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 Effect of Inlet and Outlet Locations on Transverse Mixed Convection Inside a Vented Enclosure

1970 ◽  
Vol 36 ◽  
pp. 27-37 ◽  
Author(s):  
Sumon Saha ◽  
Md. Tofiqul Islam ◽  
Mohammad Ali ◽  
Md. Arif Hassan Mamun ◽  
M Quamrul Islam
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
Mixed Convection ◽  
Vertical Wall ◽  
Flow Fields ◽  
Temperature Fields ◽  
Heated Wall ◽  
Element Method

Transverse mixed convection is studied numerically in a vented enclosure with constant heat flux from uniformly heated bottom wall. An external airflow enters the enclosure through an opening in one vertical wall and exits from another opening in the opposite wall. The two-dimensional mathematical model includes the system of four partial differential equations of continuity, linear momentum and energy, solved by the finite element method. Flow fields are investigated by numerical simulations for air flowing with a Reynolds number in the range 50 ≤ Re ≤ 1000, for Richardson numbers: 0 ≤ Ri ≤ 10. Four different locations of inlet and outlets are introduced to analyze the effect of heat transfer in terms of velocity and temperature fields within the enclosure. The computational results show that the location of inlet and outlets alters significantly the temperature distribution in the flow fields and the heat transfer across the heated wall of the cavities. Empirical correlation is developed for relations using Nusselt number, Reynolds number and Richardson number, based on the enclosure height.   Keywords: Mixed convection, finite element method, vented enclosure, Richardson number.Journal of Mechanical Engineering Vol.36 Dec. 2006 pp.27-37DOI = 10.3329/jme.v36i0.808

scholarly journals Mixed Convection in a Vented Square Cavity with a Heat Conducting Horizontal Solid Circular Cylinder

2009 ◽  
Vol 5 (2) ◽  
pp. 37-46 ◽  
Author(s):  
Mustafizur Rahman ◽  
M A Alim ◽  
Suman Saha ◽  
M K Chowdhury
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Circular Cylinder ◽  
Mixed Convection ◽  
Richardson Number ◽  
Heat Conducting ◽  
Square Cavity ◽  
Flow And Heat Transfer ◽  
Solid Circular Cylinder

A finite element method based computational study of steady laminar mixed convection flow inside a vented square cavity with a heat conducting horizontal solid circular cylinder placed at the center of the cavity is carried out in this paper. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy. The present work simulates practical systems such as cooling of electronic devices, ventilation of building etc. The effects of cylinder size and Richardson number on fluid flow and heat transfer performance are investigated. Richardson number is varied from 0.0 to 5.0 and the cylinder diameter is varied from 0.0 to 0.6. The results for the case of without cylinder are compared to those with cylinder to observe the effects cylinder on the flow and heat transfer inside the cavity. The phenomenon inside the cavity for the case of with and without cylinder is analyzed through streamline and isotherm patterns. It is found that the streamlines, isotherms, average Nusselt number at the heated surface, average temperature of the fluid in the cavity and dimensionless temperature at the cylinder center strongly depend on the Richardson number as well as the diameter of the cylinder.Keywords: Mixed convection, finite element method, Richardson number, cylinder diameter, vented cavity and diffusion.DOI: 10.3329/jname.v5i2.2504Journal of Naval Architecture and Marine Engineering 5(2)(2008) 37-46

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 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)

Numerical Simulation of Mixed Convection in a Rectangular Cavity With Multiple Heat Sources

2009 ◽  
Author(s):  
Hasan Gunes ◽  
Sertac Cadırcı ◽  
Kenan Gocmen
Keyword(s):  
Reynolds Number ◽  
Heat Source ◽  
Mixed Convection ◽  
Richardson Number ◽  
Oscillatory Flow ◽  
Vertical Wall ◽  
Rectangular Cavity ◽  
Working Fluid ◽  
Heat Conducting ◽  
Heat Sources

A numerical study is presented for a mixed convection in a two-dimensional partially open rectangular cavity. The uniform heat-flux, discrete heat sources are flush-mounted on three identical heat conducting vertical boards, which are mounted on the bottom wall of a partially open cavity. An external airflow enters the cavity through an opening (inlet) in the left vertical wall and exits from the opposite opening (outlet) in the right vertical wall. In this paper, the effect of the number of boards on the flow and thermal field characteristics are investigated and compared with a single board case, where appropriate. The simulations are carried out for wide ranges of Reynolds number and Richardson number (buoyancy parameter, Ri = Gr/Re2) for a working fluid of air (Pr = 0.71). The solutions were found to be time-independent for only sufficiently low values of Re and Ri. For large Re and/or Ri, the oscillatory flow is analyzed by considering time-histories, frequencies and instantaneous snapshots for the field variables. The effect of the oscillatory flow on the heat removal from the heat source is discussed. It was observed that with the onset of oscillatory flow, the re-circulating cells set into motion and thus considerable reduction in the maximum dimensionless temperature is achieved, making the cooling with convection as an effective mode of heat transfer. The results also indicate that the Reynolds number and Richardson number have a strong effect on the temperature and velocity distributions as well as the average Nusselt number evaluated over the heat source.

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

2021 ◽  
Vol 8 (4) ◽  
pp. 807-820
Author(s):  
M. Zaydan ◽  
◽  
A. Wakif ◽  
E. Essaghir ◽  
R. Sehaqui ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Nonlinear Differential Equations ◽  
Convection Heat Transfer ◽  
Local Heat Transfer ◽  
Physical Parameters ◽  
Convection Heat ◽  
Linear Temperature ◽  
Mixed Convection Heat Transfer

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity. By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature. Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function. The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations. A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations. The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM). After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters. Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.

scholarly journals Simultaneous impacts of Joule heating and variable heat source/sink on MHD 3D flow of Carreau-nanoliquids with temperature dependent viscosity

2019 ◽  
Vol 8 (1) ◽  
pp. 356-367 ◽  
Author(s):  
J. V. Ramana Reddy ◽  
V. Sugunamma ◽  
N. Sandeep
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Joule Heating ◽  
Uniform Space ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
3D Flow ◽  
Temperature Dependent Viscosity ◽  
Source Sink

Abstract The 3D flow of non-Newtonian nanoliquid flows past a bidirectional stretching sheet with heat transfer is investigated in the present study. It is assumed that viscosity of the liquid varies with temperature. Carreau non-Newtonain model, Tiwari and Das nanofluid model are used to formulate the problem. The impacts of Joule heating, nonlinear radiation and non-uniform (space and temperature dependent) heat source/sink are accounted. Al-Cu-CH3OH and Cu-CH3OH are considered as nanoliquids for the present study. The solution of the problem is attained by the application of shooting and R.K. numerical procedures. Graphical and tabular illustrations are incorporated with a view of understanding the influence of various physical parameters on the flow field. We eyed that using of Al-Cu alloy nanoparticles in the carrier liquid leads to superior heat transfer ability instead of using only Aluminum nanoparticles. Weissenberg number and viscosity parameter have inclination to exalt the thermal field.

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.

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