Natural convection heat transfer of molten salt nanofluids around vertical array of heated horizontal cylinders

Abstract

To analyze the natural convection heat transfer of molten salt nanofluids around vertical array of horizontal cylinders, a numerical simulation is performed with cylinder numbers in the range of N?=?2–8 and pitches in the range of S/D?=?5–10. The results show that the heat transfer of nanofluids around each cylinder is affected by the position in the tube row and its distance from the adjacent cylinder. The average Nusselt number (Nu_a) of the natural convection heat transfer over the whole array of cylinders is determined by cylinder spacing S/D, cylinder number N, and Ra. When S/D?=?5, Nu_a decreases as the cylinder number increases. When S/D?=?10, Nua increases as the cylinder number increases. Compared with the molten salts, the natural convection heat transfer of nanofluids is enhanced. This study provides a theoretical basis for the design of a single-tank energy storage system.     

An Experimental and Numerical Study of Natural Convection Heat Transfer in Horizontal Annuli between Eccentric Cylinders

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Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air

Natural convective flows of air around large horizontal cylinders were investigated experimentally. The main concerns were the turbulent transition mechanisms and the heat transfer characteristics of turbulent flows. The cylinders were heated with uniform heat flux and their diameters were varied from 200 to 1200 mm to enable experiments over a wide range of modified Rayleigh numbers, Ra_D^* = 1.0 × 10⁸ to 5.5 × 10¹¹. The flow fields around the cylinders were visualized with smoke to investigate the turbulent transition mechanisms. The results show that three‐dimensional flow separations occur first at the trailing edge of the cylinder when Ra_D^* exceeds 3.5 × 10⁹, and the separation points shift upstream with increasing Rayleigh numbers. These separations become a trigger to the turbulent transition and transitional and turbulent flows appear downstream of the separations at higher Rayleigh numbers. However, they occupy a relatively small portion of the cylinder surfaces even at the maximum Rayleigh numbers of the present experiments. The local heat transfer coefficients were also measured. The results show that the coefficients are increased significantly in the transitional and turbulent regions compared with the laminar coefficients. Moreover, the present results for air were compared with previous results for water and the effects of Prandtl number on the flow and heat transfer were discussed. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 293–305, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10080     

Natural convective heat-transfers from an isothermal horizontal hemispherical cavity

A simplified analytical solution, numerical calculations with the use of the FLUENT/UNS code and experimental studies of laminar free-convection heat transfer from an isothermal hemispherical cavity in unlimited space are presented. The analytical solution is based on an adaptation of the methods used for inclined isothermal plates. In the proposed solution, the control surface of the hemisphere was considered as a small inclined surface. Inclination of this surface was a function of azimuth angle. The results of theoretical analysis, numerical calculation and experimental procedure are presented in the Nusselt and Rayleigh number: relations Nu_D=0.296 Ra_D^1/4, Nu_D=0.340 Ra_D^1/4 and Nu_D=0.316 Ra_D^1/4 respectively. The comparison of theoretical and numerical solutions with experimental results presented in this paper shows good agreement.     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

Enhanced thermal performance and entropy generation analysis in a novel cavity design with circular cylinder

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 10³ to 10⁶, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth-shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency.     

Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation

In this paper, natural convection heat transfer in an inclined square cavity filled with pure air (Pr = 0.71) was numerically analyzed with the lattice Boltzmann method. The heat source element is symmetrically embedded over the center of the bottom wall, and its temperature varies sinusoidally along the length. The top and the rest part of the bottom wall are adiabatic while the sidewalls are fixed at a low temperature. The influences of heat source length, inclination angle, and Rayleigh number (Ra) on flow and heat transfer were investigated. The Nusselt number (Nu) distributions on the heat source surface, the streamlines, and the isotherms were presented. The results show that the inclination angle and heat source length have a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In addition, the average Nu firstly increases with γ and reaches a local maximum at around γ = 45°, then decreases with increasing γ and reaches minimum at γ = 180° in the cavity with ? = 0.4. Similar behaviors are observed for ? = 0.2 at Ra = 10⁴. Moreover, nonuniform heating produces a significant different type of average Nu and two local minimum average Nu values are observed at around γ = 45° and γ = 180° for Ra = 10⁵ in the cavity with ? = 0.2.     

Heat transfer of combined forced and natural convection from horizontal cylinder to air

Experimental investigations have been carried out for combined convective flows of air induced around uniformly heated, horizontal cylinders. Three cases of aiding, opposing, and cross flows were examined. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers of Re_d=50 to 900 and Ra_d^*=5×10⁴ to 3×10⁶. The flow fields around the cylinders were visualized with smoke. The results showed that separation points gradually shift from those of the forced convection to the top edge of the cylinder with increasing wall heat fluxes. The local heat transfer coefficients of the cylinders were also measured. Although the local coefficients show complex variations with the forced flow velocities and the wall heat fluxes, the overall coefficients become higher than those estimated from pure forced and natural convections throughout the cases of aiding, opposing, and cross flows. Moreover, it was confirmed that the overall Nusselt numbers as well as the separation points can be predicted with the non‐dimensional parameter (Gr_d^*/Nu_dRe_d²). © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 474–488, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20180     

Natural convective heat transfer in uniformly heated vertical pipe annuli

Natural convective heat transfer in vertical concentric pipe annuli is investigated both numerically and experimentally for a fluid having a Prandtl number of 0.7. Numerical calculations for three cases of different heating conditions for pipes (heated inner pipe, heated outer pipe, both pipes heated) are made of laminar flows for different inner‐to‐outer‐pipe diameter ratios d_i/d_o from 0.2 to 0.8. For each case, the thermal entrance length x/b at the modified Grashof numbers Gr^*=10² to 5 × 10⁵ is well correlated with Grashof number Gr^* and annulus length to clearance ratio L/b. Local Nusselt numbers Nu_i and Nu_o in the thermally fully developed region have certain constant values dependent on the diameter ratio d_i/d_o, regardless of Gr^* and L/b. Average Nusselt numbers Nu_i and Nu_o in the thermal entrance region are also independent of Gr^* and L/b. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 676–688, 2001     

Numerical study of mixed convection in a ventilated square enclosure with the lattice Boltzmann method

In this article, numerical study of heat transfer by convection in a square cavity was investigated. The vertical walls of the cavity are differentially heated and the horizontal walls are considered adiabatic. A ventilation jet is created by a fan placed in the cavity. A lattice Boltzmann model for incompressible flow equation is used to simulate the problem. A parametric study was performed presenting the influence of Reynolds number (20 ≤ Re?≤?500), Rayleigh number (10≤Ra?≤?10⁺⁶), and fan position (0.2?≤?L_F≤0.8). It has been observed that heat transfer rate increases with the Reynolds number increasing and it is maximal for the L_F=0.2.     

Turbulent natural convection of liquid deuterium,hydrogen and nitrogen within enclosed vessels

Quasi-steady natural convection of liquid deuterium, hydrogen, and nitrogen within a sphere, hemisphere, horizontal cylinder, and vertical cylinder has been studied experimentally for the case of a nearly uniform wall temperature. A single expression relating the Nusselt and Rayleigh numbers, Nu = 0·104Ra^0·352, fits the deuterium and nitrogen data over the range 7 × 10⁸ < Ra < 6 × 10¹¹, while the hydrogen Nusselt numbers are 8 per cent lower. The temperature field within the vessels is virtually free of horizontal temperature gradients. A single dimensionless temperature profile characterizes the vertical temperature distribution for each vessel shape, with the profiles for the sphere, hemisphere, and horizontal cylinder being nearly identical.     

Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate

Natural convection heat transfer and fluid flow characteristics in horizontal and vertical narrow enclosures with heated rectangular finned base plate have been experimentally investigated at a wide range of Rayleigh number (Ra) for different fin spacings and fin lengths. Quantitative comparisons of finned surface effectiveness (ε) and heat transfer rate between horizontal and vertical enclosures have been reported. In comparison with enclosure of a bare base plate, insertion of heat conducting fins always enhances heat transfer rate. Optimization of fin-array geometry has been addressed. The results gave an optimum fin spacing at which Nusselt number (Nu_H) and finned surface effectiveness (ε) are maximum. It has been found that: (1) increasing fin length increases Nu_H and ε; (2) increasing Ra increasesNu_H for any fin-array geometries and (3) for any fin-array geometry and at Ra > 10,000, increasing Ra decreases ε while for fin-array geometries of large fin spacing and at Ra < 10,000, increasing Ra increases ε. Useful design guidelines have been suggested. Correlations of Nu_H have been developed for horizontal and vertical enclosures. Correlations predictions have been compared with previous data and good agreement was found.     

A numerical study of natural convection in a vertical cylinder bundle

Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary‐fitted coordinate system. Numerical calculations for center‐to‐center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 10⁸. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nu_i are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330–341, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10095     

Conjugate heat transfer in inclined open shallow cavities

Conjugate heat transfer in inclined open shallow cavities has been numerically studied. A thick wall facing the opening is heated by a constant heat flux, sides perpendicular to the heated wall are insulated and the opening is in contact with a fluid at constant temperature and pressure. Conjugate heat transfer by conduction and natural convection is studied by numerically solving equations of mass, momentum and energy. The governing parameters were: Rayleigh numbers, Ra from 10⁶ to 10¹², conductivity ratio, k_r from 1 to 60, cavity aspect ratio, A=H/L from 1 to 0.125, dimensionless wall thickness, ?/L from 0.05 to 0.20 and the inclination angle, ? from 0° to 45° from the horizontal. Isotherms and streamlines are produced, heat and mass transfer is calculated. It is found that volume flow rate, is an increasing function of Ra, A, ?/L, ?, and a decreasing function of k_r. Heat transfer, Nu is an increasing function of Ra, ?/L, and a decreasing function of k_r. A mixed pattern is found with respect to A and ?. In the former, Nu is an increasing function of the aspect ratio up to a critical Rayleigh number, above which the relationship changes and it becomes a decreasing function of A. In the latter case, Nu is a decreasing function at low Raleigh numbers and an increasing one at high Rayleigh numbers.     

Natural convection heat transfer from a hollow horizontal cylinder with external longitudinal fins: A numerical approach

Abstract

The continuity, momentum, and the energy equations have been solved in 3D to predict the thermal plume and flow field around an isothermal horizontal longitudinally finned hollow cylinder in air. Effect of Rayleigh number (Ra), L/D, H/D, and s/D on heat transfer from the finned cylinder have been investigated where the input parameters are varied in a wide range of 10⁴ ≤ Ra ≤10⁷, 0.5?≤?L/D?≤?5, 0.0833?≤?H/D?≤?2, and 0.0785?≤?s/D?≤?0.785. Average surface Nusselt number (Nu) increases with increase in Ra and decreases with increase in cylinder length and fin number for all H/D. Nu for a finned solid cylinder is found to be marginally higher than that of the hollow cylinder except at low H/D of 0.0833 and high Ra of 10⁷ when s/D is less than 0.2617 for all L/D. Fin effectiveness is found to be increased with addition of taller fins for both the solid and hollow cylinder with longitudinal fins. Efficiency of the finned cylinder decreases with increase in fin height and Ra for all L/D and s/D. A general correlation of Nu as a function of all the pertinent input parameters (Ra, L/D, H/D, and s/D) has been proposed separately for the hollow isothermal cylinder having longitudinal fins, which can be used for industrial and academic purposes.     

Numerical study of the laminar natural convection flow around horizontal isothermal cylinder

Natural convection around a horizontal circular cylinder under constant temperature or constant heat flux conditions in an infinite space has been the subject of numerous investigations in recent years. However, these studies use the inflow-outflow boundary in cylindrical coordinates that gives a sensible error, especially when the Rayleigh number is small. This investigation, that enters within the framework of general study dealing with natural convection from an array of cylinders, states the problem in cartesian coordinates system, involves the use of a control-volume method and resolves various apparent redundancies in boundary conditions. This problem was investigated numerically for laminar case by solving the full vorticity transport equation together with the stream function and energy equations. Results are obtained for 10¹ < Ra < 10⁶ and for Prandtl number equal to 0.7. Further, typical isotherms, local and mean Nusselt number, velocities and temperature distribution are clarified in detail. The numerical approach presented here appears to be sufficiently versatile to permit computation of a vertical array of cylinders.     

Heat transfer experiments for low flow of water in rod bundles

Heat transfer experiments are conducted for fully developed forced and natural flows of water through triangularly arrayed, seven uniformly heated rod bundles with P/D = 1.25, 1.38 and 1.5. For forced circulation experiments. Re ranges from 80 to 50000 and Pr from 3 to 8.5; while in natural circulation. Re varies from 260 to 2000, and Ra, from 8 × 10⁶ to 2.5 × 10⁸. The forced flow data fall into two basic flow regimes : turbulent and laminar flow. At the transition between these regimes, Re_T, which varies from 2200 for P/D = 1.25 to 5500 forP/D = 1.5, increases linearly with P/D. The turbulent heat transfer data is in good agreement (±15%) with Weisman's correlation, designed for fully developed turbulent flow in rod bundles at Re > 25 000. However, the laminar flow data shows the dependency of Nu on Re to be weaker than for turbulent flow. Natural circulation data indicates that rod spacing insignificantly affects heat transfer; for P/D = 1.38 and 1.5, Nu is correlated as Nu = 0.272.Ra_0.25^q.     

Transient natural convection in a cylindrical enclosure at high Rayleigh numbers

The transient state of natural convection in a vertical cylindrical enclosure is studied numerically for water at high Rayleigh numbers, extending into values characteristic of the turbulent flow regime. Several two-equation turbulence models are used for this purpose. Heating is provided along the cylindrical surface at a constant heat flux, with the horizontal bounding surfaces being adiabatic and the development of stratification is studied. Such a configuration is very relevant to thermal storage tanks or solar thermal system vessels and the study aims at providing insight into the behavior of the system at the boundary between laminar and turbulent flow so that the appropriate numerical treatment may be adopted in future studies. The main aspect ratio considered is L/D=1 and the Rayleigh number (based on the length L) varies in the range 10¹⁰?Ra?10¹³ for laminar flow and 5×10¹³?Ra?10¹⁵ for turbulent flow, values for which previous data in the literature are all but non-existent. The attainment of a quasi-steady state is achieved after the fluid undergoes an oscillating pattern where secondary flows alternately appear and vanish. These patterns affect the development of stratification in the vessel. Low-Reynolds k-? models predict eventually a relaminarization at large times, but models employing the high-Re form of the k-? model obtain sustained or very slowly decaying turbulence instead. Comparisons are made with experimental results where applicable.     

A study of laminar natural convection in a non-uniformly heated annular fluid layer

A study is made of free convection in an annular fluid layer confined between two horizontal cylinders. Results are presented for the case of an adiabatic inner boundary with a sinusoidal temperature distribution on the outer boundary. The problem is formulated in terms of the Boussinesq approximations and solved using perturbation and finite-difference techniques. It is found that the results obtained from both methods are in good mutual agreement for weak convection. The solutions reveal the existence of various flow regimes, depending on Ra and the angular position of the temperature maximum on the outer boundary, which are similar in character to earlier results for the porous medium. It is found that incipient convection may decrease Nu in one case. In particular, when heating is from below, three distinct subregimes may be obtained within the range of parameters considered (R = 2, 0 < Ra < 40,000) namely, the steady quadri-cellular flow for Ra < 1120, the circulating flow with or without secondary cells for 1120 < Ra < 40,000, and finally unsteady circulating flow for Ra > 40,000. Secondary cells begin to appear near the outer boundary at Ra = 11,000. For an arbitrary heating angle, there is always a net circulating flow around the cavity, unless heating is from the top, which leads to an enhancement of heat transfer with the surroundings. The maximum flow and heat transfer rates are obtained for a heating angle below the horizontal whose value depends on Ra.     

Heat transfer correlations for PCM-based heat sinks with plate fins

Characterization of melting process in a Phase Change Material (PCM)-based heat sink with plate fin type thermal conductivity enhancers (TCEs) is numerically studied in this paper. Detailed parametric investigations are performed to find the effect of aspect ratio of enclosure and the applied heat flux on the thermal performance of the heat sinks. Various non-dimensional numbers, such as Nusselt number (Nu), Rayleigh number (Ra), Stefan number (Ste) and Fourier number (Fo) based on a characteristic length scale, are identified as important parameters. The half fin thickness and the fin height are varied to obtain a wide range of aspect ratios of an enclosure. It is found that a single correlation of Nu with Ra is not applicable for all aspect ratios of enclosure with melt convection taken into account. To find appropriate length scales, enclosures with different aspect ratios are divided into three categories, viz. (a) shallow enclosure, (b) rectangular enclosure and (c) tall enclosure. Accordingly, an appropriate characteristic length scale is identified for each type of enclosure and correlation of Nu with Ra based on that characteristic length scale is developed.