scholarly journals Numerical Analysis of Thermal Non-Equilibrium in Porous Medium Subjected to Internal Heating

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1085 ◽  
Author(s):  
Badruddin
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Flow Behavior ◽  
New Method ◽  
Cold Surface ◽  
Porous Cavity ◽  
Solid Phases ◽  
Energy Equations ◽  
The Right ◽  
Non Equilibrium

Thermal non-equilibrium in porous medium is a prevailing condition when discrepancy of temperature exists between the two phases. The solution of a thermal non-equilibrium model requires that the two heat transport equations corresponding to fluid and solid phases, can be solved separately, which, in turn, provides the information of temperature variations of fluid as well as solid phases of the porous domain. A new method is proposed in the current article to solve the energy equations of the thermal non-equilibrium condition in a porous square cavity. The proposed method is able to predict the thermal equilibrium as well as thermal non-equilibrium accurately. The proposed method is used to investigate the heat transfer through the porous cavity subjected to two different boundary conditions with a heating strip being placed inside the porous cavity. It was found that the new method predicted the heat and fluid flow behavior accurately for the previously mentioned case studies. It is noted that the heat transfer is higher when the heating strip is placed toward the cold surface. The Nusselt number at the bottom of the strip toward the right side is almost 10 times higher than that of the left side of the strip.

Modeling Liquid Spray Evaporation in Heated Porous Media With a Local Thermal Non-Equilibrium Model

2004 ◽  
Author(s):  
Chendhil Periasamy ◽  
Sathish K. Sankara Chinthamony ◽  
S. R. Gollahalli
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Equation Model ◽  
Vapor Concentration ◽  
Computational Domain ◽  
Equilibrium Models ◽  
Radial Profiles ◽  
Energy Equations ◽  
Non Equilibrium

The situations such as rapid evaporation, and significant heat generation/convective heat transfer, typically encountered in liquid-fueled porous media combustors, warrant the use of local thermal non-equilibrium models. Knowledge of fuel vaporization and mixing is important to understand the combustion characteristics. In this paper, a two-energy equation model is presented to account for the non-equilibrium between the solid and liquid phases. In this approach, two energy equations for solid and gas phases were solved. Kerosene fuel, issued from an air-blast atomizer, was injected on to a heated porous medium. Governing equations were applied on a 2-D axisymmetric, computational domain of 20.3 cm × 2.5 cm. Computer simulations were conducted using a commercial code Fluent 6.0. Heat transfer from combustion porous medium was simulated by setting a volumetric heat source in the porous region. Accordingly, the peak temperatures in porous media varied from 473 K to 590 K. Axial temperature profiles within the porous media were obtained with equilibrium and non-equilibrium models. Results indicated that the equilibrium models slightly underpredicted the peak temperature. Using non-equilibrium models, radial profiles of kerosene vapor concentration were obtained at different axial locations and the results showed that the thermal effects of the porous medium dominated in the evaporation process. Numerical results were also compared with available data and the agreement was found to be good.

Local Thermal Non-equilibrium Analysis of Boundary Layer Flow of Carreau Fluid Over a Wedge in a Porous Medium

2021 ◽  
Author(s):  
Ramesh Kudenatti ◽  
Sandhya L
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Fluid Phase ◽  
Equilibrium Analysis ◽  
Local Thermal Equilibrium ◽  
Carreau Fluid ◽  
Layer Flow ◽  
Non Equilibrium

Abstract This work examines the steady two-dimensional mixed convection boundary layer flow of non-Newtonian Carreau fluid embedded in a porous medium. The impermeable wedge is at rest over which the momentum and thermal boundary layers form due to motion of Carreau fluid with a large Reynolds number. We consider local thermal non-equilibrium for which the temperature of the solid porous medium is different from that of fluid phase, and hence, a single heat-transport equation is replaced by a two-temperature model. The governed equations for flow and heat transfer are converted into a system of ordinary differential equations using a similarity approach. It is observed that local thermal non-equilibrium effects are dominant for small interphase heat transfer rate and porosity scaled conductivity parameters. It is shown that the temperature at any location of the solid porous medium is always higher than that of fluid phase. When these parameters are increased gradually the local thermal equilibrium phase is recovered at which the temperatures of the fluid and solid are identical at each pore. Similar trend is noticed for both shear-thinning and shear-thickening fluids. The results further show that heat exchange between the fluid and solid porous medium is similar to both assisted and opposed flows and Carreau fluid. The velocity and temperature fields for the various increasing fluid index, Grashof number and permeability show that the thickness of the momentum and thermal boundary layer is thinner.

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.

Stagnation Point Flow through a Porous Medium towards a Radially Stretching Sheet in the Presence of Uniform Suction or Injection and Heat Generation

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hazem Ali Attia ◽  
Karem Mahmoud Ewis ◽  
Mostafa A. M. Abdeen
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Uniform Suction ◽  
Flow Through ◽  
Energy Equations

An analysis is made of the steady laminar axisymmetric stagnation point flow of an incompressible viscous fluid in a porous medium impinging on a permeable radially stretching sheet with heat generation or absorption. A uniform suction or blowing is applied normal to the plate which is maintained at a constant temperature. Similarity transformation is used to transform the governing partial differential equations to ordinary differential equations. The finite difference method and generalized Thomas algorithm are used to solve the governing nonlinear momentum and energy equations. The effects of the uniform suction/blowing velocity, the stretching parameter and the heat generation/absorption coefficient on both the flow field and heat transfer are presented and discussed. The results indicate that increasing the stretching parameter or the suction/blowing velocity decreases both the velocity and thermal boundary layer thicknesses. The effect of the stretching parameter on the velocity components is more apparent for suction than blowing while its effect on the temperature and rate of heat transfer at the wall is clearer in the case of blowing than suction.

Numerical Investigation on Thermal and Fluid Dynamic Behavior of Laminar Slot-Jet Impinging on a Surface at Uniform Heat Flux in a Confined Porous Medium in Local Thermal Non-Equilibrium Conditions

2014 ◽  
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
Guy Lauriat
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Numerical Investigation ◽  
Forced Flow ◽  
Uniform Heat Flux ◽  
Nusselt Numbers ◽  
Uniform Heat ◽  
The Mean ◽  
Non Equilibrium

A numerical investigation on a single slot jet impinging in a porous parallel-plate channel containing an air-saturated high permeability porous medium is accomplished. The wall opposite the slot jet is partially heated at uniform heat flux and the buoyancy effects are taken into account. The fluid flow is assumed two dimensional, laminar and steady. The porous medium is modeled using the Brinkman–Forchheimer-extended Darcy model and the Boussinesq approximation. The local thermal non-equilibrium (LTNE) hypothesis is invoked. The results are discussed in terms of streamlines, fluid and solid phase temperature fields, wall temperature profiles and local and average Nusselt numbers. The porous medium allows a more significant heat transfer close to the end of the heated part of the plate. For low Peclet numbers, forced flow and natural convection are opposite and the mean Nusselt number shows a decrease in heat transfer, whereas they are aiding for high Peclet numbers. Porosity effects on the mean Nusselt numbers were found weak.

Heat transfer in a porous cavity with an internal heating strip towards cold surface

2020 ◽  
Vol 27 ◽  
pp. 1863-1868
Author(s):  
N. Ameer Ahamad ◽  
Azeem ◽  
Maughal Ahmed Ali Baig ◽  
J. Durga Prasad Reddy ◽  
Avala Raji Reddy
Keyword(s):  
Heat Transfer ◽  
Internal Heating ◽  
Cold Surface ◽  
Porous Cavity

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

2019 ◽  
Vol 29 (6) ◽  
pp. 1902-1919 ◽  
Author(s):  
Marina S. Astanina ◽  
Mikhail Sheremet ◽  
C. Jawali Umavathi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Porous Layer ◽  
Equilibrium Model ◽  
Local Heat ◽  
Darcy Number ◽  
Content Type ◽  
Porous Cavity ◽  
Variation Parameter ◽  
Non Equilibrium

Purpose The purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices. Design/methodology/approach The domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed. Findings The results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter. Originality/value An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

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