Analysis of Laminar Mixed Convective Heat Transfer in Horizontal Triangular Ducts

Numerical simulations for fluid flow and heat transfer in triangular ducts are carried out. Flow is considered to be laminar, hydrodynamically, and thermally developing. Heat transfer by both forced and natural convection is taken into account. Simulations are carried out for constant wall temperature cases which are at a higher temperature than the inlet temperature of the fluid. The effect of Rayleigh number on bulk mean temperature and Nusselt number is studied. Isotherm and secondary velocity profile formed because of natural convection is shown at different locations with varying Rayleigh number. The effect of the apex angle of the triangular duct on Nusselt number and bulk mean temperature is studied. Results are compared with the cases of mixed convective heat transfer in a square duct.     

Electrohydrodynamic Induced Flow and Heat Transfer in Vertical Channel with Fin Array Attached

Electrohydrodynamic heat transfer enhancement of natural convection inside the finned vertical channels is investigated via a computational fluid dynamics technique. The interactions between electric field, flow field, and temperature field are numerically determined. Flow and heat transfer enhancements are significantly influenced at low Rayleigh number. The effect of electrode arrangement and number of electrodes to the average velocity and Nusselt number are expressed. An optimum inclined angle of the channel is recommended. Relation between the number of fins and fin length to the augmented flow and heat transfer is also analyzed.     

EFFECT OF BUOYANCY ON FORCED CONVECTION IN A CUSPED DUCT

ABSTRACT

In the event of a loss of coolant accident in a pressurized water reactor, swelling of the fuel rod cladding will lead to reduction of the subchannel flow area and worsening of the core heat transfer in the region of the blockage. The four-cusped duct is an ideal geometry for the simulation of such a channel blockage. Understanding the characteristics of flow and heat transfer in the cusped duct is essential for better design of the emergency core cooling system. Thus, in this paper, combined natural and forced convection in a vertical cusped duct has been investigated in the region of both hydrodynamically and thermally fully developed flow. The thermal boundary condition imposed on the cusped duct is the axial uniform heat flux with peripheral uniform temperature. The results indicate that the fluid flow and heal transfer in the comer region of the cusped duct are improved because of the influence of natural convection. As the Rayleigh number increases, the friction factor and Nusselt number increase accordingly. It was also found that the critical Rayleigh number is 1200, at which flow reversal occurs in the buoyancy-assisted flow ( heated upflow). The velocity, temperature, and local Nusselt number distribution are presented for a range of Rayleigh numbers.     

Scaling analysis and numerical simulation of natural convection from a duct

Natural convection from a duct into the quiescent ambient is investigated. Heat transfer and dynamics of natural convection from the duct are discussed using a simple scaling analysis and the corresponding scaling relations are obtained. Additionally, numerical simulation for a wide range of Rayleigh numbers from 10⁰ to 10⁶ and the duct aspect ratios from 0 to 4 with the Prandtl number of 0.71 (air) is performed. The development of natural convection may approach a steady or an unsteady state in a fully developed stage, which is determined by the Rayleigh number and the duct aspect ratio. It is demonstrated that heat transfer of natural convection is improved by the duct for high Rayleigh numbers but depressed for low Rayleigh numbers. The scaling relations of natural convection from the duct have been validated in comparison with numerical results. The scaling predictions are consistent with the numerical results. Furthermore, the formulae of the Nusselt number, the Reynolds number, and the flow rate quantifying natural convection from the duct are presented.     

Experimental Investigations on Natural Convection Heat Transfer Around Horizontal Triangular Ducts

Experimental investigations have been reported on steady-state natural convection from the outer surfaces of horizontal ducts with triangular cross sections in air. Two different horizontal positions are considered; in the first position, the vertex of the triangle faces up, while in the other position, the vertex faces down. Five equilateral triangular cross-section ducts have been used with cross-section side length of 0.044, 0.06, 0.08, 0.10, and 0.13 m. The ducts are heated using internal constant-heat-flux heating elements. The temperatures along the surface and peripheral directions of the duct wall are measured. Longitudinal (perimeter-averaged) heat transfer coefficients along the side of each duct are obtained for natural convection heat transfer. Total overall averaged heat transfer coefficients are also obtained. Longitudinal (perimeter-averaged) Nusselt numbers and the modified Rayleigh numbers are evaluated and correlated using different characteristic lengths. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers. Moreover, a dimensionless temperature group was developed and correlated with the modified Rayleigh number. For the upward-facing case, laminar and transition regimes are obtained and characterized. However, for the downward-facing vertex case, only the transition regime is observed. The local (perimeter-averaged) or the overall total Nusselt numbers increase as the modified Rayleigh numbers increase in the transition regime. However, Nusselt numbers decrease as the modified Rayleigh numbers increase in the laminar regime.     

Laminar flow and heat transfer in plate-fin triangular ducts in thermally developing entry region

Laminar forced flow and heat transfer in plate-fin isosceles triangular ducts encountered in compact heat exchangers is investigated. The flow is hydrodynamically fully developed, but developing thermally under uniform temperature conditions. Heat conduction in the fin of finite conductance and convection in the fluid are analyzed simultaneously as a conjugate problem. The study covers a wide range of apex angles from 30° to 120°, and fin conductance parameters from 0 to infinitely large. Nusselt numbers in the developing and fully developed regions for various apex angles and fin conductance parameters are obtained, which can be used in estimation of heat transfer characteristics in plate-fin compact heat exchangers with fins of various conductivities and thickness.     

Heat and mass transfer in plate-fin sinusoidal passages with vapor-permeable wall materials

Laminar forced flow and heat mass transfer in sinusoidal plate-fin small passages encountered in compact heat mass exchangers are investigated. The duct is similar to a traditional plate-fin heat exchanger, but vapor-permeable materials like polymer membranes, paper, and ceramics can be used as the duct materials so both sensible heat and moisture can be exchanged simultaneously. Heat conduction and mass diffusion in the fins and heat and moisture convection in the fluid are analyzed simultaneously as a conjugate problem. Their fully developed Nusselt and Sherwood numbers under various aspect ratios and fin conductance parameters are calculated. The results found that though fins extend the heat transfer area, they are less effective compared to a traditional compact heat exchanger with metal foils. Most unfortunately, fin efficiencies for moisture transfer are even much smaller than those for heat transfer due to the low fin mass conductance parameters. For such heat mass exchangers, the use of fins can be regarded mostly as supporting materials, rather than as mass intensification techniques.     

Effect of tube inclination on laminar convection in uniformly heated tubes for flat-plate solar collectors

A numerical study using a combination of boundary vorticity method and line iterative relaxation method is carried out to determine the free convection effects on fully developed upward laminar forced flow in uniformly heated inclined tubes. The combined free and forced laminar convection for water with the inclined tube configuration in the low Reynolds number flow regime has practical application in flat-plate solar collectors for water heating. The tube inclination or gravitational force orientation effects on flow and heat transfer characteristics are clarified and show that in high Rayleigh number regime the tube orientation effect has considerable influence on the results, particularly in the neighborhood of horizontal direction. The numerical results show that the perturbation analysis in terms of power series of Rayleigh number is invalid for the present problem and reveal further that a maximum value for Nusselt number does not exist for any tube inclination angle with given values of the dimensionless parameters which is clearly contrary to the result from perturbation solution.     

Thermally Developing Forced Convection of Non-Newtonian Fluids Inside Elliptical Ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.     

Electrohydrodynamic enhancement of heat transfer in vertical fin array using computational fluid dynamics technique

Electrohydrodynamic enhanced heat transfer of the natural convection inside an enclosure with a vertical fin array is numerically investigated via a computational fluid dynamics technique. The parameters considered in a numerical modeling are supplied voltage, Rayleigh number, inclined angle, number of electrodes, electrode arrangement, number of fins, and fin length. The results reveal that the flow and heat transfer enhancements are significantly dependent on the number and position of electrodes around the fins. Moreover, the heat transfer coefficient is substantially improved by the electric field especially at the large number of fins and the long fin length.     

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In this study, fully developed laminar flow and convective heat transfer in an internally finned tube heat exchanger are investigated numerically. The flow is assumed to be both hydrodynamically and thermally developed with uniform outside wall temperature. Parameters of the thickness, length, and number of fins and thermal conductivity ratio between fin and working fluid are varied to obtain the friction factor as well as Nusselt number. The results show that the heat transfer improves significantly if more fins are used; however, the pressure drop turns out to be large in this heat exchanger. In addition, it is found that the emergence of closed-loop isotherms between the areas of two neighboring fins leads to heat transfer enhancement in the internally finned tube. When the fin number is smaller than 14, there appears a maximum Nusselt number at about 0.8 of the dimensionless fin length. Finally, an experiment is conducted to verify the numerical results.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall temperature

The exergy transfer characteristics of fluid flow and heat transfer inside a circular duct under fully developed laminar and turbulent forced convection are presented. Temperature is kept constant at the duct wall. The exergy transfer Nusselt number is put forward and the analytical expressions for exergy transfer Nusselt number are obtained as functions of heat transfer Nusselt number, Reynolds number, Prandtl number, etc. The variations of the local and mean convective exergy transfer coefficient, non-dimensional exergy flux, exergy transfer rate, etc. with operating parameters are presented graphically. By reference to a smooth duct and taking air as working fluid, a numerical analysis of the influence of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics has been conducted. The results show that the process parameters and configuration in the fluid flow and heat transfer inside a duct should be properly selected so that the forced convection process could have the best exergy utilization. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

A computational fluid dynamics modeling of natural convection in finned enclosure under electric field

Numerical modeling of the electric field effect on natural convection in the square enclosures with single fin and multiple fins is investigated. The interactions between electric, flow, and temperature fields are analyzed using a computational fluid dynamics technique. The parameters considered are the supplied voltage, Rayleigh number, size of enclosure, electrode arrangement, number of fins, and fin length. It can be concluded that the flow and heat transfer enhancements are the decreasing function of Rayleigh number. Moreover, the heat transfer coefficient is substantially improved by the electric field effect especially at the high number of fins and long fin length. Surprisingly, the maximum average velocity and heat transfer enhancement occur at the different electrode arrangements for the single fin and multiple fins.     

An experimental investigation into forced, natural and combined forced and natural convective heat transfer from stationary isothermal circular disks

Experimental heat transfer data are presented and dimensionless correlations developed for forced, natural and combined assisting forced and natural convection for heated stationary isothermal circular disks over wide ranges of the Reynolds, Rayleigh and modified Reynolds numbers, respectively. Experiments with air were performed for a variety of disks ranging in diameter and thickness-to-diameter aspect ratio. The correlation for combined forced and natural convection was developed utilizing the concept of a modified Reynolds number which accounts for a buoyancy-induced velocity. Utilizing this concept, the experimental data and respective empirical correlations for all three convection modes can be collapsed and plotted on the same continuous curve.     

Numerical modelling and optimisation of natural convection heat loss suppression in a solar cavity receiver with plate fins

This study details the numerical modelling and optimization of natural convection heat suppression in a solar cavity receiver with plate fins. The use of plate fins attached to the inner aperture surface is presented as a possible low cost means of suppressing natural convection heat loss in a cavity receiver. In the first part of the study a three-dimensional numerical model that captures the heat transfer and flow processes in the cavity receiver is analyzed, and the possibilities of optimization were then established. The model is laminar in the range of Rayleigh number, inclination angle, plate height and thickness considered. In the second part of the study, the geometric parameters considered were optimized using optimization programme with search algorithm. The results indicate that significant reduction on the natural convection heat loss can be achieved from cavity receivers by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 20% at 0° receiver inclination was observed. The results obtained provide a novel approach for improving design of cavity receiver for optimal performance.     

A numerical study of flow and heat transfer in internally finned rotating straight pipes and stationary curved pipes

In this article the effects of internal fins on laminar incompressible fluid flow and heat transfer inside rotating straight pipes and stationary curved pipes are numerically studied under hydrodynamically and thermally fully developed conditions. The fins are assumed to have negligible thickness with the same conditions as the pipe walls. Two cases, constant wall temperature and constant heat flux at the wall, are considered. First the accuracy of the numerical code written by a finite volume method based on SIMPLE algorithm is verified by the available data for the finless rotating straight pipes and stationary curved pipes, and then, the numerical results for those internally finned pipes are investigated in detail. The numerical results for different sizes and numbers of internal fins indicate that the flow and temperature field analogy between internally finned rotating straight pipes and stationary curved pipes still prevail. The effects of Dean number (K_L) versus friction factor, Nusselt number, and other non-dimensional parameters are studied in detail. From the numerical results obtained, an optimum fin height about 0.8 of pipe radius is determined for Dean numbers less than 100. At this optimum value, the heat transfer enhancement is maximum, and the heat transfer coefficient appears to be 6 times as that of corresponding finless pipes.     

Characteristics of forced convection heat transfer in vertical internally finned tube

This work presents a numerical investigation of a vertical internally finned tube subjected to forced convection heat transfer. The governing equations were solved numerically using the control volume technique. Nusselt number, Nu, and friction factor multiplied by Reynolds number, fRe, are influenced greatly by the height and number of the radial fins. The velocity and temperature distributions inside the tube depend on the number and height of the radial fins. This paper suggests that for best heat transfer to be achieved there is an optimum combination of fin numbers and height.     

Multi-objective genetic optimization of the heat transfer from longitudinal wavy fins

In the present work, we investigate the optimization of the heat transfer from wavy fins cooled by a laminar flow under conditions of forced convection and from a multi-objective point of view. The problem is addressed by means of a finite element method which allows to compute the velocity and the temperature distributions in a finned conduit cross section under conditions of imposed heat flux. Thereafter, the fin profile is optimized by means of multi-objective genetic algorithm which aims to find geometries that maximize the heat transfer and, at the same time, minimize the hydraulic resistance. The geometry of the fins is parameterized by means of a polynomial function and several order are investigated and compared.     

Further finite element analyses of fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts: Heat transfer predictions

Forced convection heat transfer to hydrodynamically and thermally fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts has been studied for the H1 and T thermal boundary conditions. The solutions for the velocity and temperature fields were obtained numerically using the finite element method with quartic triangular elements. From these solutions, very accurate Nusselt number values were determined. Computations were performed over a range of power-law indices and duct aspect ratios.     

NATURAL CONVECTION IN VERTICAL PARALLEL PLATES WITH AN UNHEATED ENTRY OR UN HEATED EXIT

This study aims to investigate the effects of the unhealed entry or unheated exit section on the free convection heat transfer in airflow in vertical parallel plate channels resulting from the thermal boundary conditions of uniform heat flux (VHF) and uniform wall temperature (UWT). Results of average Nusselt number and dimensionless volume flow rate are presented in terms of the ratio of the length of heated section to the full channel length and a Rayleigh number, ranging from the limit for the fully developed flow to that for single-plate behavior. Analytical equations for dimensionless volume flow rate and average Nusselt number for both unheated restrictions and both thermal boundary conditions have been developed for the fully developed flow limit. The numerical solutions are shown to approach asymptotically the approximate solution for fully developed flow as the Rayleigh number approaches 1 or less. An important finding of the study is that an unheated exit characterizes greater total heat transfer and volume flow rate than an unheated entry does. The presence of the unheated entry or unheated exit severely affects the convection process, especially at low Rayleigh number. A notable effect of an unheated exit on convection characteristics was found for the case of UHF at high Rayleigh number.