Natural convection in porous triangular enclosures with a solid adiabatic fin attached to the horizontal wall

A numerical analysis has been performed to investigate the effects of fin location onto the bottom wall of a triangular enclosure filled with porous media whose height base ratio is 1. The temperature of the bottom wall is higher than that of the inclined wall while the vertical wall is insulated. Thus, the fin divides the heated bottom wall to two separate regions. Finite difference method was applied to solve governing equations which are written using Darcy method. Solutions of algebraic equations were made by Successive Under Relaxation (SUR) technique. The effective parameters on flow and temperature fields are: Rayleigh number, location center of fin, dimensionless fin height, and dimensionless fin width. The obtained results indicated that the fin can be used as a control element for heat transfer and fluid flow.     

Control of buoyancy-induced temperature and flow fields with an embedded adiabatic thin plate in porous triangular cavities

Natural convection has been performed in an insulated horizontally thin plate embedded in a triangular enclosure filled with fluid saturated porous medium, numerically. Bottom and inclined wall of triangular enclosure are isothermally heated and cooled, respectively. Vertical wall of enclosure is adiabatic. Steady, two-dimensional, laminar governing equations, which are written with Darcy model, were solved with finite-difference method. Calculations are conducted for different lengths and locations of thin plate, different aspect ratios, and Darcy-modified Rayleigh number. Prandtl number was chosen as 0.71. It is observed that the change on plate location in vertical and horizontal axes makes small effect on heat transfer; however flow field and temperature distribution strongly affected from these parameters.     

Finite element simulation of mixed convection heat and mass transfer in a right triangular enclosure

A simulation of mixed convection heat and mass transfer in a right triangular enclosure is investigated numerically. The bottom surface of the enclosure is maintained at uniform temperature and concentration that are higher than that of the inclined surface. Moreover, the left wall of cavity moves upward (case 1) and downward (case 2) directions, which have constant flow speed, and is kept adiabatic. The enclosure represents the most common technology utilizing solar energy for desalination or waste-water treatment. A simple transformation is employed to transfer the governing equations into a dimensionless form. A finite-element scheme is used for present analysis. Comparison with the previously published work is made and found to be an excellent agreement. The study is performed for pertinent parameters such as buoyancy ratio, Richardson number and the direction of the sliding wall motion. The effect of aforesaid parameters on the flow and temperature fields as well as the heat and mass transfer rate examined. The results show that the increase of buoyancy ratio enhances the heat and mass transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the direction of the sliding wall motion can be a good control parameter for the flow and temperature fields.     

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 Convection in a Square Cavity with Discrete Heating at the Bottom with Different Fin Shapes

Numerical study is carried out to investigate the effect of different fin shapes on heating a square cavity by small heating strip located at the bottom wall. The natural convection of air is considered with constant heat flux from heat source which is located at the center of the bottom wall. The width of the heating strip is assumed to be 20% of the total width of the bottom wall. The remaining (non-heated) part of the bottom wall and the top wall are adiabatic and the side walls are maintained at constant temperature. The investigation considered four shapes of aluminum fins with equal area and equal base width. The easy to fabricate fin shapes are considered as: rectangular, one triangular, two opposite triangular and two isosceles triangular shape. Other parameters considered are the total area of the fin (or the height of the fin) and the Grashof number in the laminar flow range. It is found that the heat transfer can be enhanced by either increasing the Grashof number or the height of the fins. In most of the investigated cases the heat transfer in the case of the two opposite triangular fins shape is found to be higher than that of the other shapes under the same conditions.     

Visualization of natural convection heat transport using heatline method in porous non-isothermally heated triangular cavity

Natural convection heat transfer in a porous media filled and non-isothermally heated from the bottom wall of triangular enclosure is analyzed using finite difference technique. Darcy law was used to write equations of porous media. Dimensionless heatfunction was used to visualize the heat transport due to buoyancy forces. Three different boundary conditions were applied for the vertical and inclined boundaries of triangular enclosures as Case I; both vertical and inclined walls were isothermal, Case II; vertical wall was adiabatic and inclined one was isothermal, Case III; vertical wall is isothermal and inclined one is adiabatic. A cosine function was utilized to get non-isothermal wall condition. The study was performed for different aspect ratios (0.25 ? AR ? 1.0) and Darcy-modified Rayleigh numbers (100 ? Ra ? 1000). It was observed that heat transfer enhancement was formed when vertical and inclined walls were isothermal while bottom wall was at non-uniform temperature. Heat transfer from bottom wall did not vary when the value of aspect ratio was higher than 0.50. In addition, heatline visualization technique was a useful technique for non-isothermally heated and porous media filled triangular enclosures.     

Free convection in porous media filled right-angle triangular enclosures

Steady-state free convection heat transfer in a right-angle triangular enclosure, whose vertical wall insulated and inclined and bottom walls are differentially heated, is performed in this study. The governing equations are obtained using Darcy model. In this study, the governing equations were solved by finite difference method and solution of algebraic equations was made via Successive Under Relaxation method. The effect of aspect ratios ranging from 0.25 to 1.0 and Rayleigh numbers 50 ≤ Ra ≤ 1000 is investigated as governing parameters on heat transfer and flow field. It is observed that heat transfer is increased with the decreasing of aspect ratio and multiple cells are formed at high Rayleigh numbers.     

Two-dimensional natural convection in a porous triangular enclosure with a square body

A two-dimensional numerical solution for steady-state buoyancy induced convection in a right-triangular enclosure with a square body is obtained using finite difference technique. The solid body is located far from the origin with the distance of 0.3 in both directions. It is considered that the temperature of the bottom wall of triangular enclosure is higher than that of inclined wall while the vertical wall is insulated. To obtain the effects of the presence of a square body on heat transfer and fluid flow inside the enclosure, four different temperature boundary conditions were applied for the body as heated, cooled, neutral and adiabatic at different Ra numbers. It is observed that fluid flow and temperature fields strongly depend on thermal boundary conditions of the body.     

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.     

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity

A numerical study on natural convection heat transfer of cold water near 4 °C in a thick bottom walled cavity filled with a porous medium has been performed. It is assumed that the cavity is isothermally heated from the outside of the thick bottom wall and cooled from ceiling. The finite-difference method has been used to solve the governing partial differential equations of heat and fluid flow. Effects of thermal conductivity ratio, Rayleigh number and bottom wall thickness on heat transfer from the bottom to the ceiling have been studied. The heatline visualization technique has been used to demonstrate the path of heat transport through the enclosure. Moreover, streamlines and isotherms have been used to present fluid flow and temperature distributions. The obtained results show that multiple circulation cells are formed in the cavity and the local Nusselt numbers at the bottom wall and solid–fluid interface are highly affected by formed cells. The increase of Rayleigh number and thermal conductivity ratio increases heat transfer through the cavity. However, the increase of thickness of the bottom wall reduces the mean Nusselt number. Almost one-dimensional conduction heat transfer is observed in the solid bottom wall of the cavity.     

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.     

Effects of discrete isoflux heat source size and angle of inclination on natural convection heat transfer flow inside a sinusoidal corrugated enclosure

The main objective of this article is to study numerically a two-dimensional, steady and laminar viscous incompressible flow in a sinusoidal corrugated inclined enclosure. In this analysis, two vertical sinusoidal corrugated walls are maintained at a constant low temperature whereas a constant heat flux source whose length is varied from 20 to 80% of the total length of the enclosure is discretely embedded at the bottom wall. The Penalty finite element method has been used to solve the governing Navier–Stokes and energy conservation equation of the fluid medium in the enclosure in order to investigate the effects of inclination angles and discrete heat source sizes on heat transfer for different values of Grashof number. Results are presented in the form of streamline and isotherm plots. It is concluded that the average Nusselt number increases as inclination angle increases for different heat source sizes.     

Magneto-convection of nanofluids in a lid-driven trapezoidal cavity with internal heat generation and discrete heating

The present work investigates numerically the effect of an inclined magnetic field on the mixed convection flow in a trapezoidal enclosure in the presence of internal heat generation or absorption. The trapezoidal enclosure is filled with water-based nanofluid containing copper nanoparticles. Both the inclined left and right walls are adiabatic. A heat source with constant heat flux placed on the bottom wall of the enclosure and the remaining portions are thermally insulated. The top wall of the enclosure is maintained at a constant low temperature and is moving with a constant speed in its own plane from left to right. The governing equations are discretized by the control volume method and are solved numerically by the SIMPLE algorithm. A parametric study is performed and a set of graphical results is presented and discussed to demonstrate the interesting features of the solution.     

Heat transfer from a horizontal fin array by natural convection and radiation—A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.     

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 heat transfer in a nanofluid-filled trapezoidal enclosure

Heat transfer enhancement utilizing nanofluids in a trapezoidal enclosure is investigated for various pertinent parameters. Transport equations are modelled by a stream-vorticity formulation and solved numerically by finite difference approach. The inclined sloping boundaries is treated by adopting staircase-like zigzag lines. Based upon the numerical predictions, the effects of Grashof number, inclination angle of the sloping wall, volume fraction of nanoparticles on flow and temperature patterns as well as the heat transfer rate within the enclosure are presented. Water–Cu and water–Al₂O₃ nanofluids were tested. We found that acute sloping wall and Cu nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle of the sloping wall, effective thermal conductivity and viscosity as well as Grashof number.     

Control of mixed convection in lid-driven enclosures using conductive triangular fins

Control of mixed convection (combined forced and natural convection) in a lid-driven square cavity is performed using a short triangular conductive fin. A numerical technique is used to simulate the flow and temperature fields. The vertical walls of the cavity are differentially heated. Both the top lid and the bottom wall are adiabatic. The fin is located on one of the motionless walls of the cavity. Three different cases have been studied based on the location of the fin. In this context, Cases I, II and III refer to the fin on the left, bottom and right walls, respectively. Results are presented for +x and −x directions of the top lid in horizontal axis and different Richardson numbers as Ri = 0.1, 1.0 and 10.0. It is observed that the triangular fin is a good control parameter for heat transfer, temperature distribution and flow field.     

Heatline Analysis on Heat Transfer and Convective Flow of Nanofluids in an Inclined Enclosure

This article presents a heatline method to analyse the transport mechanism of heat transfer and convective flow of nanofluids in an inclined square enclosure, where a heated thin plate located in the middle of the enclosure. The fluid flow, heat transfer, and heat transport characteristics are illustrated using streamlines, isotherms, Nusselt number and heatlines. Results show that fluid flow and temperature fields strongly depend on Rayleigh number, inclination angle, solid volume fraction, types of nanoparticles and the plate length, and the maximum strength of heatfunction increases as the inclination angle and Rayleigh number increase.     

Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length

This work is focused on the numerical study of steady, laminar, conjugate natural convection in a square enclosure with an inclined thin fin of arbitrary length. The inclined fin is attached to the left vertical thin side of the enclosure while the other three sides are considered to have finite and equal thicknesses of arbitrary thermal conductivities. The left wall of the enclosure to which the fin is attached is assumed heated while the external sides of the other three surfaces of the enclosure are cooled. The inclined thin fin is perfectly conductive and is positioned in the middle heated surface of the enclosure. Three different fin lengths equal to 20, 35 and 50 percent of the heated surface are considered. The problem is formulated in terms of the vorticity-stream function procedure. A numerical solution based on the finite-volume method is obtained. Representative results illustrating the effects of the thin fin inclination angle and length and the thermal conductivity of the thick surfaces on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers are presented and discussed for various parametric conditions.     

Electrohydrodynamic enhancement of heat transfer in vertical fin array using computational fluid dynamics technique

Electrohydrodynamic enhanced heat transfer of the natural convection inside an enclosure with a vertical fin array is numerically investigated via a computational fluid dynamics technique. The parameters considered in a numerical modeling are supplied voltage, Rayleigh number, inclined angle, number of electrodes, electrode arrangement, number of fins, and fin length. The results reveal that the flow and heat transfer enhancements are significantly dependent on the number and position of electrodes around the fins. Moreover, the heat transfer coefficient is substantially improved by the electric field especially at the large number of fins and the long fin length.