Entropy Generation Analysis of Radiated Magnetohydrodynamic Flow of Carbon Nanotubes Nanofluids with Variable Conductivity and Diffusivity Subjected to Chemical Reaction

2021 ◽  
Vol 10 (4) ◽  
pp. 491-505
Author(s):  
Gopinath Mandal ◽  
Dulal Pal
Keyword(s):  
Magnetic Field ◽  
Activation Energy ◽  
Carbon Nanotubes ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Entropy Generation ◽  
Concentration Profile ◽  
Fluid Temperature

The purpose of this article is to analyze the entropy generation and heat and mass transfer of carbon nano-tubes (CNTs) nanofluid by considering the applied magnetic field under the influence of thermal radiation, variable thermal conductivity, variable mass diffusivity, and binary chemical reaction with activation energy over a linearly stretching cylinder. Convective boundary conditions on heat and mass transfer are considered. An isothermal model of homogeneous-heterogeneous reactions is used to regulate the solute concentration profile. It is assumed that the water-based nanofluid is composed of single and multi-walled carbon nanotubes. Employing a suitable set of similarity transformations, the system of partial differential equations is transformed into the system of nonlinear ordinary differential equations before being solved numerically. Through the implementation of the second law of thermodynamics, the total entropy generation is calculated. In addition, entropy generation for fluid friction, mass transfer, and heat transfer is discussed. This study is specially investigated for the impact of the chemical reaction, and activation energy with entropy generation subject to distinct flow parameters. It is found that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with higher radiation parameters and thermal Biot number. Entropy and Bejan number are found to be an increasing function of solid volume fraction, magnetic field, and curvature parameters. Binary chemical reaction and activation energy on concentration profile have opposite effects.

scholarly journals Effects of Binary Chemical Reaction and Activation Energy on MHD Boundary Layer Heat and Mass Transfer Flow with Viscous Dissipation and Heat Generation/Absorption

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Kh. Abdul Maleque
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Porous Plate ◽  
Local Similarity

We study an unsteady MHD free convection heat and mass transfer boundary layer incompressible fluid flow past a vertical porous plate in the presence of viscous dissipation, heat generation/absorption, chemical reaction, and Arrhenius activation energy. The plate is moving with uniform velocity. The chemical reaction rate in the function of temperature is also considered. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque (2010)) and then are solved numerically by shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically as well as the tabular form for difference values of the various parameters.

scholarly journals Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Tesfaye Kebede ◽  
Eshetu Haile ◽  
Gurju Awgichew ◽  
Tadesse Walelign
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Analytic Approximation

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

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.

Magnetohydrodynamic flow of Carreau liquid over a stretchable sheet with a variable thickness

2020 ◽  
Vol 16 (5) ◽  
pp. 1277-1293 ◽  
Author(s):  
B. Mahanthesh
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Activation Energy ◽  
Mass Transfer ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Variable Thickness ◽  
Transfer Rate ◽  
Content Type ◽  
Biomedical Sensors

PurposeThe magnetohydrodynamic (MHD) flow problems are important in the field of biomedical applications such as magnetic resonance imaging, inductive heat treatment of tumours, MHD-derived biomedical sensors, micropumps for drug delivery, MHD micromixers, magnetorelaxometry and actuators. Therefore, there is the impact of the magnetic field on the transport of non-Newtonian Carreau fluid in the presence of binary chemical reaction and activation energy over an extendable surface having a variable thickness. The significance of irregular heat source/sink and cross-diffusion effects is also explored.Design/methodology/approachThe leading governing equations are constructed by retaining the effects of binary chemical reaction and activation energy. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. Subsequent nonlinear two-point boundary value problem is treated numerically by using the shooting method based on Runge–Kutta–Fehlberg. Graphical results are presented to analyze the behaviour of effective parameters involved in the problem. The numerical values of the mass transfer rate (Sherwood number) and heat transfer rate (Nusselt number) are also calculated. Furthermore, the slope of the linear regression line through the data points is determined in order to quantify the outcome.FindingsIt is established that the external magnetic field restricts the flow strongly and serves as a potential control mechanism. It can be concluded that an applied magnetic field will play a major role in applications like micropumps, actuators and biomedical sensors. The heat transfer rate is enhanced due to Arrhenius activation energy mechanism. The boundary layer thickness is suppressed by strengthening the thickness of the sheet, resulting in higher values of Nusselt and Sherwood numbers.Originality/valueThe effects of magnetic field, binary chemical reaction and activation energy on heat and mass transfer of non-Newtonian Carreau liquid over an extendable surface with variable thickness are investigated for the first time.

scholarly journals MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Reda G. Abdel-Rahman
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

scholarly journals Heat and Mass Transfer on MHD Flow of a Viscoelastic Fluid through Porous Media over a Shrinking Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
D. Bhukta ◽  
G. C. Dash ◽  
S. R. Mishra
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Temperature Field ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscoelastic Fluid ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Shrinking Sheet ◽  
Mass Transfer Effect

An attempt has been made to study the heat and mass transfer effect in a boundary layer flow through porous medium of an electrically conducting viscoelastic fluid over a shrinking sheet subject to transverse magnetic field in the presence of heat source. Effects of radiation, viscous dissipation, and uniform heat sink on the heat transfer have been considered. The method of solution involves similarity transformation. The coupled nonlinear partial differential equations representing momentum, concentration, and nonhomogenous heat equation are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved by applying Kummer’s function. The exact solution of temperature field is obtained for power-law surface temperature (PST) as well as power-law heat flux (PHF) boundary condition. The interaction of magnetic field is proved to be counterproductive in enhancing velocity and concentration distribution, whereas presence of porous matrix reduces the temperature field at all points.

Heat and Mass Transfer of a MHD Flows of An Oldroyd 8-Constant Nano-Fluid Through a Non-Darcy Porous Medium

2017 ◽  
Vol 14 (1) ◽  
pp. 321-329
Author(s):  
Abeer A Shaaban
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat And Mass Transfer ◽  
Induced Magnetic Field ◽  
Linear Ordinary Differential Equations ◽  
Nano Fluid ◽  
Non Linear

Explicit finite-difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which transform from the non-linear partial differential equations. These equations describe the steady magneto-hydrodynamic flow of an oldroyd 8-constant non-Newtonian nano-fluid through a non-Darcy porous medium with heat and mass transfer. The induced magnetic field was taken into our consideration. The numerical formula of the velocity, the induced magnetic field, the temperature, the concentration, and the nanoparticle concentration distributions of the problem were illustrated graphically. The effect of the material parameters (α1 α2), Darcy number Da, Forchheimer number Fs, Magnetic Pressure number RH, Magnetic Prandtl number Pm, Prandtl number Pr, Radiation parameter Rn, Dufour number Nd, Brownian motion parameter Nb, Thermophoresis parameter Nt, Heat generation Q, Lewis number Le, and Sort number Ld on those formula were discussed specially in the case of pure Coutte flow (U0 = 1, d <inline-formula> <mml:math display="block"> <mml:mrow> <mml:mover accent="true"> <mml:mi>P</mml:mi> <mml:mo stretchy="true">^</mml:mo> </mml:mover> </mml:mrow> </mml:math> </inline-formula> /dx = 0). Also, an estimation of the global error for the numerical values of the solutions is calculated by using Zadunaisky technique.

scholarly journals Heat and Mass Transfer Effects on MHD Flow Past an Inclined Porous Plate in the Presence of Chemical Reaction

2020 ◽  
Vol 25 (3) ◽  
pp. 86-102
Author(s):  
A. Sandhya ◽  
G.V. Ramana Reddy ◽  
G.V.S.R. Deekshitulu
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Mhd Flow ◽  
Transfer Effects ◽  
Partial Differential ◽  
Flow Past

AbstractThe impact of heat and mass transfer effects on an MHD flow past an inclined porous plate in the presence of a chemical reaction is investigated in this study. An effort has been made to explain the Soret effect and the influence of an angle of inclination on the flow field, in the presence of the heat source, chemical reaction and thermal radiation. The momentum, energy and concentration equations are derived as coupled second order partial differential equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless partial differential equations can be solved by using a closed analytical method. Numerical results for pertaining parameters, such as the Soret number (Sr), Grashof number (Gr) for heat and mass transfer, the Schmidt number (Sc), Prandtl number (Pr), chemical reaction parameter (Kr), permeability parameter (K), magnetic parameter (M), skin friction (τ), Nusselt number (Nu) and Sherwood number (Sh) on the velocity, temperature and concentration profiles are presented graphically and discussed qualitatively.

Heat and Mass Transfer in an Unsteady Magnetohydrodynamics Al2O3–Water Nanofluid Squeezed Between Two Parallel Radiating Plates Embedded in Porous Media With Chemical Reaction

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
R. A. Mohamed ◽  
S. Z. Rida ◽  
A. A. M. Arafa ◽  
M. S. Mubarak
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Heat Source ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Skin Friction Coefficient ◽  
Parallel Plates ◽  
Squeeze Number ◽  
Source Sink

Abstract In this paper, the influence of chemical reaction and heat source/sink on an unsteady magnetohydrodynamics (MHD) nanofluid flow that squeezed between two radiating parallel plates embedded in porous media is investigated analytically. We consider water as base fluid and aluminum oxide (Al2O3) as its nanoparticle. We reduced the basic partial differential equations to ordinary differential equations which are solved by the homotopy analysis method (HAM). The effects of the squeeze number, permeability parameter of porous media, Hartmann number, thermal radiation parameter, Prandtl number, heat source/sink parameter, Eckert number, Schmidt number, and scaled parameter of chemical reaction on the flow, heat, and mass transfer are considered and assigned to graphs. The physical quantities such as Sherwood number, Nusselt number, and skin friction coefficient are computed for Al2O3–water, TiO2–water, Ag–water, and Cu–water nanofluids and assigned through graphs.

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