Natural Convection in a Trapezoidal Cavity With Linearly Heated Side Wall(s)

2007 ◽  
Author(s):  
E. Natarajan ◽  
Tanmay Basak ◽  
S. Roy
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Vertical Wall ◽  
Side Wall ◽  
Convection Flow ◽  
Left Wall ◽  
Wide Range ◽  
Stream Functions ◽  
Side Walls

The present numerical study deals with natural convection flow in a trapezoidal cavity when the bottom wall is uniformly heated and the vertical wall(s) are linearly heated and cooled whereas the top wall is well insulated. Nonlinear coupled partial differential equations governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Parametric study for the wide range of Rayleigh number (Ra), 103 ≤ Ra ≤ 105 and Prandtl number (Pr), 0.07 ≤ Pr ≤ 100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For linearly heated side walls symmetry is observed while representing the flow patterns in terms of stream functions whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. Local Nusselt number becomes negative at the side wall for linearly heated side walls and at the left wall for linearly heated left wall and cooled right wall indicating the reversal of heat flow. The effect of Prandtl number in the variation of average Nusselt numbers is more significant for Prandtl numbers in the range 0.07 to 0.7 than 10 to 100.

scholarly journals Simulation of Natural Convection Heat Transfer in a 2-D Trapezoidal Enclosure

2019 ◽  
Vol 16 (4) ◽  
pp. 7375-7390 ◽  
Author(s):  
K. Venkatadri ◽  
S. Abdul Gaffar ◽  
Ramachandra Prasad V. ◽  
B. Md. Hidayathulla Khan ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Vertical Wall ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Practical Applications ◽  
Wide Range ◽  
Trapezoidal Enclosure

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energyrelated applications, in case of proper design of enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 103 ≤ Ra ≤ 105 and Prandtl number (Pr = 0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra = 104 ). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported. 

scholarly journals Numerical Study of Natural Convection within a Wavy Enclosure Using Meshfree Approach: Effect of Corner Heating

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Sonam Singh ◽  
R. Bhargava
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Side Wall ◽  
Integration Scheme ◽  
Square Enclosure ◽  
Wide Range

This paper presents a numerical study of natural convection within a wavy enclosure heated via corner heating. The considered enclosure is a square enclosure with left wavy side wall. The vertical wavy wall of the enclosure and both of the corner heaters are maintained at constant temperature,TcandTh, respectively, withTh>Tcwhile the remaining horizontal, bottom, top and side walls are insulated. A penalty element-free Galerkin approach with reduced gauss integration scheme for penalty terms is used to solve momentum and energy equations over the complex domain with wide range of parameters, namely, Rayleigh number (Ra), Prandtl number (Pr), and range of heaters in thex- andy-direction. Numerical results are represented in terms of isotherms, streamlines, and Nusselt number. It is observed that the rate of heat transfer depends to a great extent on the Rayleigh number, Prandtl number, length of the corner heaters and the shape of the heat transfer surface. The consistent performance of the adopted numerical procedure is verified by comparison of the results obtained through the present meshless technique with those existing in the literature.

A Numerical Study of Laminar Natural Convection in Shallow Cavities

1981 ◽  
Vol 103 (2) ◽  
pp. 226-231 ◽  
Author(s):  
G. S. Shiralkar ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Numerical Study ◽  
Aspect Ratios ◽  
Shallow Cavities ◽  
Horizontal Cavity ◽  
Side Walls ◽  
Prandtl Numbers

Heat transfer by natural convection in a horizontal cavity with adiabatic horizontal walls and isothermal side walls is investigated numerically for high aspect ratios (width/height). Comparison is made with existing analytical and experimental results. Agreement is generally good at moderate and high Prandtl numbers to which most previous works have been restricted. Improvements of the existing correlation have been proposed in regions of discrepancy. Extension to the low Prandtl number case, including the range of liquid metals, has been made on the basis of an analytical model for high Rayleigh numbers as well as by numerical solution of the full equations. The agreement between the two is found to be very good. A correlation for the heat transfer is proposed for each of the two different cases of high and low Prandtl number.

A Numerical Study of Natural Convection in Partially Open Enclosures With a Conducting Side-Wall

2004 ◽  
Vol 126 (1) ◽  
pp. 76-83 ◽  
Author(s):  
G. Desrayaud ◽  
G. Lauriat
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Side Wall ◽  
Practical Applications ◽  
Hot Air ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Rayleigh Numbers

A numerical study of natural convection generated by a cold vertical wall of an enclosure with two openings on the opposite wall of finite thickness is presented. The enclosure is connected to an infinite reservoir filled with hot air. A two-dimensional laminar flow is assumed both within the enclosure and along the side of the bounding wall immersed into the reservoir. The effects of the size of the openings, spacing between the vertical walls and thermal resistance of the bounding wall are investigated. Numerical results are discussed for aspect ratios of the enclosure and Rayleigh numbers relevant to practical applications.

scholarly journals Numerical study of magneto-hydrodynamic (MHD) mixed convection flow in a lid-driven triangular cavity

2015 ◽  
Vol 12 (1) ◽  
pp. 21-32
Author(s):  
Mohammed Nasir Uddin ◽  
Aki Farhana ◽  
Md. Abdul Alim
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Numerical Study ◽  
Bulk Temperature ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Coupled Equations ◽  
Wide Range

In the present paper, the effect of magneto-hydrodynamic (MHD) on mixed convection flow within a lid-driven triangular cavity has been numerically investigated. The bottom wall of the cavity is considered as heated. Besides, the left and the inclined wall of the triangular cavity are assumed to be cool and adiabatic. The cooled wall of the cavity is moving up in the vertical direction. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Rayleigh number, Hartmann number and the cavity aspect ratio. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters Rayleigh number Ra (103-104), Prandtl number Pr (0.7 - 3) and Hartmann number Ha (5 - 50). The numerical results are presented in terms of stream functions, temperature profile and Nussult numbers. It is found that the streamlines, isotherms, average Nusselt number, average fluid bulk temperature and dimensionless temperature in the cavity strongly depend on the Rayleigh number, Hartmann number and Prandtl number.

Two-phase natural convection flow of a dusty fluid

2015 ◽  
Vol 25 (7) ◽  
pp. 1542-1556 ◽  
Author(s):  
Sadia Siddiqa ◽  
M. Anwar Hossain ◽  
Suvash C Saha
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Two Phase ◽  
Metal Mixture ◽  
Content Type ◽  
Dusty Fluid ◽  
Wide Range

Purpose – The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture. Design/methodology/approach – The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate. Findings – The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient, wall heat transfer coefficient, velocity distribution and temperature distribution for both phases. Results are interpreted for wide range of Prandtl number Pr (0.005-1,000.0). It is observed that thin boundary layer structures can be formed when mass concentration parameter or Prandtl number (e.g. oil-metal particle mixture) are high. Originality/value – The results of the study may be of some interest to the researchers of the field of chemical engineers.

scholarly journals Numerical Study of Three- Dimensional Natural Convection in a Differentially Heated Cubical Enclosure

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Numerical Study ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Cubical Enclosure ◽  
Side Walls ◽  
The Right ◽  
Rayleigh Numbers

—A high-resolution, finite difference numerical studyis reported on three-dimensional steady-state natural convectionof air, for two Rayleigh numbers, in a cubical enclosure, which isheated differentially at one side walls. The temperature of thewall is TC except for the right vertical wall, in which is TH.Thedetails of the three-dimensional flow and thermal characteristicsare described.

Numerical Study of Steady Natural Convection Flow in A Prismatic Enclosure with Strip Heater on Bottom Wall Using Flexpde

2014 ◽  
Vol 7 (1) ◽  
pp. 61-80
Author(s):  
Sana Jaafar Yaseen
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Bottom Wall ◽  
Convection Flow ◽  
Two Dimensional ◽  
Finite Element Software ◽  
Stream Functions ◽  
Vertical Walls ◽  
Temperature And Flow Fields

Laminar natural convection in two-dimensional Prismatic enclosure is studied and analysis numerically. For the enclosure top inclined walls are considered at low temperature, two vertical walls are adiabatic and strip heater at constant high temperature mounted on the bottom enclosure, while the reminder bottom wall kept at low known temperature. The partial differential equations for two dimensional conservation of mass, momentum and energy are solved using finite element software package (FLEXPDE.5). For Rayleigh number varying from 103 to 105 and for constant Prandtal number Pr=0.7 the change in temperature and flow fields (stream functions) were investigated for different heater locations and for different number of heaters. The effect of the number and locations of the strip heaters on local and mean Nusslet number were examined. Results were presented by streamlines, isotherms and Nusselt number and it indicates that the Nusselt number is significantly affected by increasing both Ra and number of heaters. A comparison of the streamlines, isotherms curves and average Nusselt at the same boundary conditions was made with that obtained by Tanmay et al.(7), and showed a good agreement.

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