scholarly journals Analysis of Energy Flux Vector on Natural Convection Heat Transfer in Porous Wavy-Wall Square Cavity with Partially-Heated Surface

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4456 ◽  
Author(s):  
Yan-Ting Lin ◽  
Ching-Chang Cho
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Energy Flux ◽  
Darcy Number ◽  
Bottom Surface ◽  
Flux Vector ◽  
Square Cavity ◽  
Vector Distribution ◽  
The Mean ◽  
Energy Flux Vector

The study utilizes the energy-flux-vector method to analyze the heat transfer characteristics of natural convection in a wavy-wall porous square cavity with a partially-heated bottom surface. The effects of the modified Darcy number, modified Rayleigh number, modified Prandtl number, and length of the partially-heated bottom surface on the energy-flux-vector distribution and mean Nusselt number are examined. The results show that when a low modified Darcy number with any value of modified Rayleigh number is given, the recirculation regions are not formed in the energy-flux-vector distribution within the porous cavity. Therefore, a low mean Nusselt number is presented. The recirculation regions do still not form, and thus the mean Nusselt number has a low value when a low modified Darcy number with a high modified Rayleigh number is given. However, when the values of the modified Darcy number and modified Rayleigh number are high, the energy flux vectors generate recirculation regions, and thus a high mean Nusselt number is obtained. In addition, in a convection-dominated region, the mean Nusselt number increases with an increasing modified Prandtl number. Furthermore, as the length of the partially-heated bottom surface lengthens, a higher mean Nusselt number is presented.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

scholarly journals Energy flux for plane waves in linear conservative systems

1977 ◽  
Vol 20 (1) ◽  
pp. 106-113 ◽  
Author(s):  
M. Hayes
Keyword(s):  
Energy Flux ◽  
Energy Equation ◽  
Plane Waves ◽  
Direct Proof ◽  
Flux Vector ◽  
Conservation Of Energy ◽  
Conservative Systems ◽  
The Mean ◽  
Point Form ◽  
Energy Flux Vector

AbstractThe point form of the conservation of energy equation is used to give simple and direct proof of results concerning the mean energy flux vector for systems of sinusoidal small amplitude waves in linear conservative systems. No constitutive equation is used explicitly.

ENERGY-FLUX VECTOR OF SURFACE THERMOELASTIC WAVES

1991 ◽  
Vol 14 (4) ◽  
pp. 563-570
Author(s):  
Tsolo P. Ivanov ◽  
Radiianka Savova
Keyword(s):  
Energy Flux ◽  
Flux Vector ◽  
Thermoelastic Waves ◽  
Energy Flux Vector

Hydromagneto quadratic natural convection on a lid driven square cavity with isothermal and non-isothermal bottom wall

2017 ◽  
Vol 34 (8) ◽  
pp. 2463-2478 ◽  
Author(s):  
Venkatadri K. ◽  
Gouse Mohiddin S. ◽  
Suryanarayana Reddy M.
Keyword(s):  
Nusselt Number ◽  
Local Nusselt Number ◽  
Bottom Wall ◽  
Bottom Surface ◽  
Square Cavity ◽  
Linear Temperature ◽  
Content Type ◽  
Alloy Casting ◽  
Non Linear ◽  
Temperature Parameter

Purpose This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface. Design/methodology/approach It is assumed that the top moving wall is adiabatic and the bottom wall is heated in two modes, and the rest of the walls are maintained at uniform cold temperature. The coupled governing non-linear partial differential equations are solved numerically with MAC algorithm for conducting a parametric study with uniform and non-uniform temperature bottom wall. Findings The numerical results are depicted in the form of streamlines, temperature contours and variation of local Nusselt number. The local Nusselt number at the bottom wall of the cavity increases in presence of non-linear temperature parameter as compared with linear temperature parameter and heat transfer reduces with increasing of Ha for uniform and non-uniform heating of bottom wall. Research limitations/implications The numerical investigation is conducted for unsteady, two-dimensional natural convective flow in a square cavity. An extension of the present study with the effect of inclination of cavity, wavy walls and triangular cavity will be the interest of future work. Originality/value This work studies the effect of magnetic field in the presence of linear convection and non-linear convection. This study might be useful to cooling of electronic components, alloy casting, crystal growth and fusion reactors, etc.

scholarly journals Natural Convection over Two Superellipse Shapes with a Porous Cavity Populated by Nanofluid

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6952
Author(s):  
Noura Alsedais
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Governing Equations ◽  
Porous Layers ◽  
Porous Cavity ◽  
The Mean ◽  
Volume Method

The influences of superellipse shapes on natural convection in a horizontally subdivided non-Darcy porous cavity populated by Cu-water nanofluid are inspected in this paper. The impacts of the inner geometries (n = 0.5,1,1.5,4) Rayleigh number (103 ≤ Ra ≤ 106), Darcy number (10−5 ≤ Da ≤ 10−2), porosity (0.2 ≤ ϵ ≤ 0.8), and solid volume fraction (0.01 ≤ ∅ ≤ 0.05) on nanofluid heat transport and streamlines were examined. The hot superellipse shapes were placed in the cavity’s bottom and top, while the adiabatic boundaries on the flat walls of the cavity were considered. The governing equations were numerically solved using the finite volume method (FVM). It was found that the movement of the nanofluid upsurged as Ra boosted. The temperature distributions in the cavity’s core had an inverse relationship with increasing Rayleigh number. An extra porous resistance at lower Darcy numbers limited the nanofluid’s movement within the porous layers. The mean Nusselt number decreased as the porous resistance increased (Da ≤ 10−4). The flow and temperature were strongly affected as the shape of the inner superellipse grew larger.

Free Convection in a Nanofluid Filled Square Cavity with an Horizontal Heated Plate

2011 ◽  
Vol 312-315 ◽  
pp. 433-438 ◽  
Author(s):  
Ali Akbar Abbasian Arani ◽  
Mostafa Mahmoodi ◽  
Meysam Amini
Keyword(s):  
Nusselt Number ◽  
Volume Fraction ◽  
Control Volume ◽  
Heated Plate ◽  
Square Cavity ◽  
Simpler Algorithm ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Control Volume Approach

The natural convection in a square cavity with a heated horizontal plate containing a nanofluid (water and Ag) is simulated numerically. The heated plate and vertical walls are maintained at a constant temperature, Th and Tc, while the horizontal walls are adiabatic. The nanofluid is assumed to be incompressible and the flow is considered to be laminar. The continuity, momentum and energy equations written in terms of the primitive variables are discretized using a control volume approach and the SIMPLER algorithm. A parametric study is performed and the effect of the Rayleigh number, the location of the heated plate and the volume fraction of the nanoparticles on the fluid flow and the heat transfer inside the cavity are investigated. The results show that the mean Nusselt number of the vertical walls increases with increasing the volume fraction of the nanoparticles. Moreover, for a constant volume fraction of the nanoparticles, the Nusselt number of the vertical walls decreases substantially as the location of the heated plate varies from top to bottom of the cavity.

Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Şahin Yİğİt ◽  
Robert J. Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Yield Stress ◽  
Local Minimum ◽  
Bingham Fluids ◽  
Bingham Number ◽  
Yield Stress Fluids ◽  
Laminar Natural Convection ◽  
The Mean

The effects of inclination 180deg≥φ≥0deg on steady-state laminar natural convection of yield-stress fluids, modeled assuming a Bingham approach, have been numerically analyzed for nominal values of Rayleigh number Ra ranging from 103 to 105 in a square enclosure of infinite span lying horizontally at φ=0deg, then rotated about its axis for φ>0deg cases. It has been found that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number but Nu¯ values for yield-stress fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to the weakening of convective transport. For large values of Bingham number Bn (i.e., nondimensional yield stress), the mean Nusselt number Nu¯ value settles to unity (Nu¯=1.0) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number Nu¯ for both Newtonian and Bingham fluids decreases with increasing φ until reaching a local minimum at an angle φ* before rising with increasing φ until φ=90deg. For φ>90deg the mean Nusselt number Nu¯ decreases with increasing φ before assuming Nu¯=1.0 at φ=180deg for all values of Ra. The Bingham number above which Nu¯ becomes unity (denoted Bnmax) has been found to decrease with increasing φ until a local minimum is obtained at an angle φ* before rising with increasing φ until φ=90deg. However, Bnmax decreases monotonically with increasing φ for 90deg<φ<180deg. A correlation has been proposed in terms of φ, Ra, and Bn, which has been shown to satisfactorily capture Nu¯ obtained from simulation data for the range of Ra and φ considered here.

scholarly journals Enhancement of natural convection heat transfer in a U-shaped cavity filled with Al2O3-water nanofluid

2012 ◽  
Vol 16 (5) ◽  
pp. 1317-1323 ◽  
Author(s):  
Ching-Chang Cho ◽  
Her-Terng Yau ◽  
Cha’o-Kuang Chen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Heated Wall ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
The Mean

This paper investigates the natural convection heat transfer enhancement of Al2O3-water nanofluid in a U-shaped cavity. In performing the analysis, the governing equations are modeled using the Boussinesq approximation and are solved numerically using the finite-volume numerical method. The study examines the effects of the nanoparticle volume fraction, the Rayleigh number and the geometry parameters on the mean Nusselt number. The results show that for all values of the Rayleigh number, the mean Nusselt number increases as the volume fraction of nanoparticles increases. In addition, it is shown that for a given length of the heated wall, extending the length of the cooled wall can improve the heat transfer performance.

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