scholarly journals Joule Heating Effect on MHD Combined Convection in a Wavy Chamber Having Conducting Square Cylinder

2011 ◽  
Vol 4 (1) ◽  
pp. 39 ◽  
Author(s):  
R. Nasrin
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Joule Heating ◽  
Vertical Wall ◽  
Convection Flow ◽  
Element Formulation ◽  
Heat Conducting ◽  
Square Cylinder ◽  
Combined Convection ◽  
The Right

The current simulation is focused on MHD combined convection flow and heat transfer characteristics in a square lid driven chamber. At the centre of this chamber a heat conducting solid square cylinder is located. Galerkin weighted residual finite element method is used to solve the governing equations of mass, momentum and energy. The left vertical wall of the chamber is mechanically lid driven and having temperature Tcold and velocity V0.  But the right wall is sinusoidal wavy pattern and contains more temperature (Thot) than the left lid. The top and bottom surfaces are adiabatic. The behavior of the fluid for the values of Joule heating parameter J (0, 1, 4, 7) and Richardson number Ri (0.1, 1, 10) is described in details. The variations of the average Nusselt number (Nu), the mean temperature of the fluid ( ) and the temperature at cylinder centre ( ) for various Ri and J are also presented. Maximum rate of heat transfer is occurred for the lowest J at each Ri.Keywords:  MHD; Wavy chamber; Conducting cylinder; Combined convection; Finite element formulation.© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v4i1.8014J. Sci. Res. 4 (1), 39-49 (2012)

scholarly journals A numerical study of mixed convection in a square cavity with a heat conducting square cylinder at different locations

1970 ◽  
Vol 39 (2) ◽  
pp. 78-85 ◽  
Author(s):  
Md Mustafizur Rahman ◽  
MA Alim ◽  
Sumon Saha ◽  
MK Chowdhury
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Mixed Convection ◽  
Numerical Study ◽  
Convection Flow ◽  
Heat Conducting ◽  
Mixed Convection Flow ◽  
Square Cylinder ◽  
Weighted Residuals ◽  
Laminar Mixed Convection

Numerical simulations are carried out for mixed convection flow in a vented cavity with a heat conducting horizontal square cylinder. A two-dimensional solution for steady laminar mixed convection flow is obtained by using the finite element scheme based on the Galerkin method of weighted residuals for different Richardson numbers varying over the range of 0.0 to 5.0. The study goes further to investigate the effect of the inner cylinder position on the fluid flow and heat transfer in the cavity. The location of the inner cylinder is changed horizontally and vertically along the centerline of the cavity. The effects of both Richardson numbers and cylinder locations on the streamlines, isotherms, average rate of heat transfer from the hot wall, the average temperature of the fluid inside the cavity and the temperature at the cylinder center inside the cavity are investigated. The results indicate that the flow field and temperature distributions inside the cavity are strongly dependent on the Richardson numbers and the position of the inner cylinder. Keywords: Finite element method, square cylinder, vented cavity, mixed convection. doi:10.3329/jme.v39i2.1850 Journal of Mechanical Engineering, Vol. ME39, No. 2, Dec. 2008 78-85

scholarly journals Influence of centered conducting obstacle on MHD combined convection in a wavy chamber

2011 ◽  
Vol 8 (2) ◽  
pp. 93-104 ◽  
Author(s):  
Rehena Nasrin
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Heat Conducting ◽  
Vertical Side ◽  
Left Wall ◽  
Flow Equations ◽  
Combined Convection ◽  
Two Dimensional Flow ◽  
Marine Engineering ◽  
Element Technique

The development of centered heat conducting obstacle effect on combined magnetoconvective flow in a lid driven chamber has been numerically studied. The enclosure considered has rectangular horizontal lower surfaces and vertical side surfaces. The lower and upper surfaces are insulated. The left wall is mechanically lid driven having uniform temperature Ti and velocity v0 while other vertical side is wavy and maintains higher temperature Th than the lid. The governing two-dimensional flow equations have been solved by using Galerkin weighted residual finite element technique. The investigations are conducted for different values of Richardson number (Ri) and physical parameter i.e. diameter (D) of square solid body. Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the mean Nusselt number (Nu), the average temperature (?av) of the fluid and temperature of obstacle center (?c) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the chamber. Conducting largest obstacle is preferable for effective heat transfer mechanism in presence of magnetic field.Keywords: Combined convection, MHD, wavy chamber, heat conducting obstacle, finite element simulation.doi: http://dx.doi.org/10.3329/jname.v8i2.7392 Journal of Naval Architecture and Marine Engineering 8(2011) 93-104

scholarly journals Finite Element Analysis of Mixed Convection in a Rectangular Cavity with a Heat-Conducting Horizontal Circular Cylinder

2009 ◽  
Vol 14 (2) ◽  
pp. 217-247 ◽  
Author(s):  
Md. M. Rahman ◽  
M. A. Alim ◽  
M. A. H. Mamun
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Heat Source ◽  
Mixed Convection ◽  
Rectangular Cavity ◽  
Heated Wall ◽  
Physical Parameters ◽  
Element Formulation ◽  
Heat Conducting ◽  
Coupled Equations

. Combined free and forced convection in a two dimensional rectangular cavity with a uniform heat source applied on the right vertical wall is studied numerically. A circular heat conducting horizontal cylinder is placed somewhere within the cavity. The present study simulates a practical system, such as a conductive material in an inert atmosphere inside a furnace with a constant flow of gas from outside. Importance is placed on the influences of the configurations and physical properties of the cavity. The development mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by employing Galerkin weighted residual finite element method. In this paper, a finite element formulation for steadystate incompressible conjugate mixed convection and conduction flow is developed. The computations are carried out for wide ranges of the governing parameters, Reynolds number (Re), Richardson number (Ri), Prandtl number (Pr) and some physical parameters. The results indicate that both the heat transfer rate from the heated wall and the dimensionless temperature in the cavity strongly depend on the governing parameters and configurations of the system studied, such as size, location, thermal conductivity of the cylinder and the location of the inflow and outflow opening. Detailed results of the interaction between forced airstreams and the buoyancy-driven flow by the heat source are demonstrated by the distributions of streamlines, isotherms and heat transfer coefficient.

scholarly journals Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 89-104 ◽  
Author(s):  
Rachid Bennacer ◽  
Marcelo Reggio ◽  
Nicolas Pellerin ◽  
Xiaoyan Ma
Keyword(s):  
Heat Transfer ◽  
Lattice Boltzmann ◽  
Vertical Wall ◽  
Distribution Model ◽  
Heat Conducting ◽  
Driven Cavity ◽  
Thermal Fields ◽  
Wide Range ◽  
Multiple Relaxation Time ◽  
The Right

The multiple-relaxation-time (MRT) lattice-Boltzmann method is implemented to investigate combined natural and forced convection occurring in a two-dimensional square cavity. The top wall slides to the right at constant speed, while the other three remain stationary. The solution is performed for a left vertical wall at a constant temperature, which is higher than of the right wall. This yields a ?cooperating? case, in which dynamic and buoyancy forces are added together. The enclosure is filled with air and contains a heat conducting circular cylinder, which is placed at various positions. The double distribution model used in lattice Boltzmann methods has been adopted to simulate the hydrodynamic and thermal fields, with the D2Q9 and D2Q5 lattices selected to perform the corresponding computations. Simulations have been conducted over a wide range of Rayleigh (Ra) and Reynolds (Re) numbers, and the features of dynamic and thermal fields are presented for the spectra of this mixed convection phenomenon. The flow and heat transfer characteristics of the cylinder position are described and analyzed in terms of the average Nusselt number (Nu). The computed results show the influence of the cylinder on the corresponding heat transfer in the enclosure. It has been found that the power (i.e. shear stress) needed to lid the upper surface will depend on the governing parameters.

scholarly journals A finite element analysis on combined convection and conduction in a channel with a thick walled cavity

2014 ◽  
Vol 24 (8) ◽  
pp. 1888-1905 ◽  
Author(s):  
M.M. Rahman ◽  
Hakan Oztop ◽  
S. Mekhilef ◽  
R. Saidur ◽  
A. Chamkha ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Mixed Convection ◽  
Conjugate Heat Transfer ◽  
Transfer Problem ◽  
Thick Wall ◽  
Thermal Conductivity Ratio ◽  
Element Analysis ◽  
Content Type ◽  
Combined Convection

Purpose – The purpose of this paper is to examine the effects of thick wall parameters of a cavity on combined convection in a channel. In other words, conjugate heat transfer is solved. Design/methodology/approach – Galerkin weighted residual finite element method is used to solve the governing equations of mixed convection. Findings – The streamlines, isotherms, local and average Nusselt numbers are obtained and presented for different parameters. It is found heat transfer is an increasing function of dimensionless thermal conductivity ratio. Originality/value – The literature does not have mixed convection and conjugate heat transfer problem in a channel with thick walled cavity.

Ferrofluid Convection in a Lid-Driven Cavity

2018 ◽  
Vol 388 ◽  
pp. 407-419
Author(s):  
Fatih Selimefendigil ◽  
Ali Jawad Chamkha
Keyword(s):  
Heat Transfer ◽  
Magnetic Dipole ◽  
Richardson Number ◽  
Vertical Wall ◽  
Thermal Characteristics ◽  
Dipole Source ◽  
Dipole Strength ◽  
Square Enclosure ◽  
Lower Temperature ◽  
The Right

This study numerically investigates the mixed convection of ferrofluids in a partially heated lid driven square enclosure. The heater is located to the left vertical wall and the right vertical wall is kept at constant lower temperature while other walls of the cavity are assumed to be adiabatic. The governing equations are solved with Galerkin weighted residual finite element method. The influence of the Richardson number (between 0.01 and 100), heater location (between 0.25 H and 0.75H), strength of the magnetic dipole (between 0 and 4), and horizontal location of the magnetic dipole source (between-2H and-0.5H) on the fluid flow and heat transfer are numerically investigated. It is found that local and averaged heat transfer deteriorates with increasing values of Richardson number and magnetic dipole strength. The flow field and thermal characteristics are sensitive to the magnetic dipole source strength and its position and heater location.

scholarly journals MHD mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating

2010 ◽  
Vol 15 (2) ◽  
pp. 199-211 ◽  
Author(s):  
M. M. Rahman ◽  
M. A. Alim
Keyword(s):  
Joule Heating ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
Convection Flow ◽  
Heat Conducting ◽  
Mixed Convection Flow ◽  
Square Enclosure ◽  
Average Temperature ◽  
Horizontal Circular Cylinder

In the present numerical investigation we studied the effect of magnetohydrodynamic (MHD) mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter (Hartmann number) Ha, Joule heating parameter J, Reynolds number Re and Richardson number Ri. The streamlines, isotherms, average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number, Reynolds number and Richardson number have strong influence on the streamlines and isotherms. On the other hand, Joule heating parameter has little effect on the streamline and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.

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