Natural Convection in a Rectangular Porous Cavity With One Permeable Endwall

1983 ◽  
Vol 105 (4) ◽  
pp. 803-808 ◽  
Author(s):  
M. Haajizadeh ◽  
C. L. Tien
Keyword(s):  
Theoretical Study ◽  
Numerical Solutions ◽  
Constant Pressure ◽  
Experimental System ◽  
Governing Equations ◽  
Porous Cavity ◽  
Steady State Temperature ◽  
Shallow Cavity ◽  
Higher Temperature ◽  
Water Saturated

This paper describes a theoretical and experimental study of two-dimensional, buoyancy-driven flow in a rectangular porous cavity with one permeable endwall. Connected to a constant temperature tank, the permeable end allows for natural recharge and discharge of the saturating fluid. The other vertical endwall is impermeable and maintained at a constant but higher temperature, thus inducing a buoyancy-driven flow. The theoretical study includes an asymptotic analysis developed for a shallow cavity with one permeable endwall and the numerical solutions of the power-law difference representation of the full governing equations. The experimental system consists of water-saturated glass beads packed in a rectangular cavity with a length-to-height aspect ratio of 3.17, for which the Rayleigh number can vary up to 120. Measurements were made of the steady-state temperature distribution in the cavity and the heat transfer rate from the impermeable endwall. It is shown that the constant pressure and temperature assumptions at the permeable wall, as employed in the theoretical analysis, satisfactorily predict the experimental data. Results are also compared with those existing in the literature.

scholarly journals A Generalized Analytical Model for Joule Heating of Segmented Wires

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Vivekananthan Balakrishnan ◽  
Toan Dinh ◽  
Hoang-Phuong Phan ◽  
Dzung Viet Dao ◽  
Nam-Trung Nguyen
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Experimental Studies ◽  
Governing Equations ◽  
Steady State Temperature ◽  
The One ◽  
Good Agreement

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

scholarly journals Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Ponalagusamy ◽  
Ramakrishna Manchi
Keyword(s):  
Theoretical Study ◽  
Fluid Model ◽  
Porous Wall ◽  
Governing Equations ◽  
Rate Of Increase ◽  
Special Cases ◽  
Stenosed Artery ◽  
Flow Through ◽  
Two Fluid Model ◽  
Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Investigation of heat transfer in irregular porous cavity subjected to various boundary conditions

2019 ◽  
Vol 29 (1) ◽  
pp. 418-447 ◽  
Author(s):  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Outer Boundary ◽  
Governing Equations ◽  
Content Type ◽  
Porous Cavity ◽  
Various Boundary Conditions ◽  
Heating Source ◽  
Transfer Behavior ◽  
Vertical Walls

Purpose The purpose of this paper is to investigate the heat transfer in an arbitrary cavity filled with porous medium. The geometry of the cavity is such that an isothermal heating source is placed centrally at the bottom of the cavity. The height and width of the heating source is varied to analyses its effect on the heat transfer characteristics. The investigation is carried out for three different cases of outer boundary conditions such as two outside vertical walls being maintained at cold temperature To, two vertical and top horizontal surface being heated to. To and the third case with top surface kept at To but other surfaces being adiabatic. Design/methodology/approach Finite element method is used to solve the governing equations. Findings It is observed that the cavity exhibits unique heat transfer behavior as compared to regular cavity. The cases of boundary conditions are found to affect the heat transfer rate in the porous cavity. Originality/value This is original work representing the heat transfer in irregular porous cavity with various boundary conditions. This work is neither being published nor under review in any other journal.

Phase equilibria in NaAlSiO4–KAlSiO4–SiO2–H2O at 100 MPa pressure: equilibrium leucite composition and the enigma of primary analcime in blairmorites revisited

2014 ◽  
Vol 78 (1) ◽  
pp. 171-202 ◽  
Author(s):  
C. M. B. Henderson ◽  
D. L. Hamilton ◽  
J. P. Waters
Keyword(s):  
Mineral Assemblage ◽  
Volcanic Rocks ◽  
Stoichiometric Composition ◽  
Pressure Equilibrium ◽  
Upward Transport ◽  
Higher Temperature ◽  
Invariant Points ◽  
Water Saturated ◽  
Low K ◽  
Maximum Content

AbstractExperiments in the system NaAlSiO4(Ne)−KAlSiO4(Ks)−SiO2(Qz)−H2O at 100 MPa show that the maximum content of NaAlSi2O6 in leucite is ∼4 wt.% and that analcime is close to the stoichiometric composition (NaAlSi2O6.H2O). Analcime forms metastably on quenching the higher-temperature experiments; it is secondary after leucite in experiments quenched from 780°C, while from 850°C it forms by alteration of leucite, and by devitrification of water-saturated glass. Both processes involve reaction with Na-rich aqueous fluids. Stable analcime forms at 500°C, well below the solidus, and cannot form as phenocrysts in shallow volcanic systems. New data for natural analcime macrocrysts in blairmorites are presented for the Crowsnest volcanics, Alberta, Canada. Other researchers have suggested that primary analcime occurs as yellow-brown, glassy, analcime phenocrysts. Our microprobe analyses show that such primary analcime is close to stoichiometric, with very low K2O (<0.1 wt.%), minor Fe2O3 (0.5−0.8 wt.%) and CaO (∼0.5 wt.%). An extrapolation of published experimental data for Ne−Ks−Qz at >500 MPa PH2O, where Anl + melt coexist, suggests that at >800 MPa two invariant points are present: (1) a reaction point involving Kf + Ab + Anl + melt + vapour; and (2) a eutectic with Kf + Anl + Ne + melt + vapour. We suggest that the nepheline-free equilibrium mineral assemblage for Crowsnest samples is controlled by reaction point (1). In contrast, blairmorites from Lupata Gorge, Mozambique, form at eutectic (2), consistent with the presence of nepheline phenocrysts. Our conclusions, based on high- vs. low-pressure experiments, confirm the suggestion made by other authors, that Crowsnest volcanic rocks must have been erupted explosively to preserve glassy analcime phenocrysts during very rapid, upward transport from deep in the crust (H2O pressures ≫500 MPa). Only rare examples survived the deuteric and hydrothermal alteration that occurred during and after eruption.

Effects of Viscous Dissipation and Radiation on MHD Natural Convection in Oblique Porous Cavity with Constant Heat Flux

2017 ◽  
Vol 9 (2) ◽  
pp. 463-484 ◽  
Author(s):  
Ammar I. Alsabery ◽  
Habibis Saleh ◽  
Ishak Hashim
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Viscous Dissipation ◽  
Inclination Angle ◽  
Hartmann Number ◽  
Constant Heat Flux ◽  
Governing Equations ◽  
Constant Heat ◽  
Left Wall ◽  
Porous Cavity

AbstractEffects of viscous dissipation and radiation on MHD natural convection in oblique porous cavity with constant heat flux is studied numerically in the present article. The right inclined wall is maintained at a constant cold temperatureTcand the left inclined wall has a constant heat fluxqwith lengthS, while the remainder of the left wall is adiabatic. The horizontal walls are assumed to be adiabatic. The governing equations are obtained by applying the Darcy model and Boussinesq approximations. COMSOL's finite element method is used to solve the non-dimensional governing equations together with specified boundary conditions. The governing parameters of this study are Rayleigh number (Ra=10,100,200,250,500 and 1000), Hartmann number (0≤Ha≤20), inclination angle of the magnetic field (0° ≤ω≤π/2), Radiation (0≤R≤15), the heater flux length (0.1≤H≤1) and inclination angle of the sloping wall (–π/3≤ϕ≤π/3). The results are considered for various values of the governing parameters in terms of streamlines, isotherms and averageNusselt number. It is found that the intensity of the streamlines and the isotherm patterns decrease with an increment in Hartmann number. The overall heat transfer is significantly increased with the increment of the viscous dissipation and the radiation parameters.

scholarly journals Transient free convection in an inclined square porous cavity filled with a nanofluid using LTNE and Buongiorno’s models

2018 ◽  
Vol 240 ◽  
pp. 03014
Author(s):  
Mikhail Sheremet ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Inclination Angle ◽  
Equilibrium Temperature ◽  
Brownian Diffusion ◽  
Governing Equations ◽  
Nanofluid Flow ◽  
Porous Cavity ◽  
Flow And Heat Transfer ◽  
The Finite Difference Method ◽  
Porous Enclosure

The combined effect of Brownian diffusion, thermophoresis and cavity inclination angle on natural convective heat transfer in an inclined porous enclosure has been studied numerically. Fluid containing nanoparticles of low concentration circulates inside the cavity under the effect of the buoyancy force. Governing equations with corresponding boundary conditions formulated using the non-dimensional stream function and vorticity variables have been solved by the finite difference method. An influence of the cavity inclination angle, Darcy and Nield numbers on nanofluid flow and heat transfer has been investigated. It has been found that high Nield numbers illustrate more equilibrium temperature distribution inside the porous cavity.

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