Natural convection in a triangle enclosure with flush mounted heater on the wall (original) (raw)
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Natural convection in triangular enclosures with protruding isothermal heater
International journal of heat and mass transfer, 2007
Natural convection heat transfer from a protruding heater located in a triangular enclosure has been analyzed numerically. Temperature of inclined boundary of the triangle is lower than the temperature of the heater, which has constant temperature boundary condition. The remaining walls are insulated. The study is formulated in terms of the vorticity-stream function procedure and numerical solution was performed using the finite difference method. Air was chosen as working fluid with Pr = 0.71. Governing parameters, which are effective on flow field and temperature distribution, are; Rayleigh number, aspect ratio of triangle enclosure, dimensionless height of heater, dimensionless location of heater and dimensionless width of heater. Streamlines, isotherms, velocity profiles, local and mean Nusselt numbers are presented. It is found that all parameters related with geometrical dimensions of the heater are effective on temperature distribution, flow field and heat transfer.
Proceedings of The Institution of Mechanical Engineers Part C-journal of Mechanical Engineering Science, 2008
A numerical was performed analysis on laminar natural convection heat transfer and fluid flow in both protruding heaters (PHs) and flush-mounted heaters (FMHs) located in a triangular enclosure using finite-difference technique. The heaters were isothermal and the temperature of the inclined wall was lower than that of the heaters while the remaining walls of the triangular enclosure were adiabatic. Results are presented according to the location of the heaters in two cases. In the first case, the PH was located near the vertical wall and the FMH near the right corner. In the second case, the PH was located near the right corner of the enclosure, whereas the FMH was located close to the vertical wall. The governing parameters on natural convection were Rayleigh number (10 4 Ra 10 6 ), dimensionless length of the PH (W 1 ), dimensionless length of the FMH (W 2 ), dimensionless height of the PH (Hp), dimensionless distance between the heater and the vertical wall (S 1 ), dimensionless distance between the PH and the FMH (S 2 ), and aspect ratio of the triangular enclosure (0.25 AR 1.0). It was found that better heat transfer occured when the PH was located near the right corner of the triangular enclosure, while the other heater was mounted near the left vertical wall. Heaters behaved as a single heater when they were close to each other.
NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A RIGHT- ANGLED TRIANGULAR ENCLOSURE
A numerical investigation has been performed for heat transfer analysis in a right-angled triangular enclosure filled with water. The side wall of the enclosure is maintained at high temperature compare to the base wall while hypotenuse is kept thermally insulated. Two-dimensional steady-state continuity, momentum and energy equations along with the boussinesq approximation are solved by finite volume method using commercial available software, FLUENT 6.3. The computational results are shown in terms of isotherms, streamlines and velocity contour for Rayleigh number (10 5 ≤ Ra ≤ 10 7). The heat transfer is presented in terms of local and average Nusselt number. The result encapsulates that both flow field and temperature distributions are affected with Rayleigh number. The simulated results are validated with the experimental and numerical results and it shows a good agreement with the published results. Finally, a correlation for Nusselt number (Nu) with Rayleigh number (Ra) has been developed for vertical hot wall.
CFD-Analysis of Natural Convection in A Triangular Enclosure
Natural convection in enclosed cavities is widely studied because of its importance in many engineering applications. The most commonly used enclosures in the industries are rectangular, cylindrical, trapezoidal, triangular etc. In recent years, natural convection in triangular shaped enclosures have received a considerable attention. The reason for considering this geometry is, it has application in various fields such as building and thermal insulation systems. In the present study natural convection inside a triangular enclosure is analyzed. The analysis is conducted as 3 different cases. For the first case the bottom wall is heated and other two sides are kept at ambient temperature. For the second case, left wall is heated and other two sides are kept at ambient temperature and for the final case right wall is heated and other two sides are kept at ambient temperature. Simulations are carried out for varying Rayleigh number. Heat transfer rate from the hot surface is obtained numerically. The fluid flow characteristics and heat transfer characteristics are analyzed using computational fluid dynamic software ANSYS FLUENT 14.0.
Numerical Analysis of Natural Convection in a Right-Angle Triangular Enclosure
Frontiers in Heat and Mass Transfer, 2014
A numerical investigation has been performed for heat transfer analysis in a right-angled triangular enclosure filled with water. The side wall of the enclosure is maintained at high temperature compare to the base wall while hypotenuse is kept thermally insulated. Two-dimensional steady-state continuity, momentum and energy equations along with the boussinesq approximation are solved by finite volume method using commercial available software, FLUENT 6.3. The computational results are shown in terms of isotherms, streamlines and velocity contour for Rayleigh number (10 5 ≤ Ra ≤ 10 7). The heat transfer is presented in terms of local and average Nusselt number. The result encapsulates that both flow field and temperature distributions are affected with Rayleigh number. The simulated results are validated with the experimental and numerical results and it shows a good agreement with the published results. Finally, a correlation for Nusselt number (Nu) with Rayleigh number (Ra) has been developed for vertical hot wall.
International Communications in Heat and Mass Transfer, 2007
The effect of Prandtl number on natural convection heat transfer and fluid flow in triangular enclosures with localized heating has been analyzed by solving governing equations of natural convection in streamfunction-vorticity form with finite-difference technique. Solution of linear algebraic equations was made by Successive Under Relaxation (SUR) method. Bottom wall of triangle is heated partially while inclined wall is maintained at a lower uniform temperature than heated wall while remaining walls are insulated. Computations were carried out for dimensionless heater locations (0.15 ≤ s ≤ 0.95), dimensionless heater length (0.1 ≤ w ≤ 0.9), Prandtl number (0.01 ≤ Pr ≤ 15) and Rayleigh number (10 3 ≤ Ra ≤ 10 6 ). Aspect ratio of triangle was chosen as unity. It is observed that both flow and temperature fields are affected with the changing of Prandtl number, location of heater and length of heater as well as Rayleigh number.
Natural Convection Heat Transfer within Octagonal Enclosure
The problem of steady, laminar and incompressible natural convection flow in an octagonal enclosure was studied. In this investigation, two horizontal walls were maintained at a constant high temperature, two vertical walls were kept at a constant low temperature and all inclined walls were considered adiabatic. The enclosure was assumed to be filled with a Bousinessq fluid. The study includes computations for different Prandtl numbers Pr such as 0.71, 7, 20 and 50 whereas the Rayleigh number Ra was varied from 103 to 106. The pressure-velocity form of Navier-Stokes equations and energy equation were used to represent the mass, momentum and energy conservations of the fluid medium in the enclosure. The governing equations and boundary conditions were converted to dimentionless form and solved numerically by penalty finite element method with discretization by triangular mesh elements. Flow and heat transfer characteristics were presented in terms of streamlines, isotherms and average Nusselt number Nu. Results showed that the effect of Ra on the convection heat transfer phenomenon inside the enclosure was significant for all values of Pr studied (0.71-50). It was also found that, Pr influence natural convection inside the enclosure at high Ra (Ra > 104 ).
Natural convection and fluid flow in inclined enclosure with a corner heater
Applied Thermal Engineering, 2009
The phenomena of natural convection in an inclined square enclosure heated via corner heater have been studied numerically. Finite difference method is used for solving momentum and energy equations in the form of stream function-vorticity. One wall of the enclosure is isothermal but its temperature is colder than that of heaters while the remaining walls are adiabatic. The numerical procedure adopted in this analysis yields consistent performance over a wide range of parameters; Rayleigh number, Ra (10 3 6 Ra 6 10 6 ); Prandtl number, Pr (0.07 6 Pr 6 70); dimensionless lengths of heater in x and y directions (0.25 6 hx 6 0.75, 0.25 6 hy 6 0.75); and inclination angle, / (0°6 / 6 270°). It is observed that heat transfer is maximum or minimum depending on the inclination angle and depending on the length of the corner heaters. The effect of Prandtl number on mean Nusselt number is more significant for Pr < 1.
The 4th International Conference on Computational Methods (ICCM2012), Gold Coast, Australia
In this study, natural convection heat transfer and buoyancy driven flows have been investigated in a right angled triangular enclosure. The heater located on the bottom wall while the inclined wall is colder and the remaining walls are maintained as adiabatic. Governing equations of natural convection are solved through the finite volume approach, in which buoyancy is modeled via the Boussinesq approximation. Effects of different parameters such as Rayleigh number, aspect ratio, prantdl number and heater location are considered. Results show that heat transfer increases when the heater is moved toward the right corner of the enclosure. It is also revealed that increasing the Rayleigh number, increases the strength of free convection regime and consequently increases the value of heat transfer rate. Moreover, larger aspect ratio enclosure has larger Nusselt number value. In order to have better insight, streamline and isotherms are shown.
International Journal of Heat and Mass Transfer, 2008
A penalty finite element analysis with bi-quadratic elements is carried out to investigate the effects of uniform and non-uniform heating of inclined walls on natural convection flows within a isosceles triangular enclosure. Two cases of thermal boundary conditions are considered; case I: two inclined walls are uniformly heated while the bottom wall is cold isothermal and case II: two inclined walls are non-uniformly heated while the bottom wall is cold isothermal. The numerical solution of the problem is presented for various Rayleigh numbers (Ra), (10 3 6 Ra 6 10 6) and Prandtl numbers (Pr), (0:026 6 Pr 6 1000). It has been found that at small Prandtl numbers, geometry does not have much influence on flow structure while at Pr ¼ 1000, the stream function contours are nearly triangular showing that geometry has considerable effect on the flow pattern. In addition, the presence of multiple circulations are observed for small Pr ðPr ¼ 0:026Þ which causes wavy distribution of local Nusselt number. It is observed that non-uniform heating produces greater heat transfer rates at the center of the walls than the uniform heating; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominant regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented for specific Prandtl numbers.