Heat transfer reduction between two finite concentric cylinders using radiation shields; Experimental and numerical studies

Energy consumption and its efficient utilization are two important factors of thermal systems. This work concerns with numerical and experimental studies about the surface radiation and natural convection effects on the heat transfer and flow field between two finite concentric cylinders, using one radiation shield between them. This study reveals material and geometric effects of the radiation shield on heat losses from two concentric cylinders enclosure at different temperatures and enclosure pressures. The enclosure consists of two concentric cylinders with hotter inner cylinder and colder outer one. The radiation shield with three different materials (aluminum, copper and steel) is inserted between the cylinders at two different radial positions. Validations are carried out for the temperature of the radiation shield with experimental data and numerical ones. After validation, forty eight different experiments and numerical simulations are carried out by varying the inner cylinder temperature between 373 K and 673 K at two enclosure pressures of 0.2 and 1.0 atm, corresponding to three different materials as radiation shields. The outer cylinder temperature from experiments is used in numerical simulations. The results show that the enclosure pressure and radiation shield emissivity together are responsible for reduction in the total heat loss from the inner cylinder. It was also found that among the three considered materials as radiation shields, copper is the most effective one to reduce the heat loss. In a specific case, the total heat loss with copper radiation shield was 14.99% and 57.7% lower than steel and aluminum shields, respectively.     

Transient natural convective heat transfer of a low-Prandtl-number fluid inside a horizontal circular cylinder with an inner coaxial triangular cylinder

A numerical study of transient natural convection of liquid gallium (Pr = 0.023) from a horizontal triangular cylinder to its coaxial cylindrical enclosure is performed. The aspect ratio is fixed at 2 and two positions of the inner triangular cylinder are considered. The development of the convective flow and heat transfer is shown via the time histories of the average Nusselt number over the outer circular wall for various Grashof numbers. Temporal phases of the flow development are identified as: initializing, developing, transitioning, and steady/quasi-steady state or oscillating. Typical flow patterns and temperature distributions at these phases are presented by means of streamlines and isotherms, respectively. Pitchfork bifurcation is present for both positions of the inner triangular cylinder when Gr ? 5 × 10⁴. The time-averaged Nusselt number over the outer circular cylinder, the flow development time, and the onset time of pitchfork bifurcation are predicted and scaled with the Grashof number. It is found that the time-averaged Nusselt number is apparently increased by horizontally placing the top side of the inner triangular cylinder for Gr ? 1 × 10⁵.     

An experimental and theoretical study of solidification in a free-convection flow inside a vertical annular enclosure

The natural convection and solidification in an annular enclosure has been studied experimentally and theoretically. Here the inner cylinder of the annular enclosure was cooled below the solidification temperature of the water, while the outer cylinder was kept on a uniform temperature well above 0 °C. The problem of the unsteady growth of the ice-layer on the inner cold cylindrical surface is studied theoretically and an approximate solution has been obtained for the quasi-steady development of the ice-layer thickness. In addition, it has been found that the influence of the contact layer between the frozen layer and the cold surface is of significant importance for the solidification process. Results are presented and compared between the experimental and the analytical investigation.     

Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method

In this paper the lattice Boltzmann method is used to investigate the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus. The study consists of an annular-shape enclosure, which is created between a heated triangular inner cylinder and a circular outer cylinder. The inner and outer surface temperatures were set as hot (T_h) and cold temperatures (T_c), respectively and assumed to be isotherms. The effect of nanoparticle volume fraction to the enhancement of heat transfer was examined at different Rayleigh numbers. Furthermore, the effect of vertical, horizontal, and diagonal eccentricities at various locations is examined at Ra = 10⁴. The result is presented in the form of streamlines, isotherms, and local and average Nusselt number. Results show that the Nusselt number and the maximum stream functions increase by augmentation of solid volume fraction. Average Nusselt number increases when the inner cylinder moves downward, but it decreases, when the location of inner cylinder changes horizontally.     

A numerical study of natural convection around a square,horizontal, heated cylinder placed in an enclosure

In this paper, natural convection around a tilted heated square cylinder kept in an enclosure has been studied in the range of 10³ ⩽ Ra ⩽ 10⁶. Streamfunction-vorticity formulation of the Navier–Stokes equation is solved numerically using finite-difference method in non-orthogonal body-fitted coordinate system. Detailed flow and heat transfer features for two different thermal boundary conditions are reported. Effects of the enclosure geometry has been assessed using three different aspect ratio placing the square cylinder at different heights from the bottom. The concept of heatfunction has been employed to trace the path of heat transport. It is found that the uniform wall temperature heating is quantitatively different from the uniform wall heat flux heating. Flow pattern and thermal stratification are modified, if aspect ratio is varied. Overall heat transfer also changes for different aspect ratio.     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

Effect of pool rotation on flow pattern transition of silicon melt thermocapillary flow in a slowly rotating shallow annular pool

In order to understand the mechanism of the flow pattern transitions on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a slowly rotating shallow annular pool in the counter-clockwise direction. The pool was heated from the outer cylinder and cooled at the inner cylinder. The temperature differences between the vertical outer and inner cylinders ranged from 5 K to 28 K and annular pool rotation rate from 0 and 2 rpm. Bottom and top surfaces of the melt pool were adiabatic. The simulation results indicate that two flow transitions occur when increasing the radial temperature difference along the free surface. At first, the steady two-dimensional flow becomes the first hydrothermal wave and then the second hydrothermal wave with less wave number. The critical conditions for the onset of the instability and the transition zone between the first and the second hydrothermal wave are determined at various rotation rates. Characteristics of the steady and the three-dimensional flows are discussed.     

Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids

Convective heat transfer in a differentially heated square enclosure with an inner rotating cylinder is studied theoretically. The free space between the cylinder and the enclosure walls is filled with water–Ag, water–Cu, water–Al₂O₃ or water–TiO₂ nanofluids. The governing equations are formulated for velocity, pressure and temperature formulation and are modeled in COMSOL, a partial differential equation (PDE) solver based on the Galerkin finite element method (GFEM). The governing parameters considered are the solid volume fraction, 0.0 ? ? ? 0.05, the cylinder radius, 0 ? R ? 0.3 and the angular rotational velocity, ?1000 ? Ω ? 1000. The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the strength of the flow circulation is much stronger for a higher nanoparticle concentration, a better thermal conductivity value and a smaller cylinder with a faster, negative rotation. The maximum heat transfer are obtained at a high nanoparticle concentration with a good conductivity value, a slow positive rotation and a moderate cylinder size located in the center of the enclosure.     

Transient and steady-state natural convection heat transfer from a heated horizontal concrete cylinder

In refrigeration systems, it is possible to reduce energy consumption (compressor power) and increase COP by decreasing the condensation temperature. Decreasing the condensation temperature can be achieved either by increasing the overall heat transfer coefficient or heat transfer surface area of the condenser. Usually, the radiuses of condenser tubes of domestic refrigerators are quite smaller than the critical radius. Thus, the radius can be increased up to the critical radius by coating the bare condenser tube to increase heat transfer. On the other hand, refrigerators operate discontinuously depending on the ambient temperatures. Coating material stores some of the heat during the working period and continues heat transfer during the off period so that the condenser continues transferring heat while the compressor is not working. Storage effect depends on the specific heat and density of the coating material. Transient and steady-state natural convection heat transfer from a heated horizontal cylinder covered with concrete layer by molding is studied experimentally and numerically to determine the effects of the parameters considered above. The copper and the concrete test cylinders used in the experimental study have a length of 1 m and outer diameter of 9.45 mm and 68.5 mm respectively. The ambient and copper cylinder surface temperatures varied between 20 °C÷30 °C and 30 °C÷50 °C respectively. Constant heat flux was applied to bare and concrete cylinders. Transient heat transfer experiments were performed when bare, and concrete cylinders were reached to steady state condition. Heat transfer rates under transient conditions from bare and concrete horizontal cylinders were compared and heat transfer enhancement was determined. Based on the experimental data average Nusselt numbers were calculated and compared with the well known correlations. Also temperature distributions obtained from numerical simulations were very close to the experimental data. The effect of the decrease in the temperature of the inner copper cylinder surface (condensation temperature) on COP was investigated considering an ideal Carnot refrigeration cycle. It is found that the enhancement in COP of a Carnot refrigeration cycle is 35.7% under transient condition.     

Natural convection heat transfer of molten salts around a vertically aligned horizontal cylinder set

The heat transfer from the vertical arrays of a set of equally spaced cylinders in molten salts is studied numerically to obtain the laminar natural convection heat transfer mechanism of molten salts around a vertically aligned horizontal cylinder set. Simulations are performed for arrays of 2–10 horizontal cylinders at a Rayleigh number based on a cylinder diameter between 2 × 10³ and 5 × 10⁵. Results show that the natural convective heat transfer of molten salts from the bottom cylinder of the array remains the same as that from a single cylinder. By contrast, the downstream cylinders may either be enhanced or reduced mainly depending on their location in the array and on the tube spacing. Heat transfer dimensionless correlating equations are proposed for any individual cylinder in the two vertically aligned horizontal cylinders. The heat transfer mechanism from the horizontal cylinders set in a vertical array is also simulated, and the results show that cylinder spacing can influence the average heat transfer rate around the whole tube array. Thus, in real applications, adjusting the cylinder spacing better enhances the average heat transfer from the whole tube array.     

Mixed convective transport in a lid-driven cavity containing a nanofluid and a rotating circular cylinder at the center

The mixed convective transport of Cu-H₂O nanofluid in a differentially heated and lid-driven square enclosure in the presence of a rotating circular cylinder is investigated numerically. The top wall of the enclosure is sliding from left to right at a uniform speed while all other walls are stationary. A thermally insulated circular cylinder is placed centrally within the enclosure. The cylinder can rotate about its centroidal axis. The top and bottom walls are kept isothermal at different temperatures while the side walls are assumed adiabatic. Simulations are performed for, Richardson number 1 ≤ Ri ≤ 10, dimensionless rotational speed 0 ≤ Ω ≤ 5 and nanoparticle concentration 0 ≤ ϕ ≤ 0.20 keeping the Grashof number fixed as Gr = 10⁴. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ω and Ri. Furthermore, the drag coefficient of the moving lid and Nusselt number of the hot wall are also computed to understand the effects of Ω and Ri on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder, mixed convective strength and the nanoparticle concentration.     

Heat transfer in a small gap between co-axial rotating cylinders

This paper investigates the local heat transfer of a co-axial rotating cylinder. In the inner flow field of the rotating cylinder, the dimensionless parameters include the rotational Reynolds number (Re_Ω) and buoyancy parameter (Gr). The test rig is designed to make the rotating in the inner cylinder and stationary in the outer cylinder. The local temperature distributions of the inner and outer cylinder on axial direction were measured. Under the experimental condition, whereas the ranges of the rotational Reynolds number are 2400 ≤ Re_Ω ≤ 45,000. Experimental results reveal that the rotational Reynolds number's increase is with the heat transfer coefficient distributions increase types. Finally, the local heat transfer rate on the wall are correlated and compared with that in the existing literature.     

Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate

The current study centers around a numerical investigation of natural convection heat transfer within a two-dimensional, horizontal annulus that is partially filled with a fluid-saturated porous medium. In addition, the porous sleeve is considered to be press fitted to the inner surface of the outer cylinder. Both cylinders are maintained at constant and uniform temperatures with the inner cylinder being subjected to a relatively higher temperature than the outer one. Moreover, the Forchheimer and Brinkman effects are taken into consideration when simulating the fluid motion inside the porous sleeve. Furthermore, the local thermal equilibrium condition is assumed to be applicable for the current investigation. The working fluid is air while copper is used to represent the solid phase. The porosity is considered to be uniform and constant with ε = 0.9. The main objective of this study is to examine the effect of the porous sleeve on the buoyancy induced flow motion under steady-state condition. Such an effect is studied using the following dimensionless parameters: Pr = 0.05–50, Ra = 10²–10⁶ and Da = 10^?4–10^?6. Also, the study highlights the effect of the dimensionless porous sleeve thickness (b) and thermal conductivity ratio (k_s/k_f) in the range between 1.1–1.9 and 1–150, respectively.     

Numerical simulation of double diffusive mixed convection in an open enclosure with different cylinder locations

This article reports numerical simulation of the double diffusive mixed convection around a cylinder in an open enclosure with an inlet and exit ports. The temperature and mass concentration of the cylinder are higher than those of the inlet flow and the cylinder can be at three different locations (lower, middle and upper) in the enclosure. The inlet flow with low temperature and mass concentration is located at the lower-left wall of the enclosure and the exit is at the upper-right wall. Other walls are assumed to be adiabatic. Effects of Lewis number Le, buoyancy ratio Br, and cylinder locations on the double diffusive mixed convection are investigated at Richardson number Ri = 1.0 and 0.01 while Prandtl number Pr is kept at 0.7. Streamlines, isotherms, isoconcentrations, and the average and local Sherwood number at different parameters are reported to characterize the double diffusive mixed convection phenomena in the open enclosure.     

Effects of viscous dissipation on slip-flow heat transfer in a micro annulus

This study deals numerically with the laminar slip-flow forced convection in a micro annulus with constant wall temperature. The solution takes the effects of viscous dissipation, velocity-slip and temperature-jump conditions at the surface into considerations. A hybrid application of the Laplace transformation technique and the local adaptive differential quadrature method (La-DQM) is used to solve the energy equation for the developing temperature field. Of interest are the effects of the Brinkman number Br, the Knudsen number Kn, and the radius ratio β of inner to outer cylinders on the temperature distribution and the Nusselt number.The results indicate that fully developed Nusselt number increases with an increase in the radius ratio β or a decrease in the Knudsen number Kn, but it is rather insensitive to the Brinkman number. The local Nusselt number in the thermal entrance region increases as Br increases. Comparisons are also made of the dimensionless temperature gradient at the outer cylinder between the present results and published data for the circular tube case β = 0, and the agreement is found out to be generally good.     

Pool boiling heat transfer on the tube surface in an inclined annulus

An experimental study was carried out to investigate the pool boiling heat transfer in an inclined annular tube submerged in a pool of saturated water at atmospheric pressure. The outer diameter and the length of the heated inner tube were 25.4 mm and 500 mm, respectively. The gap size of the annulus was 15 mm. For the tests, annuli with both open and closed bottoms were considered. The inclination angle was varied from the horizontal position to the vertical position. At a given heat flux, the heat transfer coefficient was increased with the inclination angle increase. Effects of the inclination angle on heat transfer were more clearly observed in the annulus with open bottoms. The main cause for the tendencies was considered as the difference in the intensity of liquid agitation and bubble coalescence due to the enclosure by the outer tube. One of the important factors in the annulus with open bottom was the convective fluid flow.     

Surface effects in flow boiling of R134a in microtubes

The inner surfaces of microtubes may be influenced strongly by the process of making them due to manufacturing difficulties at these scales compared to larger ones, e.g. the surface characteristics of a seamless cold drawn tube may differ from those of a welded tube. Accordingly, flow boiling heat transfer characteristics may vary. In addition, there is no common agreement between researchers on the criteria of selecting tubes for flow boiling experiments. Instead, tubes are usually ordered from commercial suppliers, in many cases without taking into consideration the manufacturing method and its effect on the heat transfer process. This may explain some of the discrepancies in heat transfer characteristics which are found in the open literature. This paper presents a comparison between experimental flow boiling heat transfer results obtained using two different metallic tubes. The first one is a seamless cold drawn stainless steel tube of 1.1 mm inner diameter while the second is a welded stainless steel tube of 1.16 mm inner diameter. Both tubes have a heated length of 150 mm and the flow direction is vertically upwards. The tubes were heated using DC current. Other experimental conditions include: 8 bar system pressure, 300 kg/m² s mass flux, about 5 K inlet sub-cooling and up to 0.9 exit quality. The results are presented in the form of local heat transfer coefficient versus local quality and axial distance. Also, the boiling curves of the two tubes are discussed. The results show a significant effect of tube inner surface morphology on the heat transfer characteristics.     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

Experimental investigation of thermal contact conductance at low temperature based on fractal description

An experimental investigation of thermal contact conductance was conducted with pressed pairs of aluminum alloy 5052 and stainless steel 304 over the low temperature range from 155 to 210 K, with nominal contact pressure from 1 to 7 MPa. The contact surfaces were prepared through bead blasting and characterized with the fractal dimension D and the parameter G of the Weierstrass–Mandelbrot function. The range of fractal dimension is 1.59–1.86 for aluminum and 1.56–1.92 for stainless steel. And the parameter G is in the magnitude of 10⁻⁷ m. From the measured results, thermal contact conductance over this temperature range (155–210 K) is less than that near or above room temperature (T > 300 K). The load sensitivity at low temperature is less than that at room temperature. The smaller fractal dimension D characterizes the rougher surface when G is on the same magnitude and results in the smaller value of the contact conductance and insensitivity to the contact pressure.     

Crystallisation of undercooled aqueous solutions: Experimental study of free dendritic growth in cylindrical geometry

This paper reports a study of crystallisation kinetics in small volumes of undercooled water–MPG (monopropylene glycol) mixture. The experimental cell is a vertical cylinder (height 5 mm, diameter 2r_e = 7.5 mm); its bottom section is closed by a Plexiglas disc that transmits light from the lower part of the cylinder to a high-speed digital camera. Photographic recordings allow the determination of the crystal growth rate. When the antifreeze mass fraction is below 25 wt%, crystallisation is clearly divided into two stages: the growth of dendritic crystals in the undercooled solution followed by the passage of the interdendritic solidification front. Dendrite growth induces a sudden temperature increase in the mixture, while the passage of the interdendritic solidification front determines the time at which sensible heat effects again predominate. The results show that the dendrite growth rate is an increasing function of the degree of undercooling and a decreasing function of the antifreeze mass fraction.