Numerical predictions of natural convection with liquid fluids contained in an inclined arc-shaped enclosure

In the present paper a numerical study has been performed of the flow behavior and natural convection heat transfer characteristics of liquid fluids contained in an inclined arc-shaped enclosure. The governing equations are discretized using the finite-volume method and curvilinear coordinates. The Prandtl number (Pr) of the liquid fluids is assigned to be 4.0 and the Grashof number (Gr) is ranged within the regime 1 × 10⁵ ≦ ≦ 4 × 10⁶. On the other hand, the inclination angle (θ) of the enclosure is varied within 0° ≦ θ ≦ 360°. Of major concern are the effects of the inclination and the buoyancy force on the flow and the thermal fields, and based on the numerical data of the thermal field the local and overall Nusselt numbers are calculated. Results show that the arc-shaped enclosure for Pr = 4.0 at Gr = 4 × 10⁶ and θ = 90° exhibits the best heat transfer performance. The poor heat transfer performance for Pr = 4.0 fixed at Gr = 1 × 10⁵ and θ = 180° exhibits the arc-shaped enclosure, respectively. As the value of Grashof number is elevated from 10⁵ to 4 × 10⁶, at θ = 90°, the magnitude of Nu is elevated from 13.946 to 25.3 (81.4% increase); however, at θ = 180°, the magnitude is elevated from 11.655 to 13.475 (15.6% increase) only.     

Magnetohydrodynamic natural convection in trapezoidal cavities

A computational numerical work has been done to see the effects of magnetic field on natural convection for a trapezoidal enclosure. Both inclined walls and bottom wall have constant temperature where the bottom wall temperature is higher than the inclined walls. Top wall of the cavity is adiabatic. To investigate the effects, finite element method is used to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure. It is found that heat transfer decreased by 20.70% and 16.15% as φ increases from 0 to 60 at Ra = 10⁵ and 10⁶ respectively. On the other hand, heat transfer decreased by 20.28% and 13.42% as Ha increases from 0 to 50 for Ra = 10⁵ and 10⁶ respectively.     

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.     

Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall

Conjugate heat transfer by mixed convection and conduction in lid-driven enclosures with thick bottom wall has been studied by a numerical method. The enclosure is heated from the bottom wall isothermally. Temperature of the top moving wall, which has constant flow speed, is lower than that of the outside of bottom wall. Vertical walls of the enclosure are adiabatic. Governing parameters are solved for a wide range of Richardson numbers (0.1 ≤ Ri ≤ 10), ratio of height of bottom wall to enclosure height (0.1 ≤ h/H ≤ 0.5) and thermal conductivity ratio (0.01 ≤ λ_f/λ_s ≤ 10). Obtained results showed that heat transfer decreases with increasing of λ_f/λ_s ratio, Richardson number and thickness ratio of the wall. Flow strength is affected for only higher values of λ_f/λ_s ratio.     

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

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

Investigation of buoyancy-driven flow and heat transfer in a trapezoidal cavity filled with water–Cu nanofluid

A numerical study is conducted to investigate the transport mechanism of free convection in a trapezoidal enclosure filled with water–Cu nanofluid. The horizontal walls of the enclosure are insulated while the inclined walls are kept at constant but different temperatures. The numerical approach is based on the finite element technique with Galerkin's weighted residual simulation. Solutions are obtained for a wide range of the aspect ratio (AR) and Prandtl number (Pr) with Rayleigh number (Ra = 10⁵) and solid volume fraction (? = 0.05). The streamlines, isotherm plots and the variation of the average Nusselt number at the left hot wall are presented and discussed. It is found that both AR and Pr affect the fluid flow and heat transfer in the enclosure. A correlation is also developed graphically for the average Nusselt number as a function of the Prandtl number as well as the cavity aspect ratio.     

Predictions of buoyancy-induced flow in various across-shape concave enclosures

The present study was conducted to numerically investigate the steady laminar buoyancy-driven and convection heat transfer characteristics within three different across-shape concave enclosures for the Prandtl number of 0.71 and 4, the Grashof number range 10⁴ ≤ Gr ≤ 2 × 10⁵_, and the gap range 0 ≤ H₁/H₂ ≤ 0.25. The steady Navier-Stokes equations, governing the flow under Boussinesq approximation, are solved with the dimensionless stream function-vorticity formulation in terms of curvilinear coordinates using the finite difference method. The results show that the effects of various shapes, the strength of the vortex is relatively bigger in the rectangular-rectangular concave enclosure than in the rectangular-circular concave enclosure at the same Grashof number. Heat transfer from the different across-shape concave enclosures is evaluated, and flow and heat transfer characteristics are discussed.     

Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations

In this model, a numerical study of two dimensional steady natural convection is performed for a uniform heat source applied on the inner circular cylinder in a square air (Pr = 0.7) filled enclosure in which all boundaries are assumed to be isothermal (at a constant low temperature). The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of vertical cylinder locations and Rayleigh numbers on fluid flow and heat transfer performance are investigated. Rayleigh number is varied from 10³ to 10⁶ and the location of the inner cylinder is changed vertically along the centerline of the enclosure from − 0.25 L to 0.25 L upward and downward, respectively. It is found that at small Rayleigh numbers does not have much influence on the flow field while at high Rayleigh numbers have considerable effect on the flow pattern. In addition, the numerical solutions yield a two cellular flow field between the inner cylinder and the enclosure. Also, the total average Nusselt number behaves nonlinearly as a function of locations. Results are presented in terms of the streamlines, isotherms, local and average Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.     

Local turbulent opposing mixed convection heat transfer in inclined flat channel for unstably stratified airflow

Local turbulent mixed convection heat transfer in inclined (from ? = 0° (horizontal position) till ? = 90° (vertical position)) flat channels for opposing flows was investigated for the case when only bottom wall is heated (unstably stratified flow conditions). Wide ranges of airflow parameters are covered: Re = 4 × 10³-6.6 × 10⁴, Gr_q = 4.7 × 10⁷-6.3 × 10¹⁰, pressure p = 0.1; 0.2; 0.4; 0.7; 1.0 MPa. Correlation for calculation of heat transfer in inclined flat channels was suggested for the region without buoyancy instabilities. The experimental data were compared with the recent experimental data for inclined flat channels when upper wall is heated (stably stratified flow conditions).     

Transient natural convection in 3D tilted enclosure heated from two opposite sides

In the present work, we investigate numerically the natural convection flow in 3D cubic enclosure tilted at an angle (γ) with respect to the vertical position. The enclosure is heated and cooled from the two opposite walls while the remaining walls are adiabatic. The numerical procedure adopted in this analysis yield consistent performance over a wide range of parameters. Simulations have been carried out for Rayleigh numbers Ra ranging from 10³ to 1.3 × 10⁵, Prandtl number, Pr, (0.71 ≤ Pr ≤ 75) and inclination angle γ (0° ≤ γ ≤ 90°). Particular attention is focused on the three-dimensional steady effects that can arise in such configuration that seem to be unknown in the literature, even for relatively small values of the Rayleigh number. The 3D flow characteristics and thermal fields are analyzed in terms of streamlines, isotherms and Nusselt numbers. A periodic behavior of the 3D flow has been observed at Ra = 8.5 × 10⁴ with a fundamental frequency of 8.27. The Hopf bifurcation is localized. In addition, time-dependent solutions reveal that the flow characteristics depend on the inclination angle γ. The effects of Prandtl number on heat transfer and fluid flow is significant for Pr ≥ 6.     

Local turbulent opposing mixed convection heat transfer in inclined flat channel for stably stratified airflow

Local turbulent mixed convection heat transfer in inclined flat channels (?=20-90° from horizontal position) for opposing flows was investigated for the case when only upper wall is heated (under stably stratified flow conditions). Wide ranges of airflow parameters are covered: Re=4 × 10³-4 × 10⁴, Gr_q=1.7 × 10⁸-1.4 × 10¹⁰, pressures; p=0.2; 0.4; 0.6; 0.8 MPa. Based on analysis of local heat transfer data and existing information in the literature three characteristic regions in the buoyancy parameter range investigated were identified: region without buoyancy instabilities, transition region and region with buoyancy instabilities in whole heated section. For the region without buoyancy instabilities correlation for calculation of heat transfer in inclined flat channels was suggested.     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

Conjugate natural convection in air filled tube inserted a square cavity

Numerical analyses of fluid flow and heat transfer due to buoyancy forces in a tube inserted square cavity filled with fluid were carried out by using control volume method in this study. The cavity was heated from the left wall and cooled from the right isothermally and horizontal walls were adiabatic. A circular tube filled with air was inserted into the square cavity. The case that the inside and outside of the tube were filled with the same fluid (air) was examined. Varied solid materials were chosen as the tube wall. Results were obtained for different Rayleigh numbers (Ra = 10⁴, 10⁵ and 10⁶), thermal conductivity ratio of the fluid to the tube wall (k = 0.1, 1 and 10) and different location centers of the tube (c (0.25 ≤ x ≤ 0.75, 0.25 ≤ y ≤ 0.75)). Comparison with benchmark solutions of the natural convection in a cavity was performed and numerical results gave an acceptable agreement. It was found that varied location of the tube center can lead to different flow fields and heat transfer intensities which are also affected by the value of Rayleigh number.     

Effect of magnetic field on convection heat transfer inside a tilted square enclosure

Steady, laminar, natural-convection flow in the presence of a magnetic field in a tilted enclosure heated from below and cooled from top is considered. The enclosure is filled with liquid gallium. In our formulation of governing equations, mass, momentum and energy are applied to the enclosure. To solve the nonlinear governing differential equations a finite volume code based on PATANKAR's SIMPLER method is utilized. It is shown that for a given inclination angle (φ), as the value of Hartmann number (Ha) increases, the convection heat transfer reduces. Furthermore it is found that at Ra = 10⁴, value of Nusselt number depends strongly upon the inclination angle for relatively small values of Hartmann number. At Ra = 10⁵, the Nusselt number increases up to about φ = 45^o and then decrease as φ increases.     

Natural convective characteristics of a heat source module at different angles in the closed and ventilated cabinets

A numerical analysis is performed to study the characteristics of heat transfer from a block heat source module at different angles in two-dimensional cabinets. Great efforts are carried out to conduct the effects of thermal interaction between the air steams inside and outside the cabinet on the conjugate conduction–natural convection phenomena. Moreover, the enhancement of cooling performance of the heat source module through the construction of air vents on cabinet wall is rigorously examined. The computation domain covers the cabinet and the surrounding area, and the temperature and velocity fields of the cabinet and surrounding area are solved simultaneously. Comparing the results for cases with and without the consideration of thermal interaction between the air streams, the difference in hot spot temperature of module can be up to 26% for Pr = 0.7, K_bf = K_wf = 100, 0 ≦ K_pf ≦ 100, 10⁵ ≦ Ra ≦ 10⁷ and φ = 0°, 90°, 270°. The maximum reduction in hot spot temperature is about 41% when two air vents are constructed on the cabinet wall. The variation of module angle results in the maximum difference of the hot spot temperature is 17% for closed cabinet, and 10% for ventilated cabinet. In addition, the hot spot temperatures for cases with K_pf = 10 are about two times of that for K_pf = 100.     

Prediction of flow fields and temperature distributions due to natural convection in a triangular enclosure using Adaptive-Network-Based Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN)

Artificial Neural Network (ANN) and Adaptive-Network-Based Fuzzy Inference System (ANFIS) were used to predict the natural convection thermal and flow variables in a triangular enclosure which is heated from below and cooled from sloping wall while vertical wall is maintained adiabatic. Governing equations of natural convection were solved using finite difference technique by writing a FORTRAN code to generate database for ANN and ANFIS in the range of Rayleigh number from Ra = 10⁴ to Ra = 10⁶ and aspect ratio of triangle AR = 0.5 and AR = 1. Thus, the results obtained from numerical solutions were used for training and testing the ANN and ANFIS. A comparison was performed among the soft programming and Computational Fluid Dynamic (CFD) codes. It is observed that although both ANN and ANFIS soft programming codes can be used to predict natural convection flow field in a triangular enclosure, ANFIS method gives more significant value to actual value than ANN.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

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.     

Forced convection heat transfer from a circular cylinder in crossflow to air and liquids

Local and average heat transfer by forced convection from a circular cylinder is studied for Reynolds number from 2 × 10³ to 9 × 10⁴ and Prandtl number from 0.7 to 176. For subcritical flow, the local heat transfer measurement indicates three regions of flow around the cylinder: laminar boundary layer region, reattachment of shear layer region and periodic vortex flow region. The average heat transfer in each region is calculated and correlated with the Reynolds number and the Prandtl number. The Nusselt number in each region strongly depends on the Reynolds number and the Prandtl number with different power indices. An empirical correlation for predicting the overall heat transfer from the cylinder is developed from the contributions of heat transfer in these three regions.