Notes on Steady Natural Convection Heat Transfer by Double Diffusion From a Heated Cylinder Buried in a Saturated Porous Media

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Carlos Alberto Chaves ◽  
Wendell de Queiroz Lamas ◽  
Luiz Eduardo Nicolini do Patrocinio Nunes ◽  
Jose Rui Camargo ◽  
Francisco Jose Grandinetti
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Heat Transfer ◽  
Double Diffusion ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Number Range ◽  
Heated Cylinder

This paper aims to present numerical solutions for the problem of steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous media exposed to constant uniform temperature and concentration in the cylinder and in the media surface. A square finite domain 3 × 3 and acceptance criterion converged solution with an absolute error under 1 × 10−3 were considered to obtain results presented. The Patankar's power law for approaching of variables calculated T, C, and ϕ also was adopted. In order of method validation, an investigation of mesh points number as function of Ra, Le, and N was done. A finite volume scheme has been used to predict the flow, temperature, and concentration distributions at any space from a heat cylinder buried into a fluid-saturated porous medium for a bipolar coordinates system. Examples presented show that the differences in the flow distribution caused not only when Rayleigh number range is considered but also when Lewis number range is considered. Further, increase in the Rayleigh number has a significant influence in the flow distribution when the concentration distribution is considered. Steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous medium is studied numerically using the finite volume method. To model fluid flow inside the porous medium, the Darcy equation is used. Numerical results are obtained in the form of streamlines, isotherms, and isoconcentrations. The Rayleigh number values range from 0 to 1000, the Lewis number values range from 0 to 100, and the buoyancy ratio number is equal to zero. Calculated values of average heat transfer rates agree reasonably well with values reported in the literature.

Experiments and Theory on Natural Convection Heat Transfer From Bodies of Complex Shape

1985 ◽  
Vol 107 (3) ◽  
pp. 624-629 ◽  
Author(s):  
M. J. Chamberlain ◽  
K. G. T. Hollands ◽  
G. D. Raithby
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Complex Shape ◽  
Convection Heat Transfer ◽  
Average Error ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Transient Method ◽  
Number Range

Measurements of the heat transfer by natural convection from isothermal bodies to air are reported and compared to the predictions of the method proposed by Raithby and Hollands [7, 8]. The bodies tested were the cube in various orientations and a body consisting of two touching spheres (a bisphere). The experimental Rayleigh number range extended from 10 to 107. The experimental method incorporated measuring the heat transfer by the transient method and varying the Rayleigh number by varying the pressure. The predictions agreed with the measurements to within an average error of about 3 percent. The results are correlated by single equations, which can be extended to fluids other than air.

scholarly journals Free Convection Heat Transfer from Horizontal Cylinders

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 559
Author(s):  
Janusz T. Cieśliński ◽  
Slawomir Smolen ◽  
Dorota Sawicka
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Free Convection ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Correlation Equations ◽  
Convection Heat ◽  
Number Range ◽  
Heated Cylinder ◽  
Free Convection Heat

The results of experimental investigation of free convection heat transfer in a rectangular container are presented. The ability of the commonly accepted correlation equations to reproduce present experimental data was tested as well. It was assumed that the examined geometry fulfils the requirement of no-interaction between heated cylinder and bounded surfaces. In order to check this assumption recently published correlation equations that jointly describe the dependence of the average Nusselt number on Rayleigh number and confinement ratios were examined. As a heat source served electrically heated horizontal tube immersed in an ambient fluid. Experiments were performed with pure ethylene glycol (EG), distilled water (W), and a mixture of EG and water at 50%/50% by volume. A set of empirical correlation equations for the prediction of Nu numbers for Rayleigh number range 3.6 × 104 < Ra < 9.2 × 105 or 3.6 × 105 < Raq < 14.8 × 106 and Pr number range 4.5 ≤ Pr ≤ 160 has been developed. The proposed correlation equations are based on two characteristic lengths, i.e., cylinder diameter and boundary layer length.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

Influence of Cu-Water and CNT-Water Nanofluid on Natural Convection Heat Transfer in a Triangular Solar Collector

2020 ◽  
Author(s):  
Didarul Ahasan Redwan ◽  
Md. Habibur Rahman ◽  
Hasib Ahmed Prince ◽  
Emdadul Haque Chowdhury ◽  
M. Ruhul Amin
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Solar Collector ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Abstract A numerical study on natural convection heat transfer in a right triangular solar collector filled with CNT-water and Cuwater nanofluids has been conducted. The inclined wall and the bottom wall of the cavity are maintained at a relatively lower temperature (Tc), and higher temperature (Th), respectively, whereas the vertical wall, is kept adiabatic. The governing non-dimensional partial differential equations are solved by using the Galerkin weighted residual finite element method. The Rayleigh number (Ra) and the solid volume-fraction of nanoparticles (ϕ) are varied in the range of 103 ≤ Ra ≤ 106, and 0 ≤ ϕ ≤ 0.1, respectively, to carry out the parametric simulations within the laminar region. Corresponding thermal and flow fields are presented via isotherms and streamlines. Variations of average Nusselt number as a function of Rayleigh number have been examined for different solid volume-fraction of nanoparticles. It has been found that the natural convection heat transfer becomes stronger with the increment of solid volume fraction and Rayleigh number, but the strength of circulation reduces with increasing nanoparticles’ concentration at low Ra. Conduction mode dominates for lower Ra up to a certain limit of 104. It is also observed that when the solid volume fraction is increased from 0 to 0.1 for a particular Rayleigh number, the average Nusselt number is increased to a great extent, but surprisingly, the rate of increment is more pronounced at lower Ra. Moreover, it is seen that Cu-water nanofluid offers slightly better performance compared to CNT-water but the difference is very little, especially at lower Ra.

Numerical analysis of natural convection heat transfer and entropy generation in a porous quadrantal cavity

2019 ◽  
Vol 29 (12) ◽  
pp. 4826-4849 ◽  
Author(s):  
Shantanu Dutta ◽  
Arup Kumar Biswas ◽  
Sukumar Pati
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Bottom Wall ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Uniform Temperature ◽  
Content Type ◽  
Temperature Heating

Purpose The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall. Design/methodology/approach Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 103 to 106 and Darcy number (Da) in the range of 10−5-10−2. Findings A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (103, 104), while there is a significant alteration in Nusselt number for Ra ≥105 and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤104), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=106) and Da (=10−2). Practical implications From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems. Originality/value This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.

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