The Onset of Convection in an Internally Heated Nanofluid Layer

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Brownian Motion ◽  
Boundary Conditions ◽  
Microwave Heating ◽  
Chemical Reaction ◽  
Vertical Gradient ◽  
Horizontal Layer ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Brownian Motion And Thermophoresis ◽  
Heating From Below

We analytically studied the onset of convection, induced by internal heating, such as that produced by microwave heating or chemical reaction, in a horizontal layer of a nanofluid subject to Brownian motion and thermophoresis. This is a fundamentally different situation from traditionally studied heating from below. Convection, when it occurs, is now concentrated in the portion of the layer where the upward vertical gradient is negative, which is the upper portion of the layer. The situation of internal heating also allows employing more realistic boundary conditions than those hitherto used.

The Effect of Local Thermal Nonequilibrium on the Onset of Convection in a Nanofluid

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Heat Capacity ◽  
Brownian Motion ◽  
Small Particle ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Onset Of Convection ◽  
Thermal Nonequilibrium ◽  
Capacity Ratio ◽  
Brownian Motion And Thermophoresis ◽  
Local Thermal Nonequilibrium

The onset of convection in a horizontal layer of a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and allows for local thermal nonequilibrium (LTNE) between the particle and fluid phases. The analysis reveals that in some circumstances, the effect of LTNE can be significant, but for a typical dilute nanofluid (with large Lewis number and with small particle-to-fluid heat capacity ratio), the effect is small.

scholarly journals A Revised Model for Magneto Convection in Binary Nanofluids

2019 ◽  
Vol 4 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Jyoti Sharma ◽  
Urvashi Gupta ◽  
Shushant Shukla
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Normal Mode ◽  
Scale Effects ◽  
Onset Of Convection ◽  
Nano Scale ◽  
Brownian Motion And Thermophoresis ◽  
Mode Technique ◽  
Double Diffusive

The paper presents double-diffusive nanofluid convection under magnetic field using more realistic revised model in which boundaries are assumed to have zero nanoparticle flux. The nanofluid layer includes the nano scale effects (Brownian motion and thermophoresis) and solutal effects (Dufour and Soret). Impact of different parameters is analyzed using normal mode technique and interpreted graphically with the help of the software Mathematica. Complex expressions for oscillatory motions are solved using approximations to confirm their non-existence and onset of convection is established as stationary. Binary nanofluids are found to be much less stable than regular fluids. Higher conductivity of metallic nanofluids makes them less stable as compared to non-metallic nanofluids.

The thermohaline Rayleigh-Jeffreys problem

1967 ◽  
Vol 29 (3) ◽  
pp. 545-558 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Rayleigh Number ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stability Boundary ◽  
Boundary Curve ◽  
Solute Concentration ◽  
Horizontal Layer ◽  
Wave Number ◽  
Convection Cell ◽  
Onset Of Convection

The onset of convection induced by thermal and solute concentration gradients, in a horizontal layer of a viscous fluid, is studied by means of linear stability analysis. A Fourier series method is used to obtain the eigenvalue equation, which involves a thermal Rayleigh numberRand an analogous solute Rayleigh numberS, for a general set of boundary conditions. Numerical solutions are obtained for selected cases. Both oscillatory and monotonic instability are considered, but only the latter is treated in detail. The former can occur when a strongly stabilizing solvent gradient is opposed by a destablizing thermal gradient. When the same boundary equations are required to be satisfied by the temperature and concentration perturbations, the monotonic stability boundary curve in the (R, S)-plane is a straight line. Otherwise this curve is concave towards the origin. For certain combinations of boundary conditions the critical value ofRdoes not depend onS(for some range ofS) or vice versa. This situation pertains when the critical horizontal wave-number is zero.A general discussion of the possibility and significance of convection at ‘zero’ wave-number (single convection cell) is presented in an appendix.

Onset and Development of Natural Convection Above a Suddenly Heated Horizontal Surface

1995 ◽  
Vol 117 (4) ◽  
pp. 808-821 ◽  
Author(s):  
R. J. Goldstein ◽  
R. J. Volino
Keyword(s):  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Fluid Motion ◽  
Horizontal Layer ◽  
Onset Of Convection ◽  
Surface Convection ◽  
Heating From Below ◽  
Conduction Layer ◽  
Moving Pattern

The onset and development of flow in a thick horizontal layer subject to a near-constant flux heating from below has been studied experimentally. The overall heat-flux-based Rayleigh number, Ra*, ranges from 2 × 108 to 7 × 1010. Flow visualization shows the growth and breakdown of a conduction layer adjacent to the heated surface. Convection is characterized by the release of warm meandering plumes and thermals from a boundary layer. The planform of convection at the heated surface begins with a pattern of small spots suggestive of Be´nard cells. Some of these cells expand, forming a larger cell pattern. This continues until a quasi-steady state is reached in which the former cell boundaries form a slowly moving pattern of warm lines on the heated surface. The lines are believed to be the source of the plumes and thermals. Quantitatively, the onset of convection occurs at a constant (critical) Rayleigh number based on the conduction layer thickness, Raδ. Based on the first observation of fluid motion, this critical Rayleigh number is approximately 1300. Based on the heated surface temperature the critical Rayleigh number is 2700. The nondimensional wavenumber associated with the observed instabilities at the onset of convection is about 2.2.

scholarly journals Influence of Chemical Reaction on the Heat and Mass Transfer of Nanofluid Flow Over a Nonlinear Stretching Sheet: A Numerical Study

2020 ◽  
Vol 25 (2) ◽  
pp. 103-121
Author(s):  
Santoshi Misra ◽  
K. Govardhan
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Similarity Transformations ◽  
Brownian Motion And Thermophoresis ◽  
Layer Flow ◽  
Predictor Corrector

AbstractA numerical study on a steady, laminar, boundary layer flow of a nanofluid with the influence of chemical reaction resulting in the heat and mass transfer variation is made. The non-linear governing equations with related boundary conditions are solved using Adam’s predictor corrector method with the effect of a Brownian motion and thermophoresis being incorporated as a model for the nanofluid, using similarity transformations. Validation of the current numerical results has been made in comparison to the existing results in the absence of chemical reaction on MHD flows. The numerical solutions obtained for the velocity, temperature and concentration profiles for the choice of various parameters are represented graphically. Variations of heat and mass transfer across a Brownian motion and thermophoresis are studied and analyzed.

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