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.     

Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter

This paper presents the results of a study of conjugate turbulent natural convection inside a building attic in the shape of a rectangular enclosure bounded by realistic walls made from composite construction materials under winter day boundary conditions. The effects of cavity aspect ratio, Rayleigh number (Ra), depth of the external concrete beam, and external wall construction materials on the flow and heat transfer characteristics were the main focus of the investigation. The Shear stress transport k–ω turbulence model is implemented to calculate air-flow velocities and temperatures in a steady, turbulent, two-dimensional conjugate natural convection heat transfer inside an attic. The governing equations were solved by employing the line-by-line tri-diagonal matrix algorithm (TDMA) control volume method. For Ra ranging from 10⁷ to 10¹⁰, steady-state results of the streamline and temperature contours in addition to local and mean Nusselt numbers at all surfaces of the cavity were obtained. The results show that the values of Ra, attic aspect ratio and the composite wall materials have significant effect on the temperature and stream function contours within the enclosure, and the heat flux out of the room through the enclosure.     

Experimental and numerical analysis of buoyancy-induced flow in inclined triangular enclosures

The buoyancy‐induced heat transfer and fluid flow in a triangular enclosure are investigated both numerically and experimentally. The enclosure is heated from one wall and the adjacent wall is insulated. Hypotenuse of the triangle is cooled isothermally. The numerical tests and experiments covered a range of Rayleigh number, Ra, from 1.5 × 10⁴ to 1.5 × 10⁵. The local and average Nusselt numbers are given for different orientation angles. A code was written based on finite difference method in Fortran platform to solve governing equations of natural convection. Experimental and numerical results show good agreement. It is observed that inclination angle can be used as a control parameter for heat transfer.     

Numerical investigation of natural convection in an inclined enclosure filled with porous medium under magnetic field

In the present study, natural convection of fluid in an inclined enclosure filled with porous medium is numerically investigated in a strong magnetic field. The physical model is heated from left-hand side vertical wall and cooled from opposing wall. Above this enclosure an electric coil is set to generate a magnetic field. The Brinkman–Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for fluid and solid are solved with the local thermal non-equilibrium (LTNE) models. Computations are performed for a range of the Darcy number from 10⁻⁵ to 10⁻¹, the inclination angle from 0 to π/2, and magnetic force parameter γ from 0 to 100. The results show that both the magnetic force and the inclination angle have significant effect on the flow field and heat transfer in porous medium.     

Effects of inclination angle on conduction—natural convection in divided enclosures filled with different fluids

Laminar natural convection in inclined enclosures filled with different fluids was studied by a numerical method. The enclosure was divided by a solid impermeable divider. One side of partition of enclosure was filled with air and the other side had water. The enclosure was heated from one vertical wall and cooled from the other while horizontal walls were adiabatic. The governing equations which were written in stream function–vorticity form were solved using a finite difference technique. Results were presented by streamlines, isotherms, mean and local Nusselt numbers for different thermal conductivity ratios of solid impermeable material (plywood or concrete), inclination angle (0° ≤ ? ≤ 360°) and Grashof numbers (10³ ≤ Gr ≤ 10⁶). The code was validated by earlier studies, which are available in the literature on conjugate natural convection heat transfer. Analytical solutions were obtained for low Grashof numbers. Obtained results showed that both heat transfer and flow strength strongly depended on thermal conductivity ratio of the solid material of partition, inclination angle and Grashof numbers. The heat transfer was lower in the air side of the enclosure than that of the water side.     

Experimental study of natural convection heat transfer in a semicircular enclosure

An experimental study of natural convection heat transfer in a differentially heated semicircular enclosure was carried out. The flat surface was heated and the radial surface was cooled isothermally. The effects of angle of enclosure inclination on the heat transfer across semicircular regions of several radii were measured for Rayleigh numbers Ra_R ranging from 6.72 × 10⁶ to 2.33 × 10⁸, using water as the working fluid. The angle of inclination varied from −90 degrees to 90 degrees with radii R of 50, 40, and 30 mm. The flow patterns were sketched from the results of a visualization experiment using aluminum powder. The temperature measurements in the enclosure were carried out using liquid crystals and thermocouples. The results indicate that different flow patterns were encountered as the angle of inclination varied, and the heat transfer rate was largely dependent on the flow pattern. In particular, enhanced heat transfer rates can be obtained when plume-like flow occurs along both hot and cold walls in the case of an upward-facing hot wall. Heat transfer for the inclined enclosure can be predicted using the equation for a vertical enclosure presented in this paper. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 131–142, 1997     

Numerical Analysis of the Effects of Selected Geometrical Parameters and Fluid Properties on MHD Natural Convection Flow in an Inclined Elliptic Porous Enclosure with Localized Heating

Magnetohydrodynamic (MHD) natural convection flow and associated heat convection in an oriented elliptic enclosure has been investigated with numerical simulations. A magnetic field was applied to the cylindrical wall of the configuration, the top and bottom walls of the enclosure were circumferentially cooled and heated, respectively, while the extreme ends along the cross‐section of the elliptic duct were considered adiabatic. The full governing equations in terms of continuity, momentum, and energy transport were transformed into nondimensional form and solved numerically using finite difference method adopting Gauss–Seidel iteration technique. The selected geometrical parameters and flow properties considered for the study were eccentricity (0, 0.2, 0.4, 0.6, and 0.8), angle of inclination (0°, 30°, 60°, and 90°), Hartmann number (0, 25, and 50), Grashof number (10⁴, 10⁵, and 10⁶), and Darcy number (10^?3, 10^?4, and 10^?5). The Prandtl number was held constant at 0.7. Numerical results were presented by velocity distributions as well as heat transfer characteristics in terms of local and average Nusselt numbers (i.e., rate of heat transfer). The optimum heat transfer rate was attained at e value of 0.8. Also, the heat transfer rate increased significantly between the angles of inclination 58° and 90°. In addition, Hartmann number increased with decreased heat transfer rate and flow circulation. A strong flow circulation (in terms of velocity distribution) was observed with increased Grashof and Darcy numbers. The combination of the geometric and fluid properties therefore can be used to regulate the circulation and heat transfer characteristics of the flow in the enclosure.     

Three-dimensional numerical analysis of the natural convection and entropy generation of MWCNTs-H2O and air as two immiscible fluids in a rectangular cuboid with fillet corners

A numerical investigation has been carried out to study the natural convection and entropy generation within the three-dimensional enclosure with fillets. There are two immiscible fluids of Multi-Walled Carbon Nano-Tubes (MWCNTs)-water and air in the enclosure, which is simulated as two discrete phases. There are two heaters with constant heat flux at the sides, and the top and bottom walls are kept at cold constant temperature. The finite volume approach is applied to solve the governing equations. Moreover, a numerical method is developed based on the three-dimensional solution of Navier–Stokes equations. The fluid flow, heat transfer, and total volumetric entropy generation due to natural convection are studied carefully in a three-dimensional enclosure. The effects of the corner radius of fillets (r?=?0, 0.15, 0.2, and 0.25), Rayleigh number (10³?Ra?6), and solid volume fraction (φ?=?0.002 and 0.01) of the nanofluid have been investigated on both natural convection characteristic and volumetric entropy generation.* The results show that the curved corner can be an effective method to control fluid flow and energy consumption, and three dimensional solutions render more accurate results.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom

Laminar mixed convective heat transfer in two-dimensional shallow rectangular driven cavities of aspect ratio 10 is studied numerically. The top moving lid of the cavity is at a higher temperature than the bottom wall. Computations are performed for Rayleigh numbers ranging from 10⁵ to 10⁷ keeping the Reynolds number fixed at 408.21, thus encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. The fluid Prandtl number is taken as 6 representing water. The effects of inclination of the cavity on the flow and thermal fields are investigated for inclination angles ranging from 0° to 30°. Interesting behaviours of the flow and thermal fields with increasing inclination are observed. The streamline and isotherm plots and the variation of the local and average Nusselt numbers at the hot and cold walls are presented. The average Nusselt number is found to increase with cavity inclination. The rate of increase of the average Nusselt number with cavity inclination is mild for dominating forced convection case while it is much steeper in dominating natural convection case.     

Influences of a confined elliptic cylinder at different aspect ratios and inclinations on the laminar natural and mixed convection flows

Numerical investigations were carried out for natural and mixed convection within domains with stationary and rotating complex geometry by using an immersed-boundary method. The method was first validated with flows induced by natural convection in the annulus between concentric circular cylinder and square enclosure, and the grid-function convergence tests were also examined. Natural convection induced by isothermally elliptic cylinder was further investigated for different Rayleigh numbers within the range of 10⁴–10⁶ and the influence of the outer enclosure was also considered. The parameters investigated in the study included Rayleigh number, axis ratio and inclination angle of the elliptic cross-section. Local and average heat transfer characteristics were fully studied around the surfaces of both inner cylinder and outer enclosure. Finally, mixed convection in a square enclosure with an active rotating elliptic cylinder was considered and the heat transfer quantities of the system were obtained for different rotating speeds.     

Modeling of Unsteady Natural Convection for Double-Pipe in a Partially Cooled Enclosure

In this article, a model is developed for unsteady natural convection heat transfer and fluid flow in a partially cooled enclosure with a hollow cylinder through it. The right vertical wall of the enclosure is cooled partially. The location of the partial cooling is set up in three different configurations; namely, bottom (P ₁), middle (P ₂), and top (P ₃). A hollow cylinder is located at the middle of the enclosure to simulate a double-pipe heat exchanger. Three values of Grashof number are applied in this work, i.e., 10⁴, 10⁵ and 10⁶, and three lengths of the cooler, i.e., 0.2, 0.4 and 0.6. Finite element method was utilized to solve the unsteady dimensionless conservation equations of mass, momentum and energy. It is found that the length and location of cooler does not have a significant effect on the natural convection for the case of the low Grashof number. The maximum heat transfer rate is reached when the cooler is located at the middle of the vertical wall.     

Numerical analysis of natural convection in a rectangular enclosure horizontally divided into fluid and porous regions

This paper describes an analytical study of laminar natural convection heat transfer in a rectangular enclosure horizontally divided into fluid and porous regions. The Navier-Stokes equation governs the fluid motion in the fluid region, while Brinkman's extension of Darcy's law is assumed to hold within the porous region. These equations are solved using a finite-element method in the range 10³ ⩽ Ra_f ⩽ 10⁵ and 10⁻³ ⩽ Da ⩽ 10⁵. The experiment is also performed using a rectangular enclosure filled with silicone oil and glass beads. It is shown that the flow pattern, temperature distribution and Nusselt number obtained from the numerical calculation satisfactorily predict the experimental data.     

Laminar natural convection in a vertical stack of parallelogrammic partial enclosures with variable geometry

A numerical study is conducted for laminar natural convection heat transfer occurring in a vertical stack of parallelogrammic partial enclosures. The partitions separating adjacent enclosures are always parallel to each other, however their angle relative to the horizontal can change. The length of each partition is less than the width of the main enclosure, which has an aspect ratio of 5. Adjacent enclosures are thermally linked through the fluid exchange, and through the finite thermal conductivity of the partitions. The thermal diode effect offered by the geometry is analyzed in terms of the partitions’ inclination angle and materials for different thermal boundary conditions/operating conditions. The thermal diode effect, and even its actuating direction, can be changed by changing the inclination angle of the partitions. The main focus of the present work deals with the heat transfer analysis based on the overall Nusselt number, and the visualization of the flow field and heat transfer mechanisms, by using the isotherms, the streamlines and the heatlines. Results clearly indicate the high potential of this configuration, based on the thermal diode effect, to be used as an effective heat transfer device in real situations of thermal engineering. The number of governing parameters is high, and the results are presented only for situations selected on the basis of their relevance. For computational expediency, it is analyzed the solution obtained for one single parallelogrammic partial enclosure of the stack, which is thermally linked with its adjacent enclosures by using vertical cyclic boundary conditions. This procedure has some potential, since it yields results with good accuracy to predict the overall thermal behavior of the stack.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

Natural convection heat transfer by heated partitions within enclosure

In this study, natural convection heat transfer and fluid flow of two heated partitions. within an enclosure have been analysed numerically. The right side wall and the bottom wall of the enclosure were insulated perfectly while the left side wall and top wall were maintained at the same uniform temperature. The partitions were placed on the bottom of the enclosure and their temperatures were kept higher than the non-isolated walls. The effects of position and heights of the partitions on heat transfer and flow field have been investigated. Computations for Rayleigh number in the range of 10⁴ and 10⁶ have been conducted. Using the control volume approach, finite difference equations are obtained with non-staggered grid arrangement, a computer program based on the SIMPLEM algorithm was developed. The finite difference equations were solved iteratively with a line-by-line Thomas algorithm.     

Natural convection and radiation heat transfer in a vertical porous layer with a hexagonal honeycomb core (Part 1: numerical analysis)

Combined heat transfer characteristics were obtained numerically for three-dimensional natural convection and thermal radiation in a long and wide vertical porous layer with a hexagonal honeycomb core. We assumed that the porous layer was both homogeneous and isotropic. The pure Darcy law for fluid flow and Rosseland's approximation for radiation were used. The numerical methodology was based on an algebraic coordinate transformation technique and the transformed governing equations were solved using the SIMPLE algorithm. The effect of radiation on the heat transfer characteristics was investigated over a wide range of radiation numbers and temperature ratios for two Darcy-Rayleigh number values (Ra^* = 100 and 1000) and for a fixed aspect ratio of H/L = 1. The results are presented in the form of combined radiation and convection heat transfer coefficients and are compared with the corresponding values for pure natural convection. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 278–294, 1999     

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

The influence of the external Rayleigh number, inclination angle, and internal Rayleigh number on natural convection within an air‐filled parallelogrammic enclosure containing a volumetric source has been investigated numerically. The left sidewall of the enclosure is subjected to a non‐uniformly hot temperature and the right sidewall experiences a uniform cold temperature while the remaining top and bottom walls are kept adiabatic. The physical problems are represented mathematically by various sets of governing equations along with the corresponding boundary conditions. Buoyancy forces are taken into account during the analysis of the present investigation. By using the finite volume method, the dimensionless governing equations are discretized numerically based on a non‐uniform collocated grid system. Results are obtained for a wide range of external Rayleigh numbers varying from 10³ to 10⁶ with internal Rayleigh numbers varying from (0) to (10⁸) while the left sidewall from vertical is varied as 0, 30, –30, 60, and ?60^°, respectively. In the present study, the obtained results are presented in terms of streamlines, isotherms, and average Nusselt number along the hot and cold sidewalls. Two pairs of rotating vortices are observed due to the non‐uniform heating process while the shape of this rotating vortices is sensitive to the inclination angle. Furthermore, the flow field circulation and the average Nusselt number increase remarkably with the increase in the external Rayleigh number. The results of the present work are compared with other published results and give excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 542–560, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21096     

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…     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.