Correlations for Natural Convective Heat Transfer from Isothermal Surface of Octagonal and Hexagonal Shapes of Different Aspect Ratios

The effect of surface shape on laminar natural convective heat transfer from vertical isothermal hexagonal and octagonal flat plates embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the surface of the heated plate, has been numerically investigated. Results for the hexagonal and octagonal surface shapes with different aspect ratios have been obtained. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated using the Boussinesq approach. The solution has been obtained by numerically solving the full three‐dimensional form of governing equations, these equations being written in dimensionless form. The solution was obtained using the commercial finite volume method based cfd code, FLUENT^©14.5. The solution has the surface shape, the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have only been obtained for a Prandtl number of 0.7 for Rayleigh numbers between 10³ and 10⁸ for various surface shapes with width‐to‐height ratios between 0 and 0.6. The effect of these parameters on the mean Nusselt number has been studied and empirical correlation equations for the mean heat transfer rate have been derived.     

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.     

Natural convective flow in an inclined lid-driven enclosure with a heated thin plate in the middle

Natural convection heat transfer from a heated thin plate located in the middle of a lid-driven inclined square enclosure has been analyzed numerically. Left and right of the cavity are adiabatic, the two horizontal walls have constant temperature lower than the plate’s temperature. The study is formulated in terms of the vorticity-stream function procedure and numerical solution was performed using a fully higher-order compact (FHOC) finite difference scheme on the 9-point 2D stencil. Air was chosen as a working fluid (Pr = 0.71). Two cases are considered depending on the position of heated thin plate (Case I, horizontal position; Case II, vertical position). Governing parameters, which are effective on flow field and temperature distribution, are Rayleigh number values (Ra) ranging from 10³ to 10⁵ and inclination angles γ (0° ? γ < 360°). The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and Nusselt number (Nu). It is found that fluid flow and temperature fields strongly depend on Rayleigh numbers and inclination angles. Further, for the vertical located position of thin plate heat transfer becomes more enhanced with lower γ at various Rayleigh numbers.     

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio

The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10³ to 3.1 × 10⁴ by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.     

A numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder

Laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. It is assumed that the two sealed ends of the tube to be adiabatic. Governing equations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. Results are presented for the flow and temperature distributions and Nusselt numbers on different cross sectional planes and longitudinal sections for Rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium. Considering that the driven flow in the annular tube is strongly influenced by orientation of tube, study has been carried out for different inclination angles.     

Laminar natural convection in inclined open shallow cavities

Laminar steady state natural convection in inclined shallow cavities has been numerically studied. The side facing the opening is heated by a constant heat flux, sides perpendicular to the heated side are insulated and the opening is in contact with a fluid at constant temperature and pressure. Equations of mass, momentum and energy are solved using constant properties and Boussinesq approximation and assuming an approximate boundary conditions at the opening. Isotherms and streamlines are produced, heat and mass transfer is calculated for Rayleigh numbers from 10³ to 10¹⁰, cavity aspect ratio A=H/L from 1 to 0.125. The results show that flow and heat transfer are governed by Rayleigh number, aspect ratio and the inclination. Heat transfer approaches asymptotic values at Rayleigh numbers independent of the aspect ratio. The asymptotic values are close to that for a flat plate with constant heat flux. The effect of elongation of open cavities is to delay this asymptotic behavior. It is also found that the inclination angle of the heated plate is an important parameter affecting volumetric flow rate and the heat transfer.     

Effects of corrugation frequency and aspect ratio on natural convection within an enclosure having sinusoidal corrugation over a heated top surface

Natural convection of a two-dimensional laminar steady-state incompressible fluid flow in a modified rectangular enclosure with sinusoidal corrugated top surface has been investigated numerically. The present study has been carried out for different corrugation frequencies on the top surface as well as aspect ratios of the enclosure in order to observe the change in hydrodynamic and thermal behavior with constant corrugation amplitude. A constant flux heat source is flush mounted on the top sinusoidal wall, modeling a wavy sheet shaded room exposed to sunlight. The flat bottom surface is considered as adiabatic, while the both vertical side walls are maintained at the constant ambient temperature. The fluid considered inside the enclosure is air having Prandtl number of 0.71. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results in terms of isotherms, streamlines and average Nusselt numbers are obtained for the Rayleigh number ranging from 10³ to 10⁶ with constant physical properties for the fluid medium considered. It is found that the convective phenomena are greatly influenced by the presence of the corrugation and variation of aspect ratios.     

Multi-Prandtl correlating equations for free convection heat transfer from a horizontal tube of elliptic cross-section

Steady laminar free convection from a horizontal elliptic cylinder set in unbounded space is studied numerically under the assumption of uniform surface temperature. A specifically developed computer-code based on the SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for ratios between the minor and major axes of the elliptic cross-section of the cylinder in the range between 0.05 and 0.98, inclination angles of the major axis of the elliptic cross-section with respect to gravity in the range between 0° and 90°, Rayleigh numbers based on the major axis of the elliptic cross-section in the range between 10 and 10⁷, and Prandtl numbers in the range between 0.7 and 700. It is found that the heat transfer rate increases with increasing the Rayleigh and Prandtl numbers, while decreases with increasing the orientation angle of the cross-section of the cylinder, i.e., passing from the slender to the blunt configuration. In addition, a noteworthy fact is that in most cases the amount of heat exchanged at the cylinder surface has a peak at an optimum axis ratio which is practically independent of the Prandtl number, while may either increase or decrease with increasing the Rayleigh number depending on whether the orientation angle of the tube is above or below a critical value of approximately 67.5°. Dimensionless correlating equations are proposed both for the optimum axis ratio for maximum heat transfer and for the heat transfer rate from the cylinder surface to the undisturbed surrounding fluid reservoir.     

Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

NATURAL CONVECTION IN OPEN CAVITIES AND SLOTS

The present work is concerned with natural convection from open cavities or heated plates attached with parallel vertical strips. The bottom of the cavity is heated, and the vertical walls are assumed adiabatic. Numerical results are presented for steady, laminar natural convection for the geometry described. Effects of Rayleigh numbers from 1 × 10 ³ to 1 × 10 ⁷ , inclination angles from 10^° to 90^°, and aspect ratios of 0.5, 1.0, and 2.0 are investigated for a fixed Prandtl number (0.7). It is found that the average Nusselt number is not very sensitive to the inclination angle. Flow becomes unstable at high Rayleigh numbers and at low inclination angles. Flow pattern and heat transfer results are presented and discussed.     

Fluid flow and heat transfer of natural convection adjacent to upward‐facing inclined heated plates

Turbulent transition mechanism and local heat transfer characteristics of the natural convective flows over upward‐facing inclined plates were investigated experimentally. The experiments were performed in the range of modified local Rayleigh numbers from 10⁴ to 8 × 10¹⁴ and of inclination angles θ from 0 to 90°. The flow fields over the plate and the surface temperatures of the plate were visualized with dye and liquid crystal thermometry. The results showed that longitudinal vortices play a main role in the turbulent transition over the plate of θ < 72°. These vortices appear first in the laminar boundary layer, then detach from the plate and, finally become distorted. It is found that the heat transfer is enhanced markedly by the detachment and the distortion of these vortices. The local heat transfer coefficients were measured in the laminar, transitional, and turbulent regions. The results show that the coefficients in the turbulent region become identical and independent of inclination angles. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 278–291, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10091     

Numerical analysis of Grashof number,Reynolds number and inclination effects on mixed convection heat transfer in rectangular channels

Mixed convection heat transfer in rectangular channels has been investigated computationally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Solutions were obtained for Pr=0.7, inclination angles 0° ≤ θ ≤ 90°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr = 7.0×10⁵ to 4.0×10⁶. The three-dimensional elliptic governing equations were solved using a finite volume based computational fluid dynamics (CFD) code. From a parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results obtained from the simulations are compared with the literature and a parallel conducted experimental study, from which a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle.     

A numerical study of laminar natural convective heat transfer around a horizontal cylinder inside a concentric air-filled triangular enclosure

A numerical investigation of steady-state laminar natural convective heat transfer around a horizontal cylinder to its concentric triangular enclosure was carried out. The enclosure was filled with air and both the inner and outer cylinders were maintained at uniform temperatures. The buoyancy effect was modeled by applying the Boussinesq approximation of density to the momentum equation and the governing equations were iteratively solved using the control volume approach. The effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the maximum value of the dimensionless stream function and the local and average Nusselt numbers were also presented. The average Nusselt number was correlated to the Rayleigh number based on curve-fitting for each aspect ratio. At the highest Rayleigh number studied, the effects of different inclination angles of the enclosure and various cross-section geometries of the inner cylinder were investigated. The computed results indicated that at constant aspect ratio, both the inclination angle and cross-section geometry have insignificant effects on the overall heat transfer rates though the flow patterns are significantly modified.     

A heatline analysis of natural convection in a square inclined enclosure filled with a CuO nanofluid under non-uniform wall heating condition

Heatline visualization technique is used to understand heat transport path in an inclined non-uniformly heated enclosure filled with water based CuO nanofluid. The cavity has square cross-section and it is non-uniformly heated from a wall and cooled from opposite wall while other walls are adiabatic. The governing equations which are continuity, momentum and energy equations are solved using finite volume method. The dimensionless heatfunction for nanofluid heat flow is defined and solved to determine heatline patterns. Calculations were performed for Rayleigh numbers of 10³, 10⁴ and 10⁵, inclination angle of 0°, 30°, 60° and 90°, and nanoparticle fraction of 0, 0.02, 0.04, 0.06, 0.08 and 0.1. It is observed that heat transfer in the cavity increases by adding nanoparticles. The rate of increase is greater for the enclosures with low Rayleigh number. Visualization of heatline is successfully applied to nanoparticle convective flows. Based on the heatline patterns, three heat transfer regions are observed and discussed in details.     

Heat transfer on a horizontal rotating cylinder near a flat plate in a cross‐flow

An experimental study of heat transfer on a horizontal rotating cylinder near a flat plate was performed. The cylinder and plate were set in a cross‐flow. Temperature distribution and coefficients of local heat transfer were measured by a Mach–Zehnder interferometer. Flow visualization was made using smoke. Rotating Reynolds numbers (Re_r) and cross‐flow Reynolds numbers (Re_d) were varied from 0 to 2000. The spaces between cylinder and plate were varied from 1 × 10^?3 m to 5 × 10^?3 m. The rotating direction of cylinder was changed clockwise or counterclockwise. The following results are obtained: When the space between the rotating cylinder and flat plate is the same as the displacement thickness on the plate, the heat transfer on the cylinder near the plate has the best performance. We have procured the empirical equation of heat transfer from a rotating cylinder near the flat plate in the cross‐flow. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20329     

Quantification of natural convective heat transfer within air-filled hemispherical cavities. Isothermal tilted disk with dome oriented upwards and wide Ra range

This work quantifies the natural convective heat transfer occurring in hemispherical air-filled cavities whose disk is inclined at an angle varying between 0° and 90°. This active hot disk as well as the dome are maintained isothermal at different temperatures. The numerical approach by means of the control volume method allows the examination of the dynamical phenomena that occurs in many configurations obtained by varying the temperature difference between the two active walls and the radius of the hemisphere. Convective heat transfer at the hot wall is represented by the average Nusselt number associated to Rayleigh numbers varying between 10⁴ and 2.55 × 10¹². By taking into account all the studied configurations, correlations between these two dimensionless numbers are established for the set of considered inclination angles. Comparisons with results from other studies for the case of horizontal cavity show a good agreement. The relationships presented here cover the laminar, transitional and turbulent heat transfer regimes. They complement previous studies with the condition of heat flux imposed on the disk. The wide range of Rayleigh numbers considered in this survey and its association with the large inclination angle range allow the application of the correlations to various engineering fields such as nuclear technology, solar energy, building, embarked electronics, architecture, safety or domotics.     

Experimental and Numerical Investigation on Free Convection From a Horizontal Cylinder Located Above an Adiabatic Surface

Steady two-dimensional free convection heat transfer from an isothermal horizontal cylinder located above an adiabatic horizontal surface is studied experimentally and numerically. Experiments are carried out using a Mach–Zehnder interferometer for the ratios of cylinder spacing from the adiabatic surface to its diameter L/D = 0, 0.1, 0.2, 0.3, 0.5, 0.7, and 0.9 and the Rayleigh number range of 500 to 15,000. Also, a specifically developed computer code based on the finite-volume method, the SIMPLE algorithm, and nonorthogonal discretization grid system is used for the solution of the mass-, momentum-, and energy-governing equations for the Rayleigh numbers ranging from 100 to 100,000 and L/D ranging from 0.1 to 1.7. The effects of the Rayleigh number and spacing from the adiabatic surface on both local and average Nusselt numbers around the cylinder are investigated. A correlation based on the numerical data for the average Nusselt number of the cylinder as a function of Rayleigh number and L/D is presented in the aforementioned ranges.     

A Numerical Study on Natural Convention Heat Transfer From a Horizontal Isothermal Cylinder Located Underneath an Adiabatic Ceiling

A numerical analysis is performed for steady-state and two-dimensional natural convection heat transfer from a horizontal isothermal cylinder located underneath a horizontal adiabatic ceiling. The finite-volume method based on the SIMPLE algorithm and a nonorthogonal grid discretization scheme are used to solve the continuity, momentum, and energy equations for the Rayleigh numbers in the range from 10^?1 to 10⁴. The Poisson equations are solved to find the grid points, which are distributed in a nonuniform manner with higher concentration close to the solid regions. In addition, the HYBRID differencing scheme is used for the approximation of the convective terms in the curvilinear coordinate. The effects of the Rayleigh numbers and cylinder spacing from the adiabatic ceiling on both the local and average Nusselt numbers around the cylinder are investigated. Numerical results are performed for the plate-to-cylinder spacing ranging from 0.1 to 1.4.     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Effects of duct inclination angle on thermal entrance region of laminar and transition mixed convection

Experimental investigation was performed on the mixed convection heat transfer of thermal entrance region in an inclined rectangular duct for laminar and transition flow. Air flowed upwardly and downwardly with inclination angles from ?90° to 90°. The duct was made of duralumin plate and heated with uniform heat flux axially. The experiment was designed for determining the effects of inclination angles on the heat transfer coefficients and friction factors at seven orientations (θ = ? 90°, ?60°, ?30°, 0°, 30°, 60° and 90°), six Reynolds numbers (Re ≈ 420, 840, 1290, 1720, 2190 and 2630) within the range of Grashof numbers from 6.8 × 10³ to 4.1 × 10⁴. The optimum inclination angles that yielded the maximum heat transfer coefficients decreased from 30° to ?30° with the increase of Reynolds numbers from 420 to 1720. The heat transfer coefficients first increased with inclination angles up to a maximum value and then decreased. With further increase in Reynolds numbers, the heat transfer coefficients were nearly independent of inclination angles. The friction factors decreased with the increase of inclination angles from ?90° to 90° when Reynolds numbers ranged from 420 to 1290, and independent of inclination angles with higher Reynolds numbers.