Experimental and numerical study of the natural convection from a heated horizontal cylinder

Natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically. Experimental study had taken place in different environmental temperature in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The environmental and cylinder surface temperatures varied between 10 °C–40 °C and 20 °C–60 °C respectively. In the experimental study, two cylinders having different diameters of 4.8 mm–9.45 mm are used and constant heat flux was applied. On the basis of the experimental data, a correlation for the average Nusselt number over the cylinder is proposed in the range of 7.4 10¹ < Ra < 3.4 10³. The proposed correlation is compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is shown that the results are in satisfactory agreement. The problem is also investigated numerically. The experimental data and the numerical results fall in ± 20% band. The numerical results obtained in this study are also compared with the results of Merkin. The characteristics of trend lines are similar.     

Application of artificial neural networks for prediction of natural convection from a heated horizontal cylinder

A generalized neural network analysis for natural convection heat transfer from a horizontal cylinder is developed in this paper. Cylinder diameter, cylinder surface temperature and ambient temperature are selected as the input parameters, while the Nusselt number as the output. A three-layer network is used for predicting the Nusselt number. The number of the neurons in the hidden layer was determined by a trial and error process together with cross-validation of the experimental data evaluating the performance of the network and standard sensitivity analysis. The trained network gives the best values over the correlations with less than 2.5% mean relative error. The experimental data of the average Nusselt number over the horizontal cylinders having different diameters of 4.8 mm–9.45 mm are from Atay?lmaz and Teke [1]. The results from the trained network were compared with the proposed correlation for the average Nusselt number over the cylinder and it is shown that the results are in satisfactory agreement. The Nusselt numbers obtained from the experimental study were seen to be consistent by ± 20% with the well known correlations for natural convection heat transfer from horizontal cylinder developed by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4]. Moreover it is seen that that results from the trained network show absolute agreement with the experimental data in ± 5% deviation band better than the correlations given by Morgan [2], Fand and Brucker [3], and Churchill and Chu [4].     

Experimental and numerical studies of natural convection from horizontal concrete cylinder heated with a cylindrical heat source

Natural convection heat transfer from horizontal concrete cylinder heated with cylindrical heat source was investigated experimentally and numerically. Bare cylinder having a diameter of 9.45 mm was buried in a cylindrical concrete cylinder and thermocouples located outside the copper tube and inside and outside of the concrete cylinder in axial, radial and angular directions. Experiments are conducted at 20 °C and 30 °C ambient temperatures in a conditioned room. Copper cylinder surface temperatures varied between 30–50 °C and 40–50 °C for 20 °C and 30 °C ambient temperatures respectively. In a numerical study, the measured temperatures in the experimental study were used for boundary conditions. Experimental and numerical results were compared and heat transfer enhancement was seen for concrete cylinder. Also the effect of the decrease in the temperature of the copper tube surface was investigated on an ideal Carnot refrigerator. It is found that the enhancement in the coefficient of performance of a Carnot refrigerator is about 35%.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

Numerical solution of the phase change problem around a horizontal cylinder in the presence of natural convection in the melt region

This paper deals with the numerical study of melting of phase change material around a horizontal circular cylinder in the presence of the natural convection in the melt phase. A two dimensional unsteady mathematical model has been formulated in terms of primitive variables and a coordinate transformation technique has been used to fix the moving front. The finite volume approach was used to discretize the system of governing equations, boundary and initial conditions and obtain a system of linear algebraic equations. In the numerical solution an implicit scheme was used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and the numerical approach.     

Experimental study of natural convection heat transfer in a microencapsulated phase change material slurry

A new microencapsulated PCM (Phase Change Material) slurry (MEPCS) at high concentration (45% w/w) was developed based on microencapsulated Rubitherm RT6. Its heat storage and heat transfer characteristics have been experimentally investigated in order to assess its suitability for integration into a low temperature heat storage system for solar air conditioning applications. Differential scanning calorimetry tests have been conducted to evaluate the cold storage capacity and phase change temperature range. An experimental setup was built in order to quantify the natural convection heat transfer occurring from a vertical helically coiled tube immersed in the MEPCS. First, tests were carried out using water in order to obtain natural convection heat transfer correlations and then a comparison was made with the results obtained for the MEPCS. It was found that inside the phase change interval the values of the heat transfer coefficient for the MEPCS were significantly higher than for water, under identical temperature conditions.     

Mixed convection boundary layer flow past an isothermal horizontal circular cylinder with temperature-dependent viscosity

The problem of steady laminar mixed convection boundary layer flow past an isothermal horizontal circular cylinder placed in a viscous and incompressible fluid of temperature-dependent viscosity is theoretically considered in this paper. The partial differential equations governing the flow and heat transfer are shown to be non-similar. Full numerical solutions of these governing equations are obtained using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for various values of the Prandtl number Pr, the mixed convection parameter λ and the viscosity/temperature parameter θ_r. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.     

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     

An experimental and three-dimensional numerical study of natural convection heat transfer between two horizontal parallel plates

In this study, experimental and three-dimensional numerical studies were performed to investigate the effects of plate spacing and temperature difference on natural convection between isothermally heated upward-facing lower horizontal plate and externally insulated horizontal upper plate. Air is used as the heat transfer medium. Rayleigh number varied in the 1108–2.339 × 10⁵ range. Several numerical simulations for three-dimensional steady laminar and turbulent flows heat transfer were carried out using a commercial CFD code Fluent 6.2. Results have shown that there is a good agreement between the numerical and present experimental results as well as with available data in literature.     

Transient natural convection heat transfer of liquid D-mannitol on a horizontal cylinder

Transient and steady state natural convection heat transfer for D-mannitol on a horizontal cylinder was investigated experimentally at various liquid temperatures and heat input conditions. To clarify the natural convection phenomena of D-mannitol, transient and steady heat transfer coefficients were measured under various liquid temperatures of D-mannitol and periods of heat generation rates from a horizontal platinum cylinder. The platinum cylinder with a diameter of 1 mm and a length of 43.5 mm was used as the test heater in this experiment. Experimental results indicated that the steady heat transfer coefficient of D-mannitol was affected by the liquid temperature. As the liquid temperature increased, it was understood that the effect of liquid temperature weakened. When the period of the heat generation rate was changed, the heat transfer process was divided into natural convection heat transfer and conductive heat transfer. It was considered that the conductive heat transfer was more dominant as the period of the heat generation rate decreased. The empirical correlations of steady and transient heat transfer coefficients for D-mannitol were obtained.     

Laminar boundary-layer analysis of simultaneous mass and heat transfer in natural convection around A horizontal cylinder

An analytical study is presented of the combined heat and mass transfer characteristics of natural convection flow around a horizontal circular cylinder. The surface of the cylinder is assumed to be at uniform temperature and uniform concentration. Specific cases of diffusion of water vapour and naphthalene into air are studied. The results indicate that the local Nusselt number and the local wall shear stress increase and decrease from the pure free convection values as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The local Nusselt number and the local wall shear stress are found to increase with the decrease of the Schmidt number, whereas the surface mass transfer increases with increasing Schmidt number. The Sherwood number is found to become more effective as the thermal buoyancy force increases. The cumulative tangential mass flow rate is found to increase with the increase of the polar angle from the lower pole and is strongly dependent on the nature and magnitude of the concentration to thermal buoyancy force ratio, especially at low Schmidt number.     

Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below

Natural convection in air-filled 2D square enclosure heated with a constant source from below and cooled from above is studied numerically for a variety of thermal boundary conditions at the top and sidewalls. Simulations are performed for two kinds of lengths of the heated source, i.e., a small and a large source corresponding to 20% and 80% of the total length of the bottom wall, respectively. The Rayleigh number varied from 10³ to 10⁷. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface. Comparisons among the different thermal configurations considered are reported.     

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 convection from narrow horizontal plates at moderate Rayleigh numbers

The present work deals with the natural convection flow and heat transfer from a horizontal plate cooled from above. Experiments are carried out for rectangular plates having aspect ratios between φ=0.036 and 0.43 and Rayleigh numbers in the range 290?Ra_w?3.3×10⁵. These values of Ra_w and φ have been selected below those commonly considered in previous research in view of a future application to the design of printed circuit boards. The plates are made of two different metals, copper and steel. The choice of a metal is relevant to the present problem because the plates are heated by means of an electric current. Important variations of the surface temperature are observed along the transverse direction for the steel plates. The surface of the copper plates is almost isothermal because of the high thermal conductivity of the metal.Calculations for a semi-infinite plate are carried out to predict the transverse profiles of the surface temperature and heat flux and to visualize the structure of the flow. Three-dimensional calculations are also used at a qualitative level to observe the changes in the flow structure due to the finite length of the plate. Present results are compared with both previous experimental work and analyses that are based on boundary layer theory. It is shown that analyses for an infinite boundary layer are not completely applicable to the present problem because of its different physics. The most relevant feature of the natural convection flow, which is not predicted by boundary layer analyses, is a thermal plume rising near the center of the plate.Present heat transfer results differ from previous experimental work because of the lower Rayleigh numbers and aspect ratios investigated here. The Nusselt number is found to depend on Ra_wⁿ, with the exponent n=0.17 being lower than most of the values reported in the literature. This comparatively low value is related to the transverse conduction of heat through the air, which becomes increasingly significant as Ra_w approaches zero. It is shown that such a low-Ra_w effect can be accounted for in a physically consistent manner by adding a constant term to the heat transfer correlation. On the other hand, it is found that the Nusselt number does not significantly depend on the aspect ratio in the range of φ investigated contrary to what has been previously reported for wider plates.     

Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

A numerical method for natural convection and heat conduction around and in a horizontal circular pipe

Natural convection around a horizontal circular pipe coupled with heat conduction in the solid structure is numerically investigated using a preconditioning method for solving incompressible and compressible Navier–Stokes equations. In this method, fundamental equations are completely reduced to an equation of heat conduction when the flow field is static (zero velocity). Therefore, not only compressible flows but also very slow flows such as natural convection in a flow field and heat conduction in a static field can be simultaneously calculated using the same computational algorithm. In this study, we first calculated the compressible flow around a NACA0012 airfoil with conduction in the airfoil and then simulated natural convections around a horizontal circular pipe with a different heat conductivity. Finally, we numerically investigated the effect of heat conductivity of the pipe on natural convection.     

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

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The onset of natural convection in a horizontal nanofluid layer heated from below

A linear stability analysis is performed for the onset of natural convection in a horizontal nanofluid layer heated from below. The motion of nanoparticles is characterized by both the thermophoresis and Brownian diffusion effects. Different from previous studies in the literature, both the dependences of thermophoresis on nanoparticle volume fraction and Brownian motion on temperature are taken into consideration in the theoretical model. The result reveals that the base flow is mainly dominated by the effect of thermophoresis and the Brownian diffusion coefficient can be treated as a constant reasonably when a finite temperature difference is imposed across the nanofluid layer. Accordingly, a novel base solution of nanoparticle volume fraction is derived. It is found that the profile of nanoparticle concentration depends heavily on the magnitude of thermophoretic diffusion, which may exhibit a nonlinear distribution across the nanofluid layer once the effect of thermophoresis is significant. The suspended nanoparticles produce a strong destabilizing effect and a tiny volume fraction of nanoparticles is sufficient to trigger the onset of convection and make the nanofluid layer become unconditionally unstable. The dispersion spectra of unstable modes are demonstrated and the most unstable mode with the maximum growth rate is explored. The growth rate of the most unstable mode is found to increase significantly with increasing nanoparticle concentration, while the influence of heat capacity ratio of nanoparticle to base fluid on the behavior of thermal convection is negligible.     

Numerical analysis of natural convection heat transfer from rectangular shrouded fin arrays on a horizontal surface

The main aim of this investigation is to discover the effects of clearance parameters on the steady-state heat transfer. In order to solve the three-dimensional elliptic governing equations, a finite volume based CFD code was used. The clearance gap between fin tips and shroud, the base and fin temperatures and the size and configuration of the finned surfaces were varied during the parametric study. The numerical results have been compared to existing experimental values from the literature and the comparison shows a good agreement. It is found that the heat transfer coefficient increases with the increase in the clearance parameter and it approaches to the value of heat transfer coefficient obtained for unshrouded fin arrays.