Steady-state Natural Convection Heat Transfer Research Articles

Impact of grooved cylinder on heat transfer by natural convection in cylindrical geometry

The current study reports a numerical analysis of a two-dimensional steady-state natural convection heat transfer from grooved heated cylinder for laminar flow regime. Two groove shapes are investigated in this work: circular and triangular groove. Simulations were carried out by varying the groove location, radius ratio f from 0.1 to 1, and the Rayleigh number over the range [103–106]. The thermal and dynamic behaviors are carefully analyzed and compared to the case of non-grooved cylinder (model 0). It is found that the heat transfer rate rises up with the increase of Rayleigh number. In addition, the groove locations φ = −90, and 80° provide the lowest heat transfer rate. A decrease of 9.4% in the heat transfer rate is detected for the case of triangular groove with f = 0.7 and Ra = 105. On the other hand, the highest heat transfer rate is provided at a position φ = −45° and 45° for f > 0.65. For these last groove locations, lower f present optimal configurations to accumulate heat on the cylinder. In fact, circular grooved cylinder with f = 0.1 decreases the heat loss by 9.3% and 12.4% for the locations φ = −45° and 45°, respectively compared to model 0. These results would be useful for engineering applications that are interested in the accumulation or transfer of heat through cylindrical ducts.

Heat Transfer by Natural Convection in a Square Enclosure Containing PCM Suspensions

Research on using phase change material (PCM) suspension to improve the heat transfer and energy storage capabilities of thermal systems is booming; however, there are limited studies on the application of PCM suspension in transient natural convection. In this paper, the implicit finite difference method was used to numerically investigate the transient and steady-state natural convection heat transfer in a square enclosure containing a PCM suspension. The following parameters were included in the simulation: aspect ratio of the physical model = 1, ratio of the buoyancies caused by temperature and concentration gradients = 1, Raleigh number (RaT) = 103–105, Stefan number (Ste) = 0.005–0.1, subcooling factor (Sb) = 0–1.0, and initial mass fraction (or concentration) of PCM particles (ci) = 0–0.1. The results showed that the use of a PCM suspension can effectively enhance heat transfer by natural convection. For example, when RaT = 103, Ste = 0.01, ci = 0.1, and Sb = 1, the steady-state natural convection heat transfer rate inside the square enclosure can be improved by 70% compared with that of pure water. With increasing Sb, the Nusselt number can change nonlinearly, resulting in a local optimal value.

Natural convection heat transfer from a bundle of heated circular cylinders with staggered arrangement immersed in molten solar salt

A two-dimensional steady-state natural convection heat transfer from a bundle of closely spaced isothermally heated cylinders in a staggered arrangement immersed in molten solar salt was investigated in this study for a laminar flow regime using numerical analysis. The flow and temperature fields and heat transfer from the cylinder bundle were predicted as functions of tube spacing and flow conditions. It was determined that flow patterns and heat transfer are strongly affected by the transverse and longitudinal cylinder-to-cylinder spacing ST and SL, Rayleigh number and thermo-physical properties of the heat storage fluid. Performance maps in the form of contour diagrams for the average Nusselt number Nu and dimensionless heat transfer volumetric density are presented for a staggered bundle of circular horizontal cylinders immersed in a molten solar salt.The variation of the heat transfer enhancement for the staggered bundle of horizontal cylinders shows that there is an optimal transverse cylinder spacing resulting in the highest heat transfer enhancement. The heat exchanger geometry was optimized by determining the optimal set of the tube (cylinder) spacings SL/D and ST/D in the bundle resulting in the maximum volumetric heat transfer rate q ̃, and smallest size, and lowest cost of a heat exchanger. A set of correlations were developed for the maximum and optimum dimensionless heat transfer volumetric densities as functions of the Rayleigh number RaD. The analyzed geometries are important in the solar heating and storage technology, nuclear reactor safety, and waste heat recovery applications.

Natural convection heat transfer from a bundle of in-line heated circular cylinders immersed in molten solar salt

A two-dimensional steady-state natural convection heat transfer from a bundle of closely spaced isothermally heated cylinders in the in-line arrangement was investigated in this study for a laminar flow regime using numerical analysis. It was determined that flow patterns and heat transfer are strongly affected by the transverse and longitudinal cylinder-to-cylinder spacing ST and SL, Rayleigh number, and thermo-physical properties of the heat storage fluid. Performance maps in the form of contour diagrams for the average Nusselt number Nu and dimensionless heat transfer volumetric density q ̃, and corresponding correlations are presented for an in-line bundle of 9 × 5 horizontal cylinders immersed in a molten solar salt.The variation of the heat transfer enhancement for the in-line bundle of horizontal cylinders shows that there is an optimal cylinder spacing resulting in the highest heat transfer enhancement. The heat exchanger geometry was optimized by determining the optimal set of the tube (cylinder) spacings SL/D and ST/D in the bundle resulting in the maximum volumetric heat transfer rate q ̃, and smallest size and lowest cost of a heat exchanger. A set of correlations were developed for the maximum and optimum dimensionless heat transfer volumetric densities as functions of the Rayleigh number RaD. The analyzed geometries are important in the solar heating and storage technology, nuclear reactor safety, and waste heat recovery applications.

Transient natural convection heat transfer analyses from a horizontal cylinder

Experiments are conducted to analyze the power-on transient natural convection heat transfer around a horizontal cylinder heated in air. The heat flux ranges from 177 W/m2 to 2426 W/m2 and Rayleigh number from 4.13 × 104 to 4.35 × 104. The effects of transient heat transfer data on different angular position of the thermocouple (0°, 90°, 180°) are reported. The results indicate that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. The test rig working condition is verified by comparing the steady-state natural convection heat transfer data with those obtained from the literature. It is observed that the transient heat transfer data obtained at 90° and 180° are higher than that of stagnation point (0°). Finally, based on the transient data, correlations are presented to predict the heat transfer behavior around the heated cylinder.

Natural convection heat transfer from a horizontal row of finite number of heated circular cylinders immersed in molten solar salt

Abstract A two-dimensional steady-state natural convection heat transfer from a single row of closely spaced isothermally heated cylinders was investigated in this study for a laminar flow regime. A few previous studies investigated the natural convection heat transfer from a single row of isothermally heated cylinders. However, no correlations or performance maps were developed for the average Nusselt number N u ¯ D for a single row of horizontal cylinders. Using the correlations proposed for natural convection heat transfer from a single cylinder results in large errors in predicting the heat transfer for multiple cylinders. Thus, numerical and statistical modeling were performed in this study to propose correlations for the average Nusselt number N u ¯ D for a single row of horizontal cylinders immersed in molten solar salt as functions of Rayleigh number R a D and dimensionless cylinder-to-cylinder spacing ( ST/D ) . The analyzed geometries are important in the solar heating and heat storage technology, nuclear reactor safety and waste heat recovery applications.

Natural convection heat transfer from a vertical column of finite number of heated circular cylinders immersed in molten solar salt

A two-dimensional steady-state natural convection heat transfer from a vertical column consisting of 2–10 tightly packed isothermally heated horizontal circular cylinders submerged into molten solar salt was investigated numerically by using the finite volume method. Although laminar natural convection from a vertical column of multiple horizontal cylinders has been investigated in previous studies (Chouikh et al., 1999; Sparrow and Niethammer, 1981; Bejan et al., 1995; Sadeghipour and Asheghi, 1994; Corcione, 2005; Ashjaee and Yousefi, 2007; Tokura et al., 1983; Hannani et al., 2002; Kitamura et al., 2016), there are very few studies that considered natural convection heat transfer from circular cylinders immersed in molten solar salt (Lu et al., 2016, 2013; Brosseau et al., 2004). The results of the study show that Rayleigh number and longitudinal cylinder spacing SL have a significant effect on flow and heat transfer in the cylinder column.Using the correlations proposed for natural convection heat transfer from a vertical column of N circular cylinders in air or water would result in large errors in predicting heat transfer for a vertical column of cylinders in molten solar salt. Thus, correlations for the steady-state average Nusselt number Nu‾D,N for the column of N circular cylinders, where N was varied from 2 to 10, and for individual cylinders in the column Nu‾D,i are proposed as functions of the Rayleigh number (range 104–107) and dimensionless longitudinal cylinder spacing (SL/D). New correlations developed specifically for molten salt are needed to improve heat exchanger design for solar heating and heat storage technology, nuclear reactor safety, and waste heat recovery applications.

Experimentally Study the Effects of Fins Height and Space Ratio (H\\S) to the Fin thermal performance by Natural Convections

Heat transfer enhancement devices are widely used in various industrial, transportation, or domestic applications such as thermal power plants, means of transport, heating and air conditioning systems, electronic equipments and space vehicles. In all these applications, improvements in the efficiency of heat exchangers can lead to substantial cost, space and materials savings. The research work summarized in this articles presents an experimental investigation on the effect of fin space (S) on the fin performance using rectangular plate type fins. The steady-state natural convection heat transfer from vertical rectangular fins extending perpendicularly from horizontal square base was investigated experimentally at high range of temperatures from 50 to 150 C°. The effects of fin space parameter, fin height-space (H\\S) ratio and base-to-ambient temperature difference on the heat transfer performance of fin arrays were observed and the environmental condition were determined.. Five fin height-space ratios settings 1.31,1.43,1.67,1.85 and 2.27 with constant fin surface area were employed under free convection heat transfer conditions. The heat transfer area was kept the same. The performance of the fin expressed in terms of fin efficiency, effectiveness and thermal resistance as a function of the ambient temperature and fin space parameters has been study in this work. The dimensionless parameter Biot no. on the locally variable environmental condition is examined for different fin spaces and fin height-space (H\\S) ratio to the fin heat transfer rate. Also, the effect of environmental condition is study at the same (H\\S) ratio. Experimental results show that the effect of Height-Space ratio (H\\S) on fin performance is more significant.. The maximum increase in convection heat transfer coefficient value obtained is about 19 percent. The increase in heat transfer coefficient value is also manifested by a corresponding decrease in the fin base temperature. Also, it is concluded from the experimental results that the performance of heat transfer rate increase with increasing the height- space ratio (H\\S) and decreasing the fin space in respect of heat transfer coefficient, thermal resistance, overall efficiency and effectiveness.

An experimentally investigate the fin thermal performance to the different fin spaces by natural convections

In oil and gas industries there are a lot off heat transfer devices used for different purposes. These devices are widely used in various industrial, transportation, or domestic applications such as heat exchangers thermal power plants, means of transport, heating and air conditioning systems, electronic equipments and space vehicles. In all these applications, improvements in the efficiency of heat exchangers can lead to substantial cost, space and materials savings. The research work summarized in this articles presents an experimental investigation on the effect of fin space (s) and aluminum materials on the fin performance using rectangular fins. The steady-state natural convection heat transfer from vertical rectangular fins extending perpendicularly from horizontal square base was investigated experimentally at new range not found in the previous works, this range of temperatures from 50 to 150 Co . The effects of fin space parameter and base-to-ambient temperature difference on the heat transfer performance of fin arrays were observed and the environmental condition were determined. Five fin space settings,( 22, 27, 30, 35 and 38 mm) with a constant fin height is 50mm for all types of configuration are presented in this work were employed under free convection heat transfer conditions. This range of fin space not found on previous study or research. The heat transfer area was kept the same. The performance of the fin expressed in terms of fin efficiency, effectiveness and thermal resistance as a function of the ambient temperature and fin space parameters has been study in this work. The dimensionless parameter Biot no. on the locally variable environmental condition is examined for different fin spaces to the fin heat transfer rate. Also, the effect of environmental condition is study. Experimental results show that the effect fin space on fin performance is more significant.. The maximum increase in convection heat transfer coefficient value obtained is about 22 percent. The increase in heat transfer coefficient value is also manifested by a corresponding decrease in the fin base temperature. Also, it is concluded from the experimental results that the performance of heat transfer rate increase with decreasing the fin space in respect of heat transfer coefficient, thermal resistance ,overall efficiency and effectiveness.

Numerical Study of Heat Transfer Enhancement for Low-Pressure Flows in a Square Cavity with Two Fins Attached to the Hot Wall Using Al2O3-Air Nanofluid

The gaseous low-pressure nanofluid flow of a steady-state two-dimensional laminar natural convection heat transfer in a square cavity of length L with two attached solid fins to the hot wall is numerically investigated. Such flows are found in many engineering applications, such as nuclear reactors and electronic cooling equipment. Physical parameter ranges in this study are as follows: 0 ≤ Kn ≤ 0.1, 103 ≤ Ra ≤106, 0 ≤ ϕ ≤ 0.2, LF/L takes the value of 0.5, HF takes the values of 0.25 to 0.75. Simulation results show that Nusselt number depends directly on the Rayleigh number and inversely on the Knudsen number. In addition, it is found that heat transfer will be enhanced by dispersing the nanoparticles of Al2O3 in the base low-pressure gaseous flow. Moreover, it is found that the Nusselt number of such flows increases as the nano-particle volume fraction increases for the investigated range of volume fractions considered in this study. In addition, a correlation of the Nusselt number among all the investigated parameters in this study is proposed as Nu = 0.2196 Ra0.0829 Kn–0.511 ϕ0.104.

Two-dimensional analysis of low-pressure flows in an inclined square cavity with two fins attached to the hot wall

The gaseous low-pressure flow of a steady-state two-dimensional laminar natural convection heat transfer in a cavity with an attached two solid fins to the hot wall is numerically investigated. Such flows can be found in many engineering applications such as the “evacuated” solar collectors and in the receivers of the solar Parabolic Trough Collectors (PTCs), nuclear reactor cooling and electronic equipment cooling. Buoyancy effect is modeled using Boussinesq approximation. Effects of Knudsen and Rayleigh numbers, location and length of the fins, conductivity ratio and fins porosity, and the tilt angle on the flow and heat transfer characteristics are investigated. Physical parameters ranges in this study are as follows; 0≤Kn≤0.1, 103≤Ra≤106, LF takes the values of 0.25, 0.5 and 0.75 m, HF takes the values of 0.25_0.5, 0.25_0.75 and 0.5_0.75, 1≤Kr≤8000, 0≤ε≤1 and 0∘≤θ≤90∘. It is shown that Nusselt number depends directly on Rayleigh number and inversely on Knudsen number. In addition, it is found that attaching two solid fins to the hot wall will enhance the heat transfer for such flows. Moreover, it is found that the porous fins are superior to the solid fins as far as the heat transfer is concerned. In addition, it is shown that for the geometry where the lower fin height to cavity length ratio is 0.25 and the upper fin height to cavity length ratio is 0.75, the best heat transfer is achieved. In addition, for the fin lengths considered in the study, it is concluded that by increasing the length of the fin, a better heat transfer is achieved. Also, it is found that by increasing the tilt angle of the cavity, a better heat transfer is achieved up to a certain value which was found to be (30°) where beyond this value, Nusselt number will decrease. In addition, it is found that by increasing the conductivity ratio up to a certain value (103), better heat transfer is gained. Finally, a correlation among Nusselt number and the parameters investigated in this research proposed as Nu=0.02197ε0.00932sin(θ)0.00373Kr0.0273(h2/LF)2.814Ra0.13((h2−h1)/LF)1.373(h1/LF)1.615Kn0.37.

Heat transfer enhancement of vertical dimpled fin array in natural convection

This numerical study examines the steady-state three-dimensional natural convective flow and heat transfer for a set of vertical fin arrays with/without dimples. The finite volume method is adopted to solve the Navier–Stokes and energy equations using semi-implicit method for pressure-linked equation (SIMPLE) with the converged solutions from the iterative steps to acquire the velocity field, temperature field, and Nusselt number (Nu). The free convective flow and heat transfer for different vertical fin arrays are analyzed at Rayleigh numbers (Ra) of 108, 7.75×107, 5.5×107, and 3.25×107 with the fixed Prandtl number of 0.71. For each Ra tested, four vertical fin arrays, namely smooth thirteen-fin array, smooth nine-fin array, dimpled nine-fin array, and dimpled seven-fin array, with the same fin base area and fin-array volume are individually analyzed. The results indicated the respective worst and best heat transfer performances for the smooth thirteen-fin and dimpled nine-fin arrays. As Ra increases, the mean Nu over each fin surface increases, especially for the dimpled fin arrays. Relative to the smooth thirteen-fin array, the maximum increase of mean Nu is 68% for the dimpled nine-fin array.

Rarefied flow and heat transfer characteristics over a vertical stretched surface

Similarity solution for the steady-state two-dimensional laminar natural convection heat transfer for a rarefied flow over a linearly vertical stretched surface is being proposed. Similarity conditions are obtained for the boundary layer equations for the vertical flat plate subjected to power law for the temperature variations. It is found that the similarity solution exists for linear temperature variation and linear stretching surface. The study shows that there are three different parameters affecting the flow and heat transfer characteristics for the rarefied flow over a vertical linearly stretched surface. These parameters represent the effects of the velocity slip ( K1), temperature jump ( K2), and the Prandtl number ( Pr). The effects of these parameters are presented. It is found that the velocity slip parameter affects both the hydrodynamic and thermal behaviors of such flows. Correlations for the skin friction as well as Nusselt number are being proposed in terms of Grashof number ( Grx), the slip velocity parameter ( K1), and the temperature jump parameter ( K2).

Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models

Purpose – The purpose of this paper is to theoretically analysis the steady-state natural convection flow and heat transfer of nanofluids in a square enclosure filled with a porous medium saturated with a nanofluid considering local thermal non-equilibrium (LTNE) effects. Different local temperatures for the solid phase of the nanoparticles, the solid phase of porous matrix and the liquid phase of the base fluid are taken into account. Design/methodology/approach – The Buongiorno’s model, incorporating the Brownian motion and thermophoresis effects, is utilized to take into account the migration of nanoparticles. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the finite element method is utilized to solve the governing equations. Findings – The results show that the increase of buoyancy ratio parameter (Nr) decreases the magnitude of average Nusselt number. The increase of the nanoparticles-fluid interface heat transfer parameter (Nhp) increases the average Nusselt number for nanoparticles and decreases the average Nusselt number for the base fluid. The nanofluid and porous matrix with large values of modified thermal capacity ratios (γ p and γ s ) are of interest for heat transfer applications. Originality/value – The three phases of nanoparticles, base fluid and the porous matrix are in the LTNE. The effect of mass transfer of nanoparticles due to the Brownian motion and thermophoresis effects are also taken into account.

English

The industry revolution in thermal engineering started with fixed the extended surface area named a fin. Therefore, a lot off research work done in this field to enhance the performance of heat transfer. All, previous work reach to that any increase of heat transfer coefficient and the fin surface area will increase the heat transfer rate by natural convection. The research work summarized in this paper presents an experimental investigation on the effect of fin heights –width (H/w) ratios on the fin performance using rectangular plate type fins. The steady-state natural convection heat transfer from vertical rectangular fins extending perpendicularly from horizontal square aluminum base was investigated experimentally at high range of temperatures from 60 to 110°C. Four fin heights 30mm,40mm,50mm,60mm were employed under free convection heat transfer conditions. The heat transfer area was kept the same. The performance of the fin expressed in terms of fin efficiency, overall fin efficiency, fin effectiveness and thermal resistance as a function of fin height parameters has been study at fin height and width (H\w) ratios 0.2,0.35,0.55 and 0.8 respectively in this work. The dimensionless parameter Biot no. for different fin height-width (H\w) ratios to the fin heat transfer rate. Results show that's fin heat transfer performance increase with decreasing the fin heights and increasing the fin width for the range of temperatures used.

Three-dimensional natural convection in a porous enclosure filled with a nanofluid using Buongiorno’s mathematical model

Steady-state natural convection heat transfer in a three-dimensional porous enclosure filled with a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account two important slip mechanisms in nanofluids like Brownian diffusion and thermophoresis. The study is formulated in terms of the dimensionless vector potential functions, temperature and concentration of nanoparticles. The governing equations were solved by finite difference method on non-uniform mesh and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of six types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter and the aspect ratio on the fluid flow, heat and mass transfer. Three-dimensional velocity, temperature and nanoparticle volume fraction fields, average Nusselt numbers are presented. It is found that low Rayleigh and Lewis numbers and high thermophoresis parameter reflect essential non-homogeneous distribution of nanoparticles inside the cavity, hence a non-homogeneous model is more appropriate for the description of the system.

Natural Convection from Vertical Parallel Plates: An Integral Method Solution

Steady-state external natural convection heat transfer from isothermal, vertically mounted rectangular fins is modeled analytically. An integral technique is used to solve the governing equations. Compact relationships are developed for the velocity and temperature profiles for the buoyancy-driven channel flow for the range. Comprehensive numerical and experimental studies are performed. The proposed analytical model is successfully validated against the numerical data with the maximum relative differences of 9.8 and 3.5% for velocity and temperature profiles, respectively. Also, new semianalytical local and average Nusselt numbers are reported as functions of the Rayleigh number, temperature difference, and fin aspect ratio; and they are compared against the experimental data with good accuracy of 1.6% maximum relative difference.

Natural Convection From Interrupted Vertical Walls

Steady-state external natural convection heat transfer from interrupted rectangular vertical walls is investigated. A systematic numerical, experimental, and analytical study is conducted on the effect of adding interruptions to a vertical plate. Comsol multiphysics is used to develop a two-dimensional numerical model for investigation of fin interruption effects on natural convection. A custom-designed testbed is built and six interrupted wall samples are machined from aluminum. An effective length is introduced for calculating the natural convection heat transfer from interrupted vertical walls. Performing an asymptotic analysis and using a blending technique, a new compact relationship is proposed for the Nusselt number. Our results show that adding interruptions to a vertical wall can enhance heat transfer rate up to 16% and reduce the weight of the fins, which in turn, lead to lower manufacturing and material costs.

Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno’s mathematical model

Abstract Steady-state natural convection heat transfer in a square porous enclosure having solid walls of finite thickness and conductivity filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The study is formulated in terms of the vorticity-stream function procedure. The governing equations were solved by finite difference method and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of seven types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter, the thermal conductivity ratio, and solid walls thickness on the fluid flow and heat transfer. Streamlines, isotherms, isoconcentrations, local Nusselt and Sherwood numbers are presented. It has been found that the local Nusselt number at the solid-porous interface ( x = D ) is an increasing function of Ra , Nr and a decreasing function of Nt , Le and D . An effect of K r on Nu and Sh is non-monotonic. Ranges of key parameters for which a non-homogeneous model is more appropriate for the description of the system have been determined.

Natural convection from rectangular interrupted fins

Steady-state external natural convection heat transfer from vertically-mounted rectangular interrupted fins is investigated numerically and experimentally. FLUENT software is used to develop a 2-D numerical model for investigation of fin interruption effects. A custom-designed testbed was developed and 12 different aluminum alloy heatsinks with various geometric dimensions are machined and tested to verify the theoretical results. A comprehensive experimental–numerical parametric study is performed to investigate the effects of fin spacing, and fin interruption. Our results show that adding interruptions to vertically-mounted rectangular fins can enhance the thermal performance considerably and that an optimum fin interruption exists. A new compact correlation is proposed for calculating the optimum interruption length. The results of this work can be used to improve natural heat transfer from enclosures in a variety of electronics, power electronics and telecom applications.