Bivariate Pseudo-Spectral Local Linearisation Method for Mixed Convective Flow Over the Vertical Frustum of a Cone in a Nanofluid with Soret and Viscous Dissipation Effects

2017 ◽  
Vol 33 (5) ◽  
pp. 687-702
Author(s):  
Ch. RamReddy ◽  
Ch. Venkata Rao
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Spectral Method ◽  
Viscous Dissipation ◽  
Surface Drag ◽  
Special Cases ◽  
Soret Number ◽  
Uniform Wall ◽  
Mixed Convective Flow ◽  
Pseudo Spectral

AbstractIn this investigation, we intend to present the influence of the prominent viscous dissipation and Soret effects on mixed convection heat and mass transfer over the vertical frustum of a cone in a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition, the uniform wall nanoparticle condition at the surface is replaced with the zero nanoparticle mass flux condition to execute physically applicable results. The governing equations of a nanofluid flow in the dimensional form are reduced to a system of partial differential equations in the non-dimensional form by using suitable non-similarity variables and then solved by using a recently introduced spectral method named as Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM). The convergence and error analysis tests are conducted to examine the accuracy of the spectral method. To validate the method, the present numerical results are compared with the existing results in some special cases and the outcomes are observed to be in very good agreement. The effects of Brownian motion, thermophoresis, Eckert number, Soret number, nanoparticle and regular buoyancy parameters on the dimensionless surface drag, heat, nanoparticle mass and regular mass transfer rates over the vertical frustum of a cone are discussed and illustrated graphically.

scholarly journals Lie Group Analysis of Natural Convective Flow from a Convectively Heated Upward Facing Radiating Permeable Horizontal Plate in Porous Media Filled with Nanofluid

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Md. Jashim Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Lie Group ◽  
Convective Flow ◽  
Group Analysis ◽  
Lie Group Analysis ◽  
Horizontal Plate ◽  
Transfer Rates ◽  
Special Cases

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed equations are solved numerically by Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Effects of the governing parameters on the dimensionless velocity, temperature and nanoparticle volume fraction as well as on the dimensionless rate of heat and mass transfer are presented graphically and the results are compared with the published data for special cases. Good agreement is found between numerical results of the present paper and published results. It is found that Lewis number, Brownian motion and convective heat transfer parameters increase the heat and mass transfer rates whilst thermophoresis decreases both heat and mass transfer rates.

scholarly journals Slip Effects on MHD Squeezing Flow of Jeffrey Nanofluid in Horizontal Channel with Chemical Reaction

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1215
Author(s):  
Nur Azlina Mat Noor ◽  
Sharidan Shafie ◽  
Mohd Ariff Admon
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Squeeze Flow ◽  
Squeezing Flow ◽  
Jeffrey Nanofluid

The heat and mass transfer characteristics on hydromagnetic squeeze flow of Jeffrey nanofluid between two plates over a permeable medium by slip condition with the influences of viscous dissipation and chemical reaction is examined. Buongiorno’s nanofluid model, which includes Brownian motion and thermophoresis impacts, is implemented in this research. The governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations via asimilarity transformation. The transformed equations are solved by employing numerical techniques of Keller-box. A comparison of the skin friction coefficient, Nusselt and Sherwood numbers with reported outputs in the journals are carried out to validate the present outputs. An excellent agreement is found. The results show that the squeezing of plates accelerates the velocity and wall shear stress. Furthermore, the velocity, temperature and concentration profile decrease when the Hartmann number and ratio of relaxation and retardation times increases. The raise in thermophoresis and viscous dissipation elevate the temperature profile and the heat transfer rate. Furthermore, the mass transfer rate declines due to the strong Brownian motion in the nanofluid, whereas it increases with the addition of chemical reaction and thermophoresis.

scholarly journals Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

2018 ◽  
Vol 3 (1) ◽  
pp. 255-264 ◽  
Author(s):  
F. Talay Akyildiz ◽  
K. Vajravelu
Keyword(s):  
Spectral Method ◽  
Parabolic Equations ◽  
Splitting Method ◽  
Higher Order ◽  
Two Dimensional ◽  
Order Accuracy ◽  
Special Cases ◽  
Linear Parabolic Equations ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

AbstractIn this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

Viscous Dissipation and Soret Effects on Non-Darcy Mixed Convective Flow Considering Nanofluids

2013 ◽  
Author(s):  
P. K. Kameswaran ◽  
P. Sibanda ◽  
A. S. N. Murti
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Convective Flow ◽  
Volume Fraction ◽  
Dimensionless Temperature ◽  
Governing Equations ◽  
Impermeable Wall ◽  
Mixed Convective Flow ◽  
Good Agreement

We investigate the steady boundary layer mixed convective flow over a horizontal impermeable wall embedded in a porous medium filled with a water-based nanofluid. The model used for the nanofluid incorporates the effects of the volume fraction parameter. The main objective of the present study is to investigate viscous dissipation and Soret effects on heat and mass transfer in a nanofluid containing Al2O3 and TiO2 nanoparticles. The temperature and concentrations at the wall were kept constant. A similarity transformation was used to obtain a system of nonlinear ordinary differential equations. The resulting nonlinear governing equations with associated boundary conditions were solved numerically using the Matlab bvp4c solver. The effects of viscous dissipation and the Soret parameter on dimensionless temperature, concentration, heat and mass transfer are presented graphically. It was observed that the heat transfer rate decreased with an increase in nanoparticle volume fraction. Comparison of current and previously published results (Lai and Kulaki [10], Arfin et al. [12]) showed a good agreement.

scholarly journals Three-Dimensional Nanofluid Flow with Heat and Mass Transfer Analysis over a Linear Stretching Surface with Convective Boundary Conditions

2018 ◽  
Vol 8 (11) ◽  
pp. 2244 ◽  
Author(s):  
Abdul Khan ◽  
Yufeng Nie ◽  
Zahir Shah ◽  
Abdullah Dawar ◽  
Waris Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Drag Force ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Radiation Parameter ◽  
Surface Drag ◽  
Motion Parameters ◽  
The Impact

In this study, we analyzed the three-dimensional flow of Williamson (pseudoplastic) fluids upon a linear porous stretching sheet. The thermal radiation impact was taken into account. The transformed non-linear equations were solved by the homotopy analysis method (HAM). The influence of the embedded parameters tretching parameter, Williamson parameter, porosity parameter, thermal radiation parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number and Biot number are presented on velocity, temperature and concentration functions in the graphs and explained in detail. The velocity function along the x-direction reduces with the impact of the stretching, porosity and Williamson parameters. Velocity along the y-direction increases with the stretching parameter, while it reduces with the porosity and Williamson parameters. The effect of Skin friction, heat transfer and mass transfer are shown numerically. The numerical values of surface drag force and the impact of different parameters are calculated and it is observed that increasing the stretching parameter and the porosity parameter reduces the surface drag force, while increasing the Williamson parameter augments the surface drag force. Higher values of the stretching parameter, the Prandtl number and the radiation parameter enhance the heat transfer rate, while the augmented value of the thermophoresis and Brownian motion parameters reduces the heat transfer rate, where higher values of the stretching parameter, thermophoresis and Brownian motion parameters enhance the mass transfer rate.

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