Numerical simulation of steady natural convection heat transfer in a 3-dimensional single-ended tube subjected to a nanofluid

In this paper, 3-dimensional numerical simulation of steady natural convective flow and heat transfer are studied in a single-ended tube with non-uniform heat input. Apart from some other applications, it serves as a simplified model of the single-ended evacuated solar tube of a water-in-glass evacuated tube solar water heater. It is assumed that the sealed end of tube to be adiabatic and also the tube opening to be subjected to copper–water nanofluid. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been then approximated by means of a fully implicit finite volume control method (FVM), using SIMPLE algorithm on the collocated arrangement. The study has been carried out for solid volume fraction 0 ≤ φ ≤ 0.05 and maximum heat flux 100 ≤ q_m ≤ 700. Considering that the driven flow in the tube is influenced by the dimensions and the inclination angle of the solar tube, the flow patterns and temperature distributions are presented on different cross sectional planes and longitudinal sections, when the tube is positioned at different orientations.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

An experimental study of heat transfer in an open thermosyphon

An experimental study was performed on heat transfer of an open thermosyphon with constant wall heat flux. Water and aqueous glycerin were used as working fluids. The experimental range of modified Rayleigh number was 1 × 10³ < Ra_m < 3 × 10⁵. The average and local heat transfer coefficients, vertical temperature distributions of the tube wall and fluid at the centerline of the tube, and temperature fluctuations of the fluid were measured. Flow patterns were observed by adding tracer powder to the fluid. Fluid velocities were measured by laser Doppler velocimeter. Experimental results indicate that, for a water thermosyphon, there are three regimes where different heat transfer characteristics and flow patterns occur. For 1 × 10³ < Ra_m < 3 × 10³, the flow was laminar and the thermal boundary layer reached the center of the tube. Heat was exchanged between the wall and descending flow. Wall temperature increased in the downward direction. For 4 × 10³ < Ra_m < 3 × 10⁴, no turbulence was observed in the flow and the thermal boundary layer was localized in the vicinity of the wall. The wall temperature increased upward. For 3 × 10⁴ < Ra_m < 3 × 10⁵, flow was considerably disturbed by the mixing of upward and downward flow in the upper part of the tube. However, the flow was laminar in the lower part of the tube. Reduction of the flow rate induced by the flow mixing at high Ra_m can be one of the major causes of the deterioration of heat transfer from Lighthill's theory. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 301–312, 2001     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Numerical visualization of mass and heat transport for conjugate natural convection/heat conduction by streamline and heatline

The method of numerical visualization of mass and heat transport for convective heat transfer by streamlines and heatlines are comprehensively studied. Functions are directly defined in terms of dimensionless governing equations or variables. Some basic characteristics of the functions are illustrated in detail, knowledge of which is essential to perceive the results and the philosophy of heat and fluid flow. The consistency of the formulations is especially addressed when dealing with conjugate convection/conduction problem. The functions/lines are unified for both fluid and solid regions, and the diffusion coefficients of the function equations are invariant. The method has been used to visualize the heat and fluid flow structures for natural convection in an air (Pr=0.71) filled square cavity over a wide range of Ra=10³−10⁶, and those for conjugate natural convection/heat conduction problem where the conduction effect of solid body on heat transfer is investigated. As to exhibiting the nature of convective heat transfer, streamlines and heatlines provide a more practical and efficient means to visualize the results than the customary ways.     

Numerical modeling of natural convection in an open cavity with two vertical thin heat sources subjected to a nanofluid

This paper presents a numerical study of natural convection cooling of two heat sources vertically attached to horizontal walls of a cavity. The right opening boundary is subjected to the copper–water nanofluid at constant low temperature and pressure, while the other boundaries are assumed to be adiabatic. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁷, and for solid volume fraction 0 ≤ φ ≤ 0.05. In order to investigate the effect of heat source location, three different placement configurations of heat sources are considered. The effects of both Rayleigh numbers and heat source locations on the streamlines, isotherms, Nusselt number are investigated. The results indicate that the flow field and temperature distributions inside the cavity are strongly dependent on the Rayleigh numbers and the position of the heat sources. The results also indicate that the Nusselt number is an increasing function of the Rayleigh number, the distance between two heat sources, and distance from the wall. In addition it is observed that the average Nusselt number increases linearly with the increase in the solid volume fraction of nanoparticles.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

Comparative study on heat transfer enhancement of nanofluids flow in ribs tube using CFD simulation

This study presents, a numerical investigation of two‐dimensional turbulent nanofluids flow in different ribs tube configurations on heat transfer, friction, and thermal performance coefficients using ANSYS‐FLUENT software version‐16. Governing equations of mass, momentum, and energy have been solved by means of a finite volume method (FVM). Four types of nanoparticles namely; Al₂O₃, CuO, SiO₂, and ZnO with volume fraction range (1%‐4%) and different size of nanoparticles (dp = 30 nm, 40 nm, 50 nm, and 60 nm) with various Reynolds number (10 000‐30 000) in a constant heat flux tube with rectangular, triangular, and trapezoidal ribs were conducted for simulation. The results exhibit that Nusselt number for all cases enhanced with Reynolds number and nanofluid volume fraction increases. Likewise, the results also reveal that SiO₂ with volume fractions of 4% and diameters of nanoparticles of 30 nm in triangular ribs offered the highest Nusselt number at Reynolds number of Re = 30 000. In addition, the higher value of thermal performance factor was obtained at Reynolds number of Re = 10 000.     

Simulation of a pebble‐bed heat regenerator

A mathematical model to simulate the operational behaviour of a pebble‐bed heat regenerator has been developed, and an experimental study performed to test the model predictions. The model is based on finite heat balances for the solid and the fluid applied to a bed which is divided into several sections insulated from each other. Within each section, there is no radial or axial temperature gradient, i.e. the temperature of all the pebbles in a given section are the same. As the fluid stream flows through the idealized compartmented bed, there is heat exchange in each section between the pebbles and the fluid. The model, which is applicable both to the heating and cooling cycles, has been used to simulate the behaviour of a heat regenerator. To test the predictions of the model, experiments have been performed on a 7 ft by 8 in cylindrical column using a hot air stream of approximately 200°C at an average flow rate of 365 l min^‐1. A special technique, wherein a pebble is fixed to a thermocouple, was used to measure the temperature at different bed positions. Experimental conditions were such that interesting results have been generated. The model was able to predict with good accuracy all the unusual operational behaviour encountered. The deviations between the model and the experimental results can be explained by the fact that the model does not consider heat loss from the column wall. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of wind flow around a parabolic collector (2) heat transfer from receiver tube

Parabolic collectors of commercial solar thermal power plants are subject to variable convection heat transfer from the receiver tube. In the present study heat transfer from a receiver tube of the parabolic trough collector of the 250 kW solar power plants in Shiraz, Iran, is studied taking into account the effects of variation of collector angel of attack, wind velocity and its distribution with respect to height from the ground.The governing equations for the two-dimensional steady state wind flow include continuity, momentum and energy equations and RNG-based k–ε model for turbulence scheme. Finite volume discretization method is used to solve the governing equations with wall function boundary condition and the SIMPLE approach is employed to iterate for the pressure correction and convergence of the velocity field. The momentum equation contains buoyancy force when the buoyancy effect is high and force convection effect is low.Computation is carried out for various wind velocities and different collector orientations with respect to wind direction. For solution of the energy equation, temperature of the receiver tube is taken as 350 K and ambient temperature is assumed to be 300 K. Various recirculation and temperature fields were observed around the receiver tube for different flow conditions. Effect of collector orientation on the average Nu number for the receiver tube was found negligible when the wind speed is low (Re⩽4.5×10⁵ based on the collector aperture). But when the wind velocity is high (Re>4.5×10⁵), the collector effect on the variation of Nu around the glass cover of the absorber tube is considerable.     

Effect of gravity conditions on heat transfer and flow fluctuations of liquid hydrogen in a non-isothermal horizontal circular tube

Liquid hydrogen phase transition is a common phenomenon in space missions for space vehicles using low temperature liquid hydrogen as propellant. In this study, a numerical model with coupled RANS solver and VOF/Level-set method was used to simulate the liquid hydrogen phase transition in a non-isothermal horizontal circular tube under different gravity conditions (1g-10^?4 g). The gas phase hydrogen produced by evaporation of liquid hydrogen was calculated by Lee model. The statistics of the overall volume, heat flux, mass flow rate, mean velocity of gas phase hydrogen was carried out. The data results shown that the flow fluctuations were strongest under the gravity acceleration of 10^?1 g relative to other gravity conditions. The average bubble volume at 10^?1 g was the smallest, which was 11.58% smaller than that at 10^?3 g condition. The intermittent contact with the tube wall, which leaded to intermittent long bubble and flow resistance, was the main reason.     

Numerical evaluation of the heat transfer in a shell and corrugated coil tube heat exchanger with three various water-based nanofluids

In this paper, turbulence heat transfer and nanofluid flow in a shell and corrugated coil tube heat exchanger are evaluated numerically. The three-dimensional numerical simulations have been done by finite volume method using a commercial computational fluid dynamics code. The spatial discretization of mass, momentum, turbulence dissipation rate, and turbulence kinetic energy equations has been achieved by a second-order upwind scheme. A SIMPLE algorithm has been used for velocity–pressure coupling. To calculate gradients, Green-Gauss cell-based method has been utilized. The cross-section of the coil tube is lobe shaped. First, the impact of corrugated tube cross-section type and then, the impact of utilizing different types of nanofluid on thermal performance are investigated. The outcomes indicate that at high Reynolds number, utilizing a five-lobe cross-section causes augmentation in Nusselt number and pressure drop by about 4.8% and 3.7%, respectively. However, the three-lobe type shows the highest thermal performance. Moreover, water/CuO has the most thermal performance. As the volume concentration of the nanofluid increases, the thermal performance declines.     

Maximization of heat transfer density from a vertical array of flat tubes in cross flow under fixed pressure drop using constructal design

The density of heat transfer rate from a vertical array of flat tubes in cross flow is maximized under fixed pressure drop using constructal design. With the constructal design, the tube arrangement is found such that the heat currents from the tubes to the coolant flow easily. The constraint in the present constructal design is the volume where the tubes are arranged inside it. The two degrees of freedom available inside the volume are the tube‐to‐tube spacing and the length of the flat part of the tubes (tube flatness). The tubes are heated with constant surface temperature. The equations of continuity, momentums, and energy for steady, two‐dimensional, and laminar forced convection are solved by means of a finite‐volume method. The ranges of the present study are Bejan number (dimensionless pressure drop) (10³ ≤ Be ≤ 10⁵) and tube flatness (dimensionless length of the tube flat part) (0 ≤ F ≤ 0.8). The coolant used is air with Prandtl number (Pr = 0.72). The results reveal that the maximum heat transfer density decreases when the tube flatness decreases at constant Bejan number. At constant tube flatness, the heat transfer density increases as the dimensionless pressure drop (Bejan number) increases. Also, the optimal tube‐to‐tube spacing is constant, irrespective of the tube flatness at constant Bejan number.     

Prandtl number dependence of laminar natural convection heat transfer in a horizontal cylindrical enclosure with an inner coaxial triangular cylinder

A numerical study of laminar convection heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure is performed to investigate the Prandtl number effect on flow and heat transfer characteristics. The Prandtl number over several orders of magnitude (10^?2 < Pr < 10³) as well as different aspect ratios (AR = 1.2 and 2.0) and different Rayleigh numbers (Ra = 10³, 10⁴, 10⁵, and 10⁶) are considered. The finite volume approach is used to solve the governing equations, in which buoyancy is modeled via the Boussinesq approximation. The computed flow patterns and temperature fields are shown by means of streamlines and isotherms, respectively, and the local and average heat transfer coefficients are also presented. It is found that the flow and heat transfer characteristics for a low Prandtl number fluid (Pr = 0.03) are unique and they are almost independent of Prandtl number when Pr ? 0.7. The entire spectrum of Prandtl number investigated can be divided into three sections based on the variations of average heat transfer coefficients. In each section, correlating equations of the average Nusselt number to the Rayleigh number are proposed with the maximum deviation less than 3%.     

Heat transfer analysis of lateral perforated fin heat sinks

In this article fluid flow and conjugate conduction-convective heat transfer from a three-dimensional array of rectangular perforated fins with square windows that are arranged in lateral surface of fins are studied numerically. For investigation, Navier–Stokes equations and RNG based k − ε turbulent model are used. Finite volume procedure with SIMPLE algorithm is applied to coupled differential equations for both solid and gas phases. Computations are carried out for Reynolds numbers of 2000–5000 based on the fin thickness and Pr = 0.71. Numerical model is first validated with previous experimental studies and good agreement were observed. Based on a valid numerical model, numerical solution is made to find fluid flow and temperature distribution for various arrangements. For each type, fin efficiency of perforated fins is determined and compared with the equivalent solid fin. Results show that new perforated fins have higher total heat transfer and considerable weight reduction in comparison with solid fins.     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

Hydrological disturbances of the conductive heat flow in the upper crust: Problems of correcting measured heat flow data

The upper crustal-scale convection of fluids is one of the main factors distorting the conductive geothermal field. Geothermal anomalies caused by water circulation, as a rule, exceed the contributions from other factors (relief, sedimentation, structural and climatic effects). The measured temperature gradient has to be corrected before being used for calculation of the heat flow. In the present work, certain 2-D hydrothermal convection models have been analyzed using various permeability distributions and spatial configurations of fluid systems. Permeability anisotropy has also been included in some of the models, and variations of this parameter in the range 10⁻¹⁰–10⁻¹⁶ m² have been considered. Numerical simulations reveal the possibility of considerable advective disturbances to the heat flow. These disturbances depend on the physical parameters, and strongly on the geometry of fluid circulation. The magnitude of the hydrologic correction has been assessed for a variety of geological environments.     

A numerical study of natural convection heat transfer in a composed thermal diode

The effects of inclination on the steady natural convection local heat transfer characteristics in an air-filled enclosure, which is composed of rectangular and parallelogrammic portions, are studied numerically. In this investigation, two geometrical aspect ratios are introduced: one for a parallelogrammic portion of an enclosure, the other for a rectangular one. The governing equations for a two-dimensional, laminar, natural convection process in an enclosure are discretized by the control volume approach which ensures the conservative characteristics to be satisfied in the calculation domain, and then solved by a modified SIMPLE algorithm. The momentum and energy equations are coupled through the buoyancy term. Computations are carried out for Prandtl number Pr = 1 and Rayleigh number Ra = 2.7 × 10⁸. In order to obtain a greater understanding of the flow and heat transfer behaviors, flow patterns with streamlines and isotherms at different inclination angles are shown. Also, the effects of numbers of installed guide vanes in a composed enclosure are studied to consider the enhancement of heat transfer of the inner diode. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 573–582, 1999     

Effect of eccentricity and radius ratio on fluid flow and heat transfer inside an eccentric semicircular enclosure

latroductionNatural convechon heat transfer has gainedconsiderable attention because of itS' numerousaPPlications in the areas of energy conservation, coolingo f electrical and electronic components, design of solarcoil~, bed exchangers, and many others. Heattransfer inside annular space, air-filled cavity or annularsector has wide aPPlication in many engineeringProblems. In our earlier work["n, we have shown theeffeCt of eccentricity on heat transfer and flow field forradius ratio R'=2.0 f…     

Heat transfer enhancement of finned-tube heat exchanger using nozzle- and diffuser-shaped fins instead of straight fins

In this paper, a new method has been used to improve the heat transfer rate in the finned-tube heat exchanger with nozzle- and diffuser-shaped arrangement. For this study, the effect of several parameters was studied numerically. For the computational fluid dynamics simulation, the continuity, momentum, and energy equations were solved by the finite volume method using the standard k–ԑ model. The rate of heat transfer increases with the decreasing of fin bend radius (15 < R_fb < 20) for both nozzle-shaped fin and diffuser-shaped fin. By increasing of side temperature (600 < T_side < 900) and side Reynolds number (2000 < Re_side < 5000) the heat transfer rate increased for both nozzle- and diffuser-shaped fins. Results showed that a nozzle-shaped fin with a fin bend radius of 15 mm under the condition of Re_in = 20,000, T_side = 900 K, and Re_side = 3400 has a higher effect on heat transfer in comparison with the other types of fins. The maximum heat transfer rate was almost 39% and 35% for the nozzle-shaped fin with a bend radius of 15 mm and diffuser-shaped fin with a bend radius of 15 mm compared with the simple tube, respectively. Finally, correlational equations have been suggested to forecast the average Nu number as functions of various parameters of the tube equipped with different types of outer fins involving nozzle- and diffuser-shaped.