Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I

1990 ◽  
Vol 429 (1877) ◽  
pp. 555-567 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Rayleigh Number ◽  
Thermal Model ◽  
Lewis Number ◽  
Reaction Model ◽  
Heat Of Reaction ◽  
Bifurcation Diagrams ◽  
Diffusion Term ◽  
The Impact ◽  
Species Diffusion

In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t /ln t + t /( t - 1) (1 < t ≼ 3.4955), ψ / R * = ( B Ls ) 2 (( t - 1)/ t ) exp{ - B Ls + B Ls / t } ln t , where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single­-valued, isola, inverse S , mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.

Natural convection effects on thermal ignition in a porous medium. I. Semenov model

1990 ◽  
Vol 429 (1877) ◽  
pp. 533-554 ◽  
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Lewis Number ◽  
Reaction Model ◽  
Heat Of Reaction ◽  
Thermal Ignition ◽  
Lumped Model ◽  
Convection Problem ◽  
Diffusion Convection

A one-dimensional diffusion-convection-reaction model is formulated to account for natural convection effects on thermal ignition in an open system consisting of a porous medium. Various limiting cases of the model are considered. A detailed analysis of the Semenov (lumped) model is presented. Explicit relations are derived for the dependence of the critical Semenov number ( ψ c ) on the Rayleigh number ( R *). It is shown that for R * → 0, ψ c approaches the classical (conduction) limit e -1 , while for R * ≫ 1, the ignition locus is given by the convection asymptote ψ c / R * = 4 e -2 . Inclusion of reactant consumption shows that the conduction asymptote disappears at B = 4 while the convection asymptote ceases to exist for B Ls < 3 + 2√2, where Ls is a modified Lewis number and B is the heat of reaction parameter. It is shown that the Semenov model has five different types of bifurcation diagrams of temperature against Rayleigh number (particle size), (single-valued, inverse S , isola, inverse S + isola and mushroom). This behaviour is found to be qualitatively identical to that of the forced convection problem investigated by Zeldovich & Zysin.

Stability Analysis of Cross Diffusion for the Walters B Fluid Model Saturated With Permeable Nanofluid

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
J. C. Umavathi ◽  
Ali J. Chamkha
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Fluid Model ◽  
Lewis Number ◽  
Double Fourier Series ◽  
Elastic Parameter ◽  
Cross Diffusion ◽  
Nusselt Numbers ◽  
Approach To Steady State ◽  
The Impact

Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.

scholarly journals Heat generating porous matrix effects on Brownian motion of nanofluid

2019 ◽  
Vol 29 (5) ◽  
pp. 1724-1740
Author(s):  
Aydin Zehforoosh ◽  
Siamak Hossainpour ◽  
Mohammad Mehdi Rashidi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Rayleigh Number ◽  
Porous Material ◽  
Volume Fraction ◽  
Matrix Effects ◽  
Internal Heat ◽  
Porous Matrix ◽  
Content Type ◽  
The Impact

Purpose The purpose of this study is to indicate the effect of mounting heat generating porous matrix in a close cavity on the Brownian term of CuO-water nanofluid and its impact on improving the Nusselt number. Design/methodology/approach Because of the presence of heat source in porous matrix, couple of energy equations is solved for porous matrix and nanofluid separately. Thermal conductivity and viscosity of nanofluid were assumed to be consisting of a static component and a Brownian component that were functions of volume fraction of the nanofluid and temperature. To explain the effect of the Brownian term on the flow and heat fields, different parameters such as heat conduction ratio, interstitial heat transfer coefficient, Rayleigh number, concentration of nanoparticles and porous material porosity were investigated and compared to those of the non-Brownian solution. Findings The Brownian term caused the cooling of porous matrix because of rising thermal conductivity. Mounting the porous material into cavity changes the temperature distribution and increases Brownian term effect and heat transfer functionality of the nanofluid. Besides, the effect of the Brownian term was seen to be greatest at low Rayleigh number, low-porosity and small thermal conductivity of the porous matrix. It is noteworthy that because of decrement of thermal conduction in high porosities, the impact of Brownian term drops severely making it possible to obtain reliable results even in the case of neglecting Brownian term in these porosities. Originality/value The effect of mounting the porous matrix with internal heat generation was investigated on the improvement of variable properties of nanofluid.

A Finite Difference Lattice Boltzmann Method to Simulate Multidimensional Subcontinuum Heat Conduction

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Cheng Chen ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Boltzmann Transport ◽  
Conduction Model ◽  
Total Energy Density ◽  
Diffusion Term ◽  
Boltzmann Method ◽  
The Impact

In this paper, a lattice Boltzmann method (LBM)-based model is developed to simulate the subcontinuum behavior of multidimensional heat conduction in solids. Based on a previous study (Chen et al., 2014, “Sub-Continuum Thermal Modeling Using Diffusion in the Lattice Boltzmann Transport Equation,” Int. J. Heat Mass Transfer, 79, pp. 666–675), phonon energy transport is separated to a ballistic part and a diffusive part, with phonon equilibrium assumed at boundaries. Steady-state temperature/total energy density solutions from continuum scales to ballistic scales are considered. A refined LBM-based numerical approach is applied to a two-dimensional simplified transistor model proposed by (Sinha et al. 2006, “Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors,” ASME J. Heat Transfer, 128(7), pp. 638–647), and the results are compared with the Fourier-based heat conduction model. The three-dimensional (3D) LBM model is also developed and verified at both the ballistic and continuous limits. The impact of film thickness on the cross-plane and in-plane thermal conductivities is analyzed, and a new model of the supplementary diffusion term is proposed. Predictions based on the finalized model are compared with the existing in-plane thermal conductivity measurements and cross-plane thermal conductivity molecular dynamics (MD) results.

scholarly journals Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet

2020 ◽  
Vol 9 (1) ◽  
pp. 233-243 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
P.V. Satya Narayana ◽  
Bhumarapu Venkateswarlu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Variable Thermal Conductivity ◽  
Normal Velocity ◽  
Transfer Coefficients ◽  
Similarity Transformations ◽  
Frictional Coefficients ◽  
The Impact

AbstractThe present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

Characteristics of Flame Bases for V-Gutters Stabilized Premixed Flames

2013 ◽  
Author(s):  
Fan Gong ◽  
Yong Huang
Keyword(s):  
Thermal Conductivity ◽  
Temperature Gradient ◽  
Equivalence Ratio ◽  
Premixed Flames ◽  
Flame Stabilization ◽  
Operating Conditions ◽  
Inlet Temperature ◽  
Heat Conducting ◽  
Inlet Velocity ◽  
The Impact

The objective of this work is to investigate the flame stabilization mechanism and the impact of the operating conditions on the characteristics of the steady, lean premixed flames. It’s well known that the flame base is very important to the existence of a flame, such as the flame after a V-gutter, which is typically used in ramjet and turbojet or turbofan afterburners and laboratory experiments. We performed two-dimensional simulations of turbulent premixed flames anchored downstream of the heat-conducting V-gutters in a confined passage for kerosene-air combustion. The flame bases are symmetrically located in the shear layers of the recirculation zone immediately after the V-gutter’s trailing edge. The effects of equivalence ratio of inlet mixture, inlet temperature, V-gutter’s thermal conductivity and inlet velocity on the flame base movements are investigated. When the equivalence ratio is raised, the flame base moves upstream slightly and the temperature gradient dT/dx near the flame base increases, so the flame base is strengthened. When the inlet temperature is raised, the flame base moves upstream very slightly, and near the flame base dT/dx increases and dT/dy decreases, so the flame base is strengthened. As the V-gutter’s thermal conductivity increases, the flame base moves downstream, and the temperature gradient dT/dx near the flame base decreases, so the flame base is weakened. When the inlet velocity is raised, the flame base moves upstream, and the convection heat loss with inlet mixture increases, so the flame base is weakened.

scholarly journals Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Variable Thickness ◽  
Heat Mass Transfer ◽  
Mathematical Formulation ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

2021 ◽  
pp. 2150145
Author(s):  
Shuang-Shuang Zhou ◽  
M. Ijaz Khan ◽  
Sumaira Qayyum ◽  
B. C. Prasannakumara ◽  
R. Naveen Kumar ◽  
...  
Keyword(s):  
Heat Source ◽  
Lewis Number ◽  
Solution Procedure ◽  
Energy Concentration ◽  
Gyrotactic Microorganisms ◽  
Dimensionless Parameters ◽  
Flow Equations ◽  
Fluid Parameter ◽  
Source Sink ◽  
The Impact

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

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