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.

scholarly journals Integration of Group Method Analysis and Rough Sets Theory to Investigate Heat and Mass Transfer of the Flow of a Non-Newtonian Nanofluid towards a Vertical Stretching Surface

2020 ◽  
Vol 13 (6) ◽  
pp. 393-404
Author(s):  
Hossam Nabwey ◽  
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Group Method ◽  
Stretching Surface ◽  
Method Analysis

This work reports how to utilize rough set theory and group method analysis for generating 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. By utilizing group method analysis, the main partial differential equations which describe the flow are rehabilitated to nonlinear Ordinary Differential Equations (ODEs). Then, the resultant nonlinear ODEs are solved numerically by applying the implicit finite-difference scheme. The numerical values thus obtained are depicted in tabular form and the basic principles of rough sets are applied to get all reducts and finally a group of generalized rules are extracted to predict the value of local Nusselt number and local skin-friction coefficient. The outcomes demonstrate the novelty of the current work which can be summarized as hybridization of group method analysis and rough set theory to use in the field of fluid dynamics effectively. The resultant set of generalized classification rules which performed with basic logic functions can be considered as knowledge base with high accuracy and may be valuable in many engineering applications like power production, thermal extrusion systems and microelectronics.

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.

Lie Group Analysis for a Mixed Convective Flow and Heat Mass Transfer Over a Permeable Stretching Surface with Soret and Dufour Effects

2013 ◽  
Vol 30 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Reda G. Abdel-Rahman ◽  
Ahmed M. Megahed
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Analysis ◽  
Group Method ◽  
Stretching Surface ◽  
Partial Differential ◽  
Soret And Dufour Effects

ABSTRACTThe Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

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.

Stagnation-Point Flow of a Jeffrey Nanofluid over a Stretching Surface with Induced Magnetic Field and Chemical Reaction

2015 ◽  
Vol 20 ◽  
pp. 93-111 ◽  
Author(s):  
Naramgari Sandeep ◽  
Chalavadi Sulochana ◽  
Isaac Lare Animasaun
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Stretching Surface ◽  
Jeffrey Nanofluid

With every passing day the heat transfer enhancement in the convectional base fluids plays a major role in several industrial and engineering processes. During these process nanofluids has attained its great importance to enhance the heat transfer rate in the convectional flows. Keeping this into view, in this study we investigated the stagnation point flow, heat and mass transfer behaviour of MHD Jeffrey nanofluid over a stretching surface in the presence of induced magneticfield, non-uniform heat source or sink and chemical reaction. Using similarity technique, the governing boundary layer partial differential equations are transformed into nonlinear coupled ordinary differential equations. The ordinary differential equations are solved numerically using Runge-Kutta-Felhberg scheme. An excellent agreement of the present results has been observed with the existed literature under some special cases. The effects of various dimensionless governing parameters on velocity, induced magneticfield, temperature and nanoparticle concentration profiles are discussed and presented through graphs. Also, friction factor, local Nusselt and Sherwood numbers are computed and discussed. Dual solutions are presented for suction and injection cases. It is found that dual solutions exist only for certain range of suction or injection parameter. It is also observed that an increase in the heat and mass transfer rate for higher values of Deborah number.

scholarly journals Soret and Dufour effects on mixed convection in a non-Darcy porous medium saturated with micropolar fluid

2011 ◽  
Vol 16 (1) ◽  
pp. 100-115 ◽  
Author(s):  
D. Srinivasacharya ◽  
Ch. RamReddy
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Micropolar Fluid ◽  
Local Similarity ◽  
Soret And Dufour Effects ◽  
Local Skin ◽  
Laminar Mixed Convection

In this paper, the Soret and Dufour effects on the steady, laminar mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a non-Darcy porous medium saturated with micropolar fluid are studied. The governing partial differential equations are transformed into ordinary differential equations. The local similarity solutions of the transformed dimensionless equations for the flow, microrotation, heat and mass transfer characteristics are evaluated using Keller-box method. Numerical results are presented in the form of velocity, microrotation, temperature and concentration profiles within the boundary layer for different parameters entering into the analysis. Also the effects of the pertinent parameters on the local skin friction coefficient and rates of heat and mass transfer in terms of the local Nusselt and Sherwood numbers are also discussed.

scholarly journals A BINARY CHEMICAL REACTION ON UNSTEADY FREE CONVECTIVE BOUNDARY LAYER HEAT AND MASS TRANSFER FLOW WITH ARRHENIUS ACTIVATION ENERGY AND HEAT GENERATION/ABSORPTION

2014 ◽  
Vol 44 (1) ◽  
pp. 97-104
Author(s):  
KH. A. MALEQUE
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Porous Plate ◽  
Local Similarity ◽  
Arrhenius Activation Energy

We investigate a local similarity solution of an unsteady natural convection heat and mass transfer boundary layer incompressible fluid flow past a moving vertical porous plate in the presence of the heat absorption and generation. The effects of chemical reaction rate which is function of temperature and Arrhenius activation energy on the velocity, temperature and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque, 2010a). Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim- Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity, temperature and concentration profiles. The corresponding skin friction coefficient, the Nusselt number and the Sherwood number are also calculated and displayed in table showing the effects of various parameters on them.

scholarly journals Effects of viscous dissipation on MHD flow with heat and mass transfer over a stretching surface with heat source, thermal stratification and chemical reaction

2011 ◽  
Vol 7 (1) ◽  
pp. 11-18 ◽  
Author(s):  
Naikotin Kishan ◽  
P. Amrutha
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Thermal Stratification ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Momentum Equation ◽  
Stretching Surface

This paper deals with the study of  nonlinear MHD flow, with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Boussinesq fluid on a vertical stretching surface with thermal stratification and chemical reaction by taking in to account the viscous dissipation effects. Adopting the similarity transformation, governing nonlinear partial differential equations of the problem are transformed to nonlinear ordinary differential equations. The Quasi-linearization technique is used for the non-linear momentum equation and then the numerical solution of the problem is derived using implicit finite difference technique, for different values of the dimensionless parameters. The numerical values obtained for velocity profiles, temperature profiles and concentration profiles are represent graphically in figures.  The results obtained show that the flow field is influenced appreciably by the presence of viscous dissipation, thermal stratification, chemical reaction and magnetic field.DOI: 10.3329/jname.v7i1.3254 

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.

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