Natural Convection From a Pipe Buried in a Porous Medium With Variable Permeability

2003 ◽  
Author(s):  
C. C. Ngo ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat Loss ◽  
Flow Patterns ◽  
Numerical Calculations ◽  
Buried Pipe ◽  
Variable Permeability ◽  
Wide Range

Natural convection from a buried pipe with a layer of backfill is numerically examined in this study. The objective of the present study is to investigate how a change in the permeability of the backfill would affect the flow patterns and heat transfer results. Numerical calculations have covered a wide range of the governing parameters (i.e., 10 ≤ Ra1 ≤ 500 and 0.1 ≤ K1/K2 ≤ 10) for various backfill thicknesses (0.5 ≤ t/ri ≤ 2). The results suggest that a more permeable backfill can minimize the heat loss and confine the flow to a region close to the pipe.

Effects of Backfill on Heat Transfer From a Buried Pipe

2004 ◽  
Vol 127 (7) ◽  
pp. 780-784 ◽  
Author(s):  
C. C. Ngo ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Loss ◽  
Flow Patterns ◽  
Step Change ◽  
Numerical Calculations ◽  
Buried Pipe ◽  
Wide Range

Natural convection from a buried pipe with a layer of backfill is numerically examined in this study. The objective of the present study is to investigate how a step change in the permeability of the backfill would affect the flow patterns and heat transfer results. Numerical calculations have covered a wide range of the governing parameters (i.e., 10⩽Ra1⩽500 and 0.1⩽K1∕K2⩽10) for various backfill thicknesses (0.5⩽t∕ri⩽2). The results suggest that a more permeable backfill can minimize the heat loss and confine the flow to a region close to the pipe.

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.

Unsteady Conjugate Heat Transfer Investigation of a Multistage Steam Turbine in Warm-Keeping Operation With Hot Air

2018 ◽  
Author(s):  
Piotr Łuczyński ◽  
Dennis Toebben ◽  
Manfred Wirsum ◽  
Wolfgang F. D. Mohr ◽  
Klaus Helbig
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Flow Patterns ◽  
Operating Conditions ◽  
Angle Of Incidence ◽  
Time Step ◽  
Hot Air ◽  
Wide Range ◽  
Vortex Systems ◽  
Operating Points

In recent decades, the rising share of commonly subsidized renewable energy especially affects the operational strategy of conventional power plants. In pursuit of flexibility improvements, extension of life cycle, in addition to a reduction in start-up time, General Electric has developed a product to warm-keep high/intermediate pressure steam turbines using hot air. In order to optimize the warm-keeping operation and to gain knowledge about the dominant heat transfer phenomena and flow structures, detailed numerical investigations are required. Considering specific warm-keeping operating conditions characterized by high turbulent flows, it is required to conduct calculations based on time-consuming unsteady conjugate heat transfer (CHT) simulations. In order to investigate the warm-keeping process as found in the presented research, single and multistage numerical turbine models were developed. Furthermore, an innovative calculation approach called the Equalized Timescales Method (ET) was applied for the modeling of unsteady conjugate heat transfer (CHT). The unsteady approach improves the accuracy of the stationary simulations and enables the determination of the multistage turbine models. In the course of the research, two particular input variables of the ET approach — speed up factor (SF) and time step (TS) — have been additionally investigated with regard to their high impact on the calculation time and the quality of the results. Using the ET method, the mass flow rate and the rotational speed were varied to generate a database of warm-keeping operating points. The main goal of this work is to provide a comprehensive knowledge of the flow field and heat transfer in a wide range of turbine warm-keeping operations and to characterize the flow patterns observed at these operating points. For varying values of flow coefficient and angle of incidence, the secondary flow phenomena change from well-known vortex systems occurring in design operation (such as passage, horseshoe and corner vortices) to effects typical for windage, like patterns of alternating vortices and strong backflows. Furthermore, the identified flow patterns have been compared to vortex systems described in cited literature and summarized in the so-called blade vortex diagram. The comparison of heat transfer in the form of charts showing the variation of the Nusselt-numbers with respect to changes in angle of incidence and flow coefficients at specific operating points is additionally provided.

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.

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.

scholarly journals An efficient analytic approach for solving Hiemenz flow through a porous medium of a non-Newtonian Rivlin-Ericksen fluid with heat transfer

2018 ◽  
Vol 7 (4) ◽  
pp. 287-301
Author(s):  
Kourosh Parand ◽  
Yasaman Lotfi ◽  
Jamal Amani Rad
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Analytic Method ◽  
Analysis Method ◽  
Wide Range ◽  
Hiemenz Flow ◽  
Homotopy Analysis ◽  
Flow Through

AbstractIn the present work, the problem of Hiemenz flow through a porous medium of a incompressible non-Newtonian Rivlin-Ericksen fluid with heat transfer is presented and newly developed analytic method, namely the homotopy analysis method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This flow impinges normal to a plane wall with heat transfer. It has been attempted to show capabilities and wide-range applications of the homotopy analysis method in comparison with the numerical method in solving this problem. Also the convergence of the obtained HAM solution is discussed explicitly. Our reports consist of the effect of the porosity of the medium and the characteristics of the Non-Newtonian fluid on both the flow and heat.

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.

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