Predicting turbulence and heat transfer in 3-D curved ducts by near-wall second moment closures

This paper presents discussions on predicting turbulence and heat transfer in two types of square sectioned U-bend duct flows with mild and strong curvature by recent second moment closures. Batten et al.'s [AIAA J. 37 (1999) 785] modified version of Craft and Launder's [Int. J. Heat Fluid Flow 17 (1996) 245] two-component-limit (TCL) turbulence model and Shima's [Int. J. Heat Fluid Flow 19 (1998) 549] wall-reflection free model are presently focused on. They are low-Reynolds-number models totally free from geometrical parameters. The former model is realizable and called the TCL model. For turbulent heat flux, a higher order version of the generalized gradient diffusion hypothesis by Suga and Abe [Int. J. Heat Fluid Flow 21 (2000) 37] is applied along with the TCL model. The results suggest that although both second moment closures are generally good enough for predicting flow and heat transfer in the case of mild curvature, only the realizable TCL model is reliable in the strong curvature case.     

A numerical study on entropy generation induced by turbulent forced convection in curved rectangular ducts with various aspect ratios

The present paper analyzes the entropy generation induced by turbulent forced convection in a curved rectangular duct with external heating by numerical methods. The problem is assumed as steady, three-dimensional and turbulent. The flow features, including the secondary flow motions, the distribution of local entropy generation as well as the overall entropy generation in the whole flow fields, are analyzed. For a baseline case with Re = 20,000, external heat flux q? = 0.112 and aspect ratio γ = 1, the results show the entropy generation induced by the frictional irreversibility concentrates within the regions adjacent to the duct walls, whereas the entropy generation resulted from the heat transfer irreversibility only significantly occurs near the outer wall of the duct where the external heat flux imposed. Except the baseline case, two additional cases with aspect ratio equal to 0.25 and 4 are calculated. Through the comparison of the three aspect-ratio cases, it is seen that the resultant entropy generations in the flow fields for the three cases are all dominated by the frictional irreversibilities. Among the three aspect-ratio cases, the resultant entropy generation is minimal in the γ = 1 case. Accordingly, the case with γ = 1 is concluded to be the optimal aspect ratio under the current flow condition based on the minimal entropy generation principle.     

Investigation on forced convective heat transfer of molten salts in circular tubes

In this paper, experiments are carried out to obtain convective heat transfer coefficients of turbulent flow and transition flow of molten Hitec salts in a circular tube. The present experimental data together with experimental data of four kinds of molten salts from the existing literature are correlated for transitional and turbulent convective flow respectively. In addition, the Prandtl number dependence of convective heat transfer with different working fluids is examined. It is shown that the present experimental data are in good agreement with existing correlations.     

Numerical study of convective heat transfer to supercritical water in rectangular ducts

Numerical investigation has been performed to analyze forced convective heat transfer to supercritical water in horizontal rectangular ducts. Convective heat transfer near the critical region in the rectangular ducts is strongly influenced by large variations of thermodynamic and transport properties of supercritical fluid with gravity force, especially close to pseudocritical temperature. Fluid flow and heat transfer characteristics such as velocity, temperature, and local heat transfer coefficient with water properties distribution in the ducts are presented. Flow accelerates along the horizontal ducts because of decreased water density from heat transfer at the duct walls. Center of large flow recirculation in the duct section locates near the middle of vertical surface and additional secondary recirculation in clockwise direction appears with the increase of duct height. Local wall temperature severely varies along the inner surface of the duct section and its variation depends on aspect ratio of the duct. The heat transfer coefficient distributions along the ducts for various aspect ratios are compared with the proximity effect to the critical pressure.     

Turbulent convective heat transfer with molten salt in a circular pipe

In order to understand the heat transfer characteristics of molten salt and testify the validity of the well-known empirical convective heat transfer correlations, an experimental study on turbulent convective heat transfer with molten salt in a circular tube was conducted in this paper. Molten salt circulations were realized and operated in a specially designed system over 1000 h. The flow rates and temperatures of molten salt and mineral oil at the inlet and outlet in the test section were measured and the average forced convective heat transfer coefficients of molten salt were determined by least-squares method. Finally, heat transfer correlations of turbulent flow with molten salt in a circular tube were obtained. Good agreement was observed between the experimental data of molten salt and the existing well-known correlations. The experimental data of molten salt in the present work are consistent with experimental results reported by different references in a wide range of Prandtl numbers from 0.7 to 59.9.     

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10⁵ to 1.2 × 10⁷. The entrance sections used were long tube with length of 2520 mm (L/D_h = 63) and short tube with length of 504 mm (L/D_h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z_t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.     

Effects of viscous dissipation on forced convective heat transfer in a channel embedded in a power-law fluid saturated porous medium

The convective heat transfer analysis in a channel embedded in a power-law fluid saturated porous medium subject to uniform heat flux is presented and compared with a Newtonian fluid concerning the effects of viscous dissipation. Governing momentum and energy equations for non-Newtonian fluids which accounts for the viscous dissipation effects are solved numerically. The temperature profiles of the non-Newtonian fluids are found to relate closely to the velocity profiles. When viscous dissipation is taken account of, Nusselt numbers for non-Newtonian fluid are found to deviate more from Newtonian fluid with increasing Brinkman number for a certain range of the Darcy number.     

A simplified approach to solving conjugate heat transfer problems in annular and dissimilar parallel plate ducts

A simple perturbation technique is used to reformulate the energy equations which describe the treatment thermal behaviour of a radially lumped conjugate that transfer problem is annular and dissimilar parallel plate ducts of finite wall thickness. The simplified perturbation tecnique is used to eliminate the coupling between the fluid and the solid-wall energy equations when the temperature difference between the fluid and the solid-wall is a small perturbed quantity, which is true when the interface convective heat transfer coefficient between the fluid and the solid-wall is high. A mathematical criterion is derived to determine the conditions under which the fluid and the solid-wall are in thermal equilibrium. It is found that seven dimensionless parameters control the state of the thermal equilibrium between the fluid and the solid domains. © 1998 John Wiley & Sons, Ltd.     

Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate

The fluid flow and heat transfer induced by the combined effects of the mechanically driven lid and the buoyancy force within rectangular enclosures were investigated in this work. The fluid filled enclosures are heated and lid-driven either on the upper or on the lower horizontal wall, thermally isolated on the right vertical wall, and cooled on the other walls. The basis of the investigation was the numerical solutions of the equations for the conservation of mass, momentum, and energy transport using the finite difference method. The effects of the flow governing parameters including the Richardson and the Prandtl numbers, and the length-to-height aspect ratio, respectively, in the range 10⁻²  Ri  10², 10⁻³  Pr  10, and 1  AR  4 for a fixed Reynolds number, Re = 100, were studied. The results are presented in the form of the hydrodynamic and thermal fields, and the profiles for vertical and horizontal components of velocity, temperature, and the local heat flux. The fluid flow and energy distributions within the enclosures and heat flux on the heated wall are enhanced by the increase in the Richardson number. While an increase in the Prandtl number improves the heat flux on the heated wall, an increase in aspect ratio suppresses it. The results can be used as base line data in the design of systems in which mixed convection heat transfer in rectangular enclosures occurs.     

Numerical prediction of turbulent convective heat transfer in mini/micro channels for carbon dioxide at supercritical pressure

A new approach to take into account the effects of variable physical properties on turbulence is suggested. It allows to choose freely the turbulent closure model for conventional terms due to velocity fluctuations and to describe coherently the additional terms due to density fluctuations. Numerical calculations based on the suggested approach have been performed for carbon dioxide flowing within mini/micro channels under cooling conditions. The numerical predictions show that the effects due to density fluctuations are smaller than it could have been initially supposed and that the heat transfer impairment for mini/micro channels, which some experiments seem to highlight, is not completely explained by the considered model.     

An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media

The present experimental and numerical work investigates the effect of metallic porous materials, 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, porous material diameter and thermal conductivity as well as Reynolds number on the heat transfer rate and pressure drop are investigated. The results are compared with the clear flow case where no porous material was used. The results obtained lead to the conclusion that higher heat transfer rates can be achieved using porous inserts at the expense of a reasonable pressure drop. Also, it is shown that for an accurate simulation of heat transfer when a porous insert is employed its effective thermal conductivity should be carefully evaluated.     

Three dimensional numerical and experimental study of forced convection heat transfer on solar collector surface

In this study, experimental and three dimensional numerical work was carried out to determine the average heat transfer coefficients for forced convection air flow over a rectangular flat plate. Three dimensional numerical simulations were obtained using a commercial finite volume based fluid dynamics code called Fluent 6.3. The experiments were performed for mass transfer using the naphthalene sublimation technique. The results were presented in terms of heat transfer parameters using the analogy between heat and mass transfer. All the experimental results are correlated within an accuracy of ± 12%.     

Numerical study of double diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with porous medium

Two-dimensional double-diffusive natural convective heat and mass transfer in an inclined rectangular porous medium has been investigated numerically. Two opposing walls of the cavity are maintained at fixed but different temperatures and concentrations; while the other two walls are adiabatic. The generalized model with the Boussinesq approximation is used to solve the governing equations. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. A finite volume approach has been used to solve the non-dimensional governing equations and the pressure velocity coupling is treated via the SIMPLER algorithm. The results are presented in streamline, isothermal, iso-concentration, Nusselt and Sherwood contours for different values of the non-dimensional governing parameters. A wide range of non-dimensional parameters have been used including, aspect ratio (2 ≤ A ≤ 5), angle of inclination of the cavity (0 ≤ ? ≤ 85), Lewis number (0.1 ≤ Le ≤ 10), and the buoyancy ratio (− 5 ≤ N ≤ 5).     

Fluid flow and heat transfer characteristics in rectangular microchannels

Experiments were conducted to investigate flow and heat transfer characteristics of water in rectangular microchannels. All tests were performed with deionized water. The flow rate, the pressures, and temperatures at the inlet and outlet were measured. The friction factor, heat flux, and Nusselt number were obtained. The friction factor in the microchannel is lower than the conventional value. That is only 20% to 30% of the convectional value. The critical Reynolds number below which the flow remains laminar in the microchannel is also lower than the conventional value. The Nusselt number in the microchannel is quite different from the conventional value. The Nusselt number for the microchannel is lower than the conventional value when the flow rate is small. As the flow rate through the microchannel is increased, the Nusselt number significantly increases and exceeds the value of Nusselt number for the fully developed flow in the conventional channel. The micro‐scale effect was exhibited. The Nusselt number is also affected by the heat flux. The Nusselt number remains the constant value when the flow rate is small. The Nusselt number increases with the increase in the heat flux when the flow rate is large. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(4): 197–207, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20206     

开口方腔内混合对流换热的数值模拟

研究了两种不同外界来流方向的开口方腔内的混合对流换热问题。对不同的格拉晓夫数、R e以及纵横比进行了数值模拟。计算结果表明了与它们相对应的不同流型及换热效果,同时表明通过增加流速可以减小方腔与周围环境的热量交换。     

Bounds on natural convective heat transfer in a porous layer with fixed heat flux

Using the background field variational method, bounds on natural convective heat transfer in a porous layer heated from below with fixed heat flux are derived from the primitive equations. The enhancement of heat transfer beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the non-dimensional forcing scale set by the ‘effective’ Rayleigh number (Rˆ) according to Nu ≤ 0.354Rˆ^1/2 and in terms of the conventional Rayleigh number (Ra) defined by the temperature drop across the layer according to Nu ≤ 0.125Ra. It is presented that fixing the heat flux at the boundaries does not change the linear dependence between Nusselt number and Rayleigh number at high Rayleigh number region.     

Convection heat transfer from tube banks in crossflow: Analytical approach

The main objective of this analytical study is to investigate heat transfer from tube banks in crossflow under isothermal boundary condition. For this purpose, a control volume is selected from the fourth row of a tube as a typical cell to study the heat transfer from an in-line or staggered arrangement. An integral method of boundary layer analysis is employed to derive closed form expressions for the calculation of average heat transfer from the tubes of a bank, that can be used for a wide range of parameters including longitudinal pitch, transverse pitch, Reynolds and Prandtl numbers. The models for in-line and staggered arrangements are applicable for use over a wide range of parameters when determining heat transfer from tube banks.     

Theoretical analysis of heat transfer in laminar pulsating flow

Pulsation effect on heat transfer in laminar incompressible flow, which led to contradictory results in previous studies, is theoretically investigated in this work starting from basic principles in an attempt to eliminate existing confusion at various levels. First, the analytical solution of the fully developed thermal and hydraulic profiles under constant wall heat flux is obtained. It eliminates the confusion resulting from a previously published erroneous solution. The physical implications of the solution are discussed. Also, a new time average heat transfer coefficient for pulsating flow is carefully defined such as to produce results that are both useful from the engineering point of view, and compliant with the energy balance. This rationally derived average is compared with intuitive averages used in the literature. New results are numerically obtained for the thermally developing region with a fully developed velocity profile. Different types of thermal boundary conditions are considered, including the effect of wall thermal inertia. The effects of Reynold and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated. The mechanism by which pulsation affects the developing region, by creating damped oscillations along the tube length of the time average Nusselt number, is explained.     

Numerical analysis of three-dimensional flow,heat and mass transfer in arbitrary-shaped ducts

In this study, the three-dimensional flow, heat and mass transfer characteristics in a horizontal chemical vapor deposition (CVD) reactor with a tilted susceptor are analyzed numerically. As the physical domain for the CVD reactor has an irregular region, the Cartesian coordinates are transformed into a general curvilinear coordinate system. For calculating the governing equations, the SIMPLE algorithm is extended and modified to employ the curvilinear system. From the above modeling, the effects of flow rate and tilt angle of suscept on the uniformity and growth rate of reactant gas at the susceptor are investigated. The results show that the existence of return flows leads locally to the improvement of heat transfer, but it is not good for the uniformity of the susceptor. As the tilt angle of the susceptor is increased (from 0° to 9°), the amount of heat transfer and growth rate are improved irrespective of Reynolds number.© 1999 Scripta Technica, Heat Trans Asian Res, 28(6): 474–483, 1999     

Study of mixed convective heat transfer in a sintered porous channel

This investigation experimentally elucidates mixed heat convection in a rectangular channel with porous medium, and analyzes the cooling performance of electronics. The test sections are sintered copper granules with dimensions of 5 × 5 × 1 cm and average diameters of 0.704 mm and 1.163 mm. A porous channel is heated using air as the working fluid. The measured variables include the heat flux on the heat surface, the local wall temperature in the flow direction, the inlet/outlet pressure, and the flow rate. The boundary condition is that the heating surface of the lower plate of the test section is heated by an isothermal heat flux, while the other three sides are thermally insulated; the heat flux is between 0.23 and 1.86 Watt/cm². The mean air flow rate within a porous channel is between 0.3 and 4.0 m/s. The thermally developed region and the fully developed region are measured. This experiment is directed at understanding the influence on heat transfer based on the diameter of the sintered copper granules, Reynolds number, and heat flux. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(2): 64–77, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20050