scholarly journals Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

2019 ◽  
Vol 9 (10) ◽  
pp. 2124 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ezad Hafidz Hafidzuddin ◽  
Nadihah Wahi
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Transfer Rate ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Thermal Relaxation ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Flow Past

The present study emphasizes the combined effects of double stratification and buoyancy forces on nanofluid flow past a shrinking/stretching surface. A permeable sheet is used to give way for possible wall fluid suction while the magnetic field is imposed normal to the sheet. The governing boundary layer with non-Fourier energy equations (partial differential equations (PDEs)) are converted into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. The approximate relative error between present results (using the boundary value problem with fourth order accuracy (bvp4c) function) and previous studies in few limiting cases is sufficiently small (0% to 0.3694%). Numerical solutions are graphically displayed for several physical parameters namely suction, magnetic, thermal relaxation, thermal and solutal stratifications on the velocity, temperature and nanoparticles volume fraction profiles. The non-Fourier energy equation gives a different estimation of heat and mass transfer rates as compared to the classical energy equation. The heat transfer rate approximately elevates 5.83% to 12.13% when the thermal relaxation parameter is added for both shrinking and stretching cases. Adversely, the mass transfer rate declines within the range of 1.02% to 2.42%. It is also evident in the present work that the augmentation of suitable wall mass suction will generate dual solutions. The existence of two solutions (first and second) are noticed in all the profiles as well as the local skin friction, Nusselt number and Sherwood number graphs within the considerable range of parameters. The implementation of stability analysis asserts that the first solution is the real solution.

A Numerical Study of Forced Convection Casson Nanofluid Flow Past a Wedge With Melting Process

2020 ◽  
Author(s):  
Mehari Fentahun Endalew ◽  
Subharthi Sarkar
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wedge Angle ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Casson Nanofluid ◽  
Flow Past ◽  
Highly Nonlinear

Abstract A numerical investigation is carried out to analyze steady two dimensional Casson nanofluid flow past a wedge with melting. The partial differential equations that govern the nanofluid flow are transformed into highly nonlinear coupled ordinary differential equations by employing similarity transformation. Thereafter, numerical solutions of these governing equations are obtained by MATLAB routine bvp4c. A special case of the present study is compared with an existing solution in literature and is found to be in good agreement. The effects of pertinent physical entities on the nanofluid velocity, nanofluid temperature, and nanoparticle concentration are represented graphically, while skin friction, Nusselt number, and Sherwood number are recorded in tabular form. We observed that, with an increase of wedge angle parameter, nanofluid velocity and local skin friction increase. However, when the melting parameter increases, nanofluid temperature and heat transfer rate decrease. This study would be useful in unfurling novel applications of Casson nanofluids in cooling devices and heat sinks.

scholarly journals Similarity Analysis for Effects of Variable Diffusivity and Heat Generation/Absorption on Heat and Mass Transfer for a MHD Stagnation-Point Flow of a Convective Viscoelastic Fluid over a Stretching Sheet with a Slip Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
H. M. El-Hawary ◽  
Mostafa A. A. Mahmoud ◽  
Reda G. Abdel-Rahman ◽  
Abeer S. Elfeshawey
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Slip Velocity ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Local Skin

A mathematical analysis has been carried out for stagnation-point heat and mass transfer of a viscoelastic fluid over a stretching sheet with surface slip velocity, concentration dependent diffusivity, thermal convective boundary conditions, and heat source/sink. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using Lie group analysis. Numerical solutions of the resulting ordinary differential equations are obtained using shooting method. The influences of various parameters on velocity, temperature, and mass profiles have been studied. Also, the effects of various parameters on the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are given in graphics form and discussed.

scholarly journals Aligned MHD Magnetic Nanofluid Flow Past a Static Wedge

2018 ◽  
Vol 7 (3.28) ◽  
pp. 28
Author(s):  
Mohd Rijal Ilias ◽  
Noraihan Afiqah Rawi ◽  
Noor Hidayah Mohd Zaki ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Magnetic Parameter ◽  
Fluid Velocity ◽  
Graphical Form ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Magnetic Nanofluid ◽  
Flow Past ◽  
Special Cases

The problem of steady aligned MHD magnetic nanofluid flow past a static wedge is studied in this paper. The present aligned magnetic field along with constant temperature at the surface is considered. The governing partial differential equations, subject to boundary conditions are transformed into ordinary differential equations using similarity transformations. The transformed equations are then solved numerically by Keller-box method. To check the validity of the present method, numerical results for dimensionless local skin friction coefficient and rate of heat transfer are compared with results of available literature as special cases and revealed in good agreement. The influence of pertinent parameters on velocity, temperature profiles, as well as wall shear stress and heat transfer rate is displayed in graphical form and discussed. It is found that fluid velocity increases with the increase of inclined angle, magnetic parameter and thermal buoyancy parameters while decreasing for increasing in nanoparticle volume fraction.  It is also noticed that magnetic parameter influences fluid velocity and temperature significantly.   

scholarly journals Non-Similar Comutational Solutions for Double-Diffusive MHD Transport Phenomena for Non-Newtnian Nanofluid From a Horizontal Circular Cylinder

2019 ◽  
Vol 8 (1) ◽  
pp. 470-485 ◽  
Author(s):  
V. Ramachandra Prasad ◽  
S. Abdul gaffar ◽  
B. Rushi Kumar
Keyword(s):  
Mass Transfer ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Skin Friction ◽  
Heat And Mass Transfer ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Physical Parameters

Abstract This article aims to study theoretically the combined magneto hydrodynamic flows of casson viscoplastic nanofluid from a horizontal isothermal circular cylinder in non-Darcy porous medium. The impacts of Brownian motion and thermophoresis are consolidated and studied. The governing partial differential equations are converted into nonlinear ordinary differential equations using suitable non-similarity transformation and are solved numerically using Keller-Box finite difference technique. The numerical method is validated with previous published work and the results are found to be in excellent agreement. Numerical results for velocity, temperature, concentration along with skin friction coefficient, heat and mass transfer rate are discussed for various values of physical parameters. It is observed that velocity, heat and mass transfer rate are increased with increasing casson fluid parameter whereas temperature, concentration and skin friction are decreased. Velocity is reduced with increasing Forchheimer parameter whereas temperature and nano-particle concentration are both enhanced. An increase in magnetic parameter is seen to increase temperature and concentration whereas velocity, skin friction heat and mass transfer rate are decreased. The present model finds applications in electric-conductive nano-materials of potential use in aviation and different enterprises, energy systems and thermal enhancement of industrial flow processes.

A Hybrid Methodology to Extract Decision Rules of Heat and Mass Transfer of the Flow of a Non-Newtonian Nanofluid Towards a Vertical Stretching Surface

2020 ◽  
Vol 9 (2) ◽  
pp. 121-127
Author(s):  
Hossam A. Nabwey
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Rough Set ◽  
Numerical Solutions ◽  
Rough Set Theory ◽  
Group Method ◽  
Stretching Surface ◽  
Local Skin ◽  
Method Analysis

In this paper a hybridization of group method analysis, hypergraph Principle and rough set theory is established for extracting a set of rules to investigate heat and mass transfer of mixed convection stagnation point flow of a non-Newtonian nanofluid towards a vertical stretching surface. First, the mathematical model describing the flow is transformed from a set of partial differential equations (PDEs) into non linear ordinary differential equations (ODEs) with the aid of group method analysis. Thereafter, the implicit finite-difference scheme is applied to find the numerical solutions of the nonlinear ODEs and the numerical values are depicted in tabular form. Then the reduction technique based on rough set is applied to find all reducts of the decision tables. Finally, the principle of hypergraph is applied to determine the minimal transversal of reducts and mining a set of generalized rules to predict the value of local Nusselt number and local skin-friction coefficient. The results show that the proposed method can effectively predict these values with high accuracy and may be valuable in many engineering applications like power production, thermal extrusion systems and microelectronics.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

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.

A novel approach on micropolar fluid flow in a porous channel with high mass transfer via wavelet frames

2021 ◽  
Vol 10 (1) ◽  
pp. 39-45
Author(s):  
S. Kumbinarasaiah ◽  
K.R. Raghunatha
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
High Mass ◽  
Porous Channel ◽  
Physical Parameters ◽  
Wavelet Frames ◽  
Parseval Frame ◽  
Highly Nonlinear ◽  
Frame Method

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

scholarly journals Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid.

2020 ◽  
Vol 17 ◽  
pp. 50-63
Author(s):  
N. T. M. Eldabe ◽  
Ahmed Refaie Ali ◽  
Gamil Ali Shalaby
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Viscoelastic Model ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Couple Stresses ◽  
Linear Differential

A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on the steady flow of non-Newtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. The considered non-Newtonian fluid follows a viscoelastic model. The problem is modulated mathematically by a system of non-linear differential equations pertaining to describe the continuity, momentum, energy, and concentration. These equations involve the effects of viscous dissipation and chemical reaction. The numerical solutions of the dimensionless equations are found as a function of the physical parameters of this problem. The numerical formulas of the velocity (u), temperature Φ and concentration Θ as well as skin friction coefficient T*, Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameter's effects of the problem on these formulas are described and illustrated graphically through some figures and tables. It is observed that any increase in the thermophoretic parameter T leads to reduce in velocity profiles as well as concentration layers. In contrast, the velocity increases with increasing the couple stresses inverse parameter.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

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