Erratum: “Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference” (Journal of Heat Transfer, 1978, 100, pp. 191–198)

1983 ◽  
Vol 105 (3) ◽  
pp. 683-684 ◽  
Author(s):  
A. Bejan ◽  
C. L. Tein
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Temperature Difference ◽  
End To End

Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference

1978 ◽  
Vol 100 (2) ◽  
pp. 191-198 ◽  
Author(s):  
A. Bejan ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Temperature Difference ◽  
Transfer Rate ◽  
Horizontal Cylinder ◽  
Horizontal Layer ◽  
Parallel Plates ◽  
End To End

Natural convection in a porous medium filling a slender horizontal space with an end-to-end temperature difference is studied analytically. The end-to-end temperature difference gives rise to a horizontal counterflow pattern augmenting the heat transfer rate through the porous medium. Two basic geometries are considered: horizontal layer confined between two adiabatic and impermeable parallel plates, and horizontal cylinder surrounded by an adiabatic and impermeable cylindrical surface. Nusselt number relations are derived in terms of the Rayleigh number and the cavity aspect ratio. The end-wall permeability is shown to affect the heat transfer rate through the medium.

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.

THE COEFFICIENT OF HEAT TRANSFER FOR VERTICAL SURFACES IN STILL AIR

1937 ◽  
Vol 15a (7) ◽  
pp. 109-117
Author(s):  
R. Ruedy
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Loss ◽  
Temperature Difference ◽  
Plane Surface ◽  
Vertical Plane ◽  
Black Body ◽  
Average Temperature ◽  
Fourth Root

For a vertical plane surface in still air the coefficient of heat transfer, valid within the range of temperatures occurring in buildings, depends on the temperature and the height of the surface. If black body conditions are assumed for the heat lost by radiation, the coefficient is equal to 1.39, 1.50, 1.62, and 1.73 B.t.u. per sq. ft. per ° F. at 32°, 50°, 68°, and 86° F. respectively, the height of the heated surfaces being 100 cm. Convection is responsible for about one-third, and radiation, mainly in the region of 10 microns, for about two-thirds of the heat loss. Convection currents depend on the temperature difference, while radiation depends on the average temperature. When attempts are made to stop convection currents by placing obstacles across the surface, the loss of heat due to natural convection varies inversely as the fourth root of the height, providing that the nature of the flow of air remains unchanged.

2D Natural Convection and Radiation Heat Transfer Simulations of a PWR Fuel Assembly Within a Constant Temperature Support Structure

2006 ◽  
Author(s):  
Pablo E. Araya Go´mez ◽  
Miles Greiner
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fuel Assembly ◽  
Heat Generation ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Fuel Rods ◽  
Water Reactor

Two-dimensional simulations of steady natural convection and radiation heat transfer for a 14×14 pressurized water reactor (PWR) spent nuclear fuel assembly within a square basket tube of a typical transport package were conducted using a commercial computational fluid dynamics package. The assembly is composed of 176 heat generating fuel rods and 5 larger guide tubes. The maximum cladding temperature was determined for a range of assembly heat generation rates and uniform basket wall temperatures, with both helium and nitrogen backfill gases. The results are compared with those from earlier simulations of a 7×7 boiling water reactor (BWR). Natural convection/radiation simulations exhibited measurably lower cladding temperatures only when nitrogen is the backfill gas and the wall temperature is below 100°C. The reduction in temperature is larger for the PWR assembly than it was for the BWR. For nitrogen backfill, a ten percent increase in the cladding emissivity (whose value is not well characterized) causes a 4.7% reduction in the maximum cladding to wall temperature difference in the PWR, compared to 4.3% in the BWR at a basket wall temperature of 400°C. Helium backfill exhibits reductions of 2.8% and 3.1% for PWR and BWR respectively. Simulations were performed in which each guide tube was replaced with four heat generating fuel rods, to give a homogeneous array. They show that the maximum cladding to wall temperature difference versus total heat generation within the assembly is not sensitive to this geometric variation.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

Natural Convection Inside a Bidisperse Porous Medium Enclosure

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Arunn Narasimhan ◽  
B. V. K. Reddy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Solid Phase ◽  
Darcy Number ◽  
The Core ◽  
Side Walls ◽  
Porous Blocks ◽  
Rayleigh Numbers

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks (N2), macropore volume fraction (ϕE), and internal Darcy number (DaI) for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both DaI and DaE. At low Ra values, Nu is strongly affected by both DaI and ϕE. When N2 is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of Raϕ, DaE, DaI, and N2. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, RaϕDaE.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

2019 ◽  
Vol 29 (8) ◽  
pp. 2524-2544 ◽  
Author(s):  
Mikhail A. Sheremet ◽  
Ioan Pop ◽  
A. Cihat Baytas
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Good Control ◽  
Solid Matrix ◽  
Content Type ◽  
Practical Applications ◽  
Nanofluid Viscosity ◽  
Non Equilibrium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

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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