theory is integrated through a numerical calculus with a simple energy conservation model to allow estimates of the optimal length of thermoacoustic heat exchangers and of the magnitude of the related heat transfer coefficients between gas and solid walls. This information results from the analysis of the temperature and heat flux density distributions inside a thermally isolated thermoacoustic stack. The effects of acoustic amplitude, plate spacing, plate thickness and Reynolds number on the heat transfer characteristics are examined. The results indicate that a net heat exchange between the acoustically oscillating gas and the solid boundary takes place only within a limited distance from the stack edges. This distance is found to be an increasing function of the plate spacing in the range (0 ⩽ y 0/ δ κ ⩽ 2), becoming constant for y 0/ δ κ ⩾ 2. The calculated dimensionless convective heat transfer coefficients, the Nusselt numbers, between gas and solid wall are comparable to those evaluated from classical correlations for steady laminar flow revised under the “Time-Average Steady-Flow Equivalent” (TASFE) and “root-mean-square Reynolds number” (RMSRe) models. Numerical results agree with measurements of the heat transfer coefficient found in literature to within 20%.

Temperature boundary layer on a rotating surface - the problem of the constant temperature wall

Introducing the group of Loitskanskii [1] form-parameters and transformations of Saljnikov [2], the set of governing equations of the in compressible laminar temperature boundary layer was transformed in the universal form, with Prandtl number as parameter, for the case of the constant wall temperature. Using the universal results for air (Pr=0.72) the procedure for calculation of the Nusselt number (dimensionless heat transfer coefficient) on the particular contour (airfoil NACA 0010-34) was developed. The dimensionless temperature profiles within the boundary layer were presented also. The parameter of rotation ?0, as well as Eckert number, was varied, and their influences on the heat transfer from the surface to the working fluid were presented and analyzed. .

Heat Transfer Characterization of Metallic Foams

Gas−solid heat transfer coefficients were determined in open-celled metal foams as part of a study aimed at evaluating the application of metal foams as catalyst supports in gas−solid catalytic processes with short contact times and high reaction rates, typically controlled by diffusional mass transport. Examples of such processes are found in the field of environmental catalysis, including, for example, catalytic combustion, selective catalytic reduction of NOx by NH3 (SCR-DeNOx), automotive exhaust gas after treatment, and also in the catalytic partial oxidation of hydrocarbons for syngas or H2 generation processes. In this work, foam samples made of FeCrAlloy and Cu with nominal porosities of 10 and 20 pores per inch (ppi) were characterized by performing non-steady-state cooling measurements. Convective gas−solid heat transfer coefficients were determined by applying a one-dimensional, heterogeneous model of the cooling structure. The correlation Nu = 1.2Re0.43Pr1/3 well described the dependence of the dimensionless heat transfer coefficients on Re and Pr numbers for all the tests made in a range of flow superficial velocities from 1.2 to 5.7 m/s, independently from the foam cell size (20 < Re < 240). Such a correlation was derived assuming a prismatic idealization of the unit cell and selecting the equivalent strut diameter as the characteristic size of the foams. This expression satisfies the Colburn analogy with the correlation for mass transfer coefficients derived in a previous investigation and resembles semitheoretical literature correlations for heat transfer in flow across banks of tubes at low Reynolds numbers.

Characterizing heat transfer coefficients for heat exchangers in standing wave thermoacoustic coolers

The thermal performance of heat exchangers within a thermoacoustic cooler was investigated. Experimental procedures and calculation methods to evaluate the oscillating flow heat transfer coefficients were developed. Dimensionless heat transfer coefficients, or Colburn-j factors, were estimated based on the oscillating-flow variables and compared with results from steady-flow measurements. The results were also compared with heat transfer coefficients predicted from a boundary-layer conduction model, and methods that utilize steady-flow correlations with Reynolds numbers that characterize oscillating flow conditions. Although the boundary layer model is commonly employed for thermoacoustic calculations, it did not accurately predict heat transfer coefficients and the influence of Reynolds number on heat transfer performance. However, accurate predictions were obtained using a steady-flow correlation and a modified Reynolds number that accounts for the oscillating flow field, assuming a half-cycle Reynolds number correction value of 0.109.

The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface

The effect of temperature dependent viscosity on laminar mixed convection boundary layer flow and heat transfer on a continuously moving vertical surface is studied. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Local similarity solutions are obtained for the boundary layer equations subject to isothermally moving vertical surface with uniform speed. The effect of various governing parameters, such as Prandtl number Pr, the mixed convection parameter λ = S Gr x / Re x 2 , and the viscosity/temperature parameter θ r which determine the velocity and temperature distributions, the local heat transfer coefficient, and the local shear stress coefficient at the surface are studied. Significant changes are obtained in dimensionless local heat transfer and shear stress coefficient at the surface when the magnitude of θ r has small values for each λ. Critical values of λ are obtained for predominate natural convection and buoyancy shear stress for assisting and opposing flow for various θ r .

A DOS-Enhanced Numerical Simulation of Heat Transfer and Fluid Flow Through an Array of Offset Fins With Conjugate Heating in the Bounding Solid

The method of Design of Simulation (DOS) was used to guide and enhance a numerical simulation of fluid flow and heat transfer through offset-fin arrays which form the interior geometry of a cold plate. The basic problem involved 11 independent parameters. This prohibitive parametric burden was lessened by the creative use of nondimensionalization that was brought to fruition by a special transformation of the boundary conditions. Subsequent to the reduction of the number of parameters, the DOS method was employed to limit the number of simulation runs while maintaining an accurate representation of the parameter space. The DOS method also provided excellent correlations of both the dimensionless heat transfer and pressure drop results. The results were evaluated with respect to the Colburn Analogy for heat and momentum transfer. It was found that the offseting of the fins created a larger increase in the friction factor than that which was realized for the dimensionless heat transfer coefficient.

Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas

A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid–gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.

Turbulent film condensation on a horizontal elliptical tube

An investigation has been made of turbulent film condensation on a horizontal elliptical tube. The present study is based on Colburn analogy [1] and potential flow theory to determine the high tangential velocity of vapor flow at the boundary layer and to define the local interfacial shear owing to high velocity vapor flow across the tube surface. The condensate film flow and local/or mean heat transfer characteristics from a horizontal elliptical tube with variable ellipticities, e, under the influence of Froude number, sub-cooling parameter and system pressure have been performed. The present result for dimensionless mean heat transfer coefficient reduces to the same result obtained by Sarma et al.’s [2] e=0 (circular tube). Compared with laminar model by Yang and Hsu [3], the present turbulent model shows in better agreement with Michael’s experimental data [4] (for e=0). The dependence of mean Nusselt coefficient on the effect of n (power of Reynolds) [1] is also discussed.

Non-iterative estimation of heat transfer coefficients using artificial neural network models

The Inverse Heat Conduction Problem (IHCP) dealing with the estimation of the heat transfer coefficient for a solid /fluid assembly from the knowledge of inside temperature was accomplished using an artificial neural network (ANN). Two cases were considered: (a) a cube with constant thermophysical properties and (b) a semi-infinite plate with temperature dependent thermal conductivity resulting in linear and nonlinear problem, respectively. The Direct Heat Conduction Problems (DHCP) of transient heat conduction in a cube and in a semi-infinite plate with a convective boundary condition were solved. The dimensionless temperature-time history at a known location was then correlated with the corresponding dimensionless heat transfer coefficient/Biot number using appropriate ANN models. Two different models were developed for each case i.e. for a cube and a semi-infinite plate. In the first one, the ANN model was trained to predict Biot number from the slope of the dimensionless temperature ratio versus Fourier number. In the second, an ANN model was developed to predict the dimensionless heat transfer coefficient from non-dimensional temperature. In addition, the training data sets were transformed using a trigonometric function to improve the prediction performance of the ANN model. The developed models may offer significant advantages when dealing with repetitive estimation of heat transfer coefficient. The proposed approach was tested for transient experiments. A ‘parameter estimation’ approach was used to obtain Biot number from experimental data.

Optimizing the Design of Space Radiators

A procedure for optimizing the configuration of a heat pipe/fin radiating element in terms of heat rejected per radiating mass has been developed. The optimization was carried out analytically by expressing the heat radiated per radiating mass in terms of a function involving a dimensionless heat transfer coefficient and the dimensionless thermal gradient at the root of the fin where it joins the heat pipe. The dimensionless Stefan–Boltzmann radiation equation was solved numerically to determine the value that maximizes the function that determines the heat transfer per radiating mass. Once this value is obtained, the optimum width and thickness of the fins as well as the heat radiated per mass can be specified in terms of the operating temperature, emissivity, diameter, and mass/length of the heat pipe, and the density and thermal conductivity of the fin material. The resulting analytical expression can then be used to determine the maximum heat radiated per radiating mass over a wide range of operating conditions, to optimize the design of a specific heat pipe/fin combination, and to conduct analyses of the influence of design and materials properties on the performance of the system. The optimization procedure was carried out for the case of uniformly tapered fins as well as for flat fins.

Thermodynamic optimization of radial MHD flow between parallel circular disks

The radial flow between two parallel circular disks is investigated with the aim to determine the optimum convective heat transfer conditions at the external disk surfaces in order to minimize the intrinsic irreversibilities. A general situation is considered where the fluid is electrically conducting and may be under the influence of a transversal magnetic field. The velocity and electric current density fields are obtained analytically and used to solve the heat transfer equation under boundary conditions of the third kind. The analysis is in the absence of fluid inertia, under creeping flow conditions (Reynolds number ≪ 1). A perturbation approach in order to include the convective heat transfer effects in the flow is used. The Péclet number is assumed to be small. The analytic expressions for the velocity, electric current density and temperature fields are used to calculate explicitly the global entropy generation rate. When the convective heat transfer coefficients for each wall are different, this function displays a minimum for specific heat exchange conditions. The results are shown for both the hydrodynamic and the magnetohydrodynamic cases. It is also found that the mean Nusselt number at the upper wall shows a maximum value for a given value of the Hartman number, when the dimensionless heat transfer coefficients for each disk and the Péclet number are fixed. This mean Nusselt number for maximum heat transfer is near its value for minimum entropy generation conditions.

Influence of inclination angle, attack angle, and arrangement of rectangular vortex generators on heat transfer performance

AbstractWe have studied the enhancement of heat transfer by vortex generators. Experiments were performed on rectangular‐type vortex generators mounted on a parallel‐plate heater, and the heat transfer coefficient of the heater surface and pressure drop in the duct were measured. These measurements indicated that a rectangular vortex generator (called a double‐inclined winglet), with inclination angle of the vortex generator surface to the heater surface (β) at 60°, and the attack angle to the flow direction (γ) at 45°, maximizes the local Nusselt number of the heater surface. It was also found that a group of double‐inclined winglets has an optimal arrangement in a winglet array, longitudinal pitch and transverse pitch, that maximizes the ratio [Colburn's dimensionless heat transfer coefficient JH]/[friction factor f]. The results of numerical calculations showed that the double‐inclined winglet was superior to the conventional rectangular vortex generator in heat transfer. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 253–267, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10089

Heat Transfer In Turbulent Boundary Layers Subjected to Free-Stream Turbulence—Part II: Analysis and Correlation

A new heat transfer correlation for turbulent boundary layers subjected to free-stream turbulence was developed. The new correlation estimates dimensionless heat transfer coefficients without the use of conventional boundary-layer thickness measures and the associated Reynolds numbers. Using only free-stream parameters (mean velocity, turbulence intensity and length scale), the new correlation collected many authors’ elevated-turbulence, flat-plate Stanton number data to within ±11%. The level of scatter around the new correlation compared well to previous correlations that require additional flow information as input parameters. For a common subset of data, scatter using earlier correlation methods ranged from 5–10%; scatter around the new correlation varied from 6–9% over the same data subset. A length-scale dependence was identified in a Stanton number previously defined using a near-wall streamwise velocity fluctuation, St′. A new near-wall Stanton number was introduced; this parameter was regarded as a constant in a two-region boundary layer model on which the new correlation is based.

Experimental investigation in pool boiling heat transfer of ternary mixture and heat transfer correlation

Heat transfer coefficients in nucleate boiling on a smooth flat surface were measured for pure fluids, their binary and ternary mixtures under the saturated conditions at 0.6 MPa for a wide range of heat flux and mixture concentration. Refrigerants, R-134a, R-142b and R-123 were used to make up binary and ternary mixtures. Compared to the ideal heat transfer coefficients calculated from a mole fraction average of the wall superheats of pure components, both binary and ternary mixtures showed lower heat transfer coefficients. This reduction was more pronounced as heat flux was increased. The data of binary mixtures were well reproduced by Thome–Shakir and Fujita–Tsutsui correlations. For ternary mixtures, dimensionless heat transfer coefficients plotted on the concentration triangle were very similar to the contour map of boiling range. This similarity suggested the boiling range is an essential parameter to account for heat transfer reduction of ternary mixtures. Fujita–Tsutsui correlation was found applicable to ternary mixtures with a reasonable success.

Thermal patterns on a heated wall in vertical air–water flow

The thermal patterns on a heated wall, as related to the flow regime, were studied by using the heated foil infrared technique. The thermal pattern on the heated wall for the single-phase water flow has a streaky structure. For the bubble flow, the streaky structure is destroyed. This phenomenon is accompanied by a significant increase in the heat transfer coefficient. For the slug flow regime, the thermal pattern on the wall depends on whether water containing small gas bubbles (slug) or water surrounding a Taylor bubble passes the heated wall. Simultaneously, the temperature and pressure fluctuations at the wall were measured. The level of these fluctuations was discussed together with the data about the average heat transfer. The excess form of heat transfer coefficient was introduced. A correlation for the dimensionless heat transfer coefficient at slug flow was suggested.

Heat transfer to a falling power-law fluid film

Abstract Steady heat transfer to water and purely viscous non-Newtonian fluid films falling down a vertical tube, for the case of uniform wall heat flux thermal boundary condition, was measured experimentally. The power-law fluids studied were aqueous solutions of Carbopol at 250 and 500 ppm (by weight) concentration. The heat transfer to power-law fluid film was lower than the Newtonian prediction, at comparable Pr a . A new correlation is proposed for dimensionless heat transfer coefficient over a range of 500⩽ Re a ⩽5400, 6⩽ Pr a ⩽20 , and 0.7⩽ n ⩽1.

LAMINAR FILM CONDENSATION WITH CONSTANT HEAT FLUX ON A FINITE-SIZE HORIZONTAL PLATE

A theoretical analysis of two-dimensional, steady state, laminar film condensation on a finite-size horizontal plate facing upward with constant surface heat flux is studied. While the most of previous theoretical studies on the film-wise condensation problem made the assumption of isothermal surface, the present work assumes the condition of constant surface heat flux. Besides, the critical film thickness at the edge of the plate is determined by employing the principle of minimum mechanical energy instead of the method of ‘trial and error’ or arbitrary assumption used by the most of previous studies. And the dimensionless heat transfer coefficient and the film thickness along the plate are simply expressed in terms or general used parameters Prandtl number (Pr), Reynolds number (Re), and Rayleigh number (Ra).

HEAT TRANSFER TO A FALLING VISCOELASTIC FLUID FILM

Steady heat transfer to water and viscoelastic fluid films falling down a vertical tube, for the case of uniform wall heat flux thermal boundary condition, was measured experimentally. The viscoelastic fluids studied were aqueous solutions ofPraestol at 100, 200, and 500 ppm (by weight) concentration. The heat transfer to viscoelastic film was lower than the Newtonian prediction, at any given Prandtl number. A new correlation is proposed for dimensionless laminar and turbulent heat transfer coefficient in terms of ike Weissenberg number, over a range of 300 ≤ Reo ≤ 6,500, and 6 ≤Pro ≤ 30.

Computational fluid dynamics studies of fixed bed heat transfer

Fluid flow and heat transfer in a fixed bed of tube to particle ratio 2.86 were studied by solving the 3D Navier–Stokes and energy equations using a commercial finite element code, ANSYS/FLOTRAN. The geometry model consisted of an arrangement of eight spheres. Boundary conditions were given at the wall and the inlet, similar to an experimental setup, to determine the velocity and temperature at various locations. The main objective of this study was to use computational fluid dynamics (CFD) to obtain values for the dimensionless wall heat transfer coefficient, Nu w and the radial effective thermal conductivity ratio, k r/ k f, using air as the fluid. Nu w and k r/ k f were evaluated from the calculated temperatures at different locations in the bed by fitting these with the analytical solution of the usual two-dimensional pseudo-homogeneous model, using a non-linear least squares analysis. Results were obtained for Reynolds numbers in the range 9–1450. The Nu w and k r/ k f values showed reasonable qualitative agreement with both experimental values and values predicted by a model-matching theory based on experimental measurements. Studies were also carried out to verify the depth, pressure and wall temperature dependence of the effective heat parameters. The effect of the temperature profile measurement position above the bed on the estimated parameters, was investigated.

Free- and forced-convection film condensation from a horizontal elliptic tube with a vertical plate and horizontal tube as special cases

Abstract A simple mathematical model is developed for the study of the mixed-convection film condensation with downward flowing vapors onto a horizontal elliptic tube. Analytical analysis for both the local condensate film thickness and heat transfer characteristics under simultaneous effects of interfacial vapor shear and pressure gradient has been performed by adopting a unified geometry parameter, eccentricity e. The present results for two limit cases, e = 0 (circular tube) and e = 1.0 (vertical plate) are in an excellent agreement with the earlier works. For very slow vapor flow, the present result for dimensionless mean heat transfer coefficient reduces to the same form as in the earlier works, Nu(Ja/Ra) 1 4 , whose value is 0.728 for e = 0 and 0.943 for e = 1.0. As for very fast vapor flow, the dimensionless mean heat transfer coefficient, NU Re −1 2 increase with increasing eccentricity under the effects of pressure gradient caused by potential flow and surface tension.