Mixed convective 3D flow of Maxwell nanofluid induced by stretching sheet: Application of Cattaneo-Christov theory

2020 ◽  
pp. 095440622097324
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Jawad Ahmed ◽  
Asia Anjum ◽  
Sohail Nadeem
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Maxwell Fluid ◽  
Brownian Diffusion ◽  
Flow Mechanism ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Text Component

The present study invokes the application of Cattaneo-Christov theory for the thermal analysis in the buoyancy driven three dimensional flow of Maxwell nanofluid. The flow is induced above the vertical bidirectional stretching sheet. The phenomena of thermophoresis and Brownian diffusion of nanoparticles in the flow Maxwell liquid are deliberated with the help of Buongiorno model for nanofluid. The physical problem is formulated in the form of boundary layer partial differential equations (PDEs). Moreover, suitable ansatz for flow mechanism are employed to reduce the governing PDEs into the non-linear ordinary differential equations (ODEs). The flow mechanism of Maxwell fluid along with energy transport is analyzed in the form of homotopic solutions of the governing ODEs. The outcomes are presented graphically and discussed with physical explanation. The analysis revealed that both buoyancy and mixed convection parameters enhanced the [Formula: see text]-component of velocity field but declined the [Formula: see text]-component. Moreover, in assisting mode these two parameters also increased the thermal and solutal energy transport in nanofluid. It is noted that the thermophorectic force boosts up the thermal energy transport in the flow in the presence of thermal relaxation phenomenon. The validation of the present results are confirmed through tabular data with some previous studies.

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.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

MHD Reacting and Radiating 3-D Flow of Maxwell Fluid Past a Stretching Sheet with Heat Source/Sink and Soret Effects in a Porous Medium

2018 ◽  
Vol 387 ◽  
pp. 145-156 ◽  
Author(s):  
Sure Geethan Kumar ◽  
S. Vijaya Kumar Varma ◽  
Putta Durga Prasad ◽  
Chakravarthula S.K. Raju ◽  
Oluwole Daniel Makinde ◽  
...  
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Stretching Sheet ◽  
Soret Effect ◽  
Linear Equations ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Source Sink

In this study, we numerically investigate the hydromagnetic three dimensional flow of a radiating Maxwell fluid over a stretching sheet embedded in a porous medium with heat source/sink, first ordered chemical reaction and Soret effect. The corresponding boundary layer equations are reduced into set of non-linear ordinary differential equations by means of similarity transformations. The resulting coupled non-linear equations are solved numerically by employing boundary value problem default solver in MATLAB bvp4c package. The obtained results are presented and discussed through graphs and tables. It is noticed that the Deborah number reduces the velocity fields and improves the temperature and concentration fields. Nomenclature

Implicit Homotopy Perturbation Method for MHD Non-Newtonian Nanofluid Flow with Cattaneo-Christov Heat Flux Due to Parallel Rotating Disks

2019 ◽  
Vol 8 (8) ◽  
pp. 1648-1653
Author(s):  
Mohamed Y. Abou-Zeid
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Tangential Velocity ◽  
Thermal Relaxation ◽  
Physical Parameters ◽  
Rotating Disks ◽  
Linear Ordinary Differential Equations ◽  
Homotopy Perturbation

This article deals with the influence of Cattaneo-Christov heat flux on MHD flow of biviscosity nanofluid between two rotating disks through a porous media. Von Karman transformations are used to transform system of partial differential equations to non-linear ordinary differential equations. This system are solved by using homotopy perturbation method. Numerical results for the behaviors of the radial, axial and tangential velocities, temperature and nanoparticles with the physical parameters of the problem are obtained. These results are depicted graphically and discussed in details. The obtained results show that the tangential velocity increases with the increase of both the stretching and rotation parameters. Moreover, it is found that the stretching and thermal relaxation parameters increase the temperature, while they increase or decrease the nanoparticles concentration. Comparison between the obtained results and those obtained by other researchers is made during this study.

scholarly journals Numerical Study of Radiative Magnetohydrodynamics Viscous Nanofluid Due to Convective Stretching Sheet with the Chemical Reaction Effect

2020 ◽  
pp. 1733-1744
Author(s):  
G Narender ◽  
K Govardhan ◽  
G Sreedhar Sarma
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Similarity Transformation ◽  
Numerical Study ◽  
Concentration Profiles ◽  
Linear Ordinary Differential Equations ◽  
Order Four

A numerical investigation was performed for the radiative magnetohydrodynamic (MHD) viscous nanofluid due to convective stretching sheet. Heat and mass transfer were investigated in terms of viscous dissipations, thermal radiation and chemical reaction. The governing Partial Differential Equations (PDEs) were transformed into an arrangement of non-linear Ordinary Differential Equations (ODEs) by using the similarity transformation. The resulting system of ODEs is solved numerically by using shooting method along with Adams-Moulton Method of order four with the help of the computational software FORTAN. Furthermore, we compared our results with the existing results for especial cases. which are in an excellent agreement. Thenumerical solution obtained the velocity, temperature and concentration profiles. The figures showed differences among the parameters. Moreover, the numerical values of Nusselt and Sherwood numbers were presented and analyzed through tables.

Effect of Chemical Reaction on Maxwell Nanofluid Slip Flow over a Stretching Sheet

2018 ◽  
Vol 17 (1) ◽  
Author(s):  
B.C. Prasannakumara ◽  
M. Gnaneswara Reddy ◽  
M.V.V.N.L. Sudha Rani ◽  
M.R. Krishnamurthy
Keyword(s):  
Differential Equations ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Slip Flow ◽  
Maxwell Fluid ◽  
Nonlinear Thermal Radiation ◽  
Thermal Boundary Layer Thickness ◽  
Temperature Ratio ◽  
Similarity Transformations ◽  
Fifth Order

Abstract The main focus of the present study is to analyze the effect of chemical reaction and nonlinear thermal radiation on Maxwell fluid suspended with nanoparticles through a porous medium along horizontal stretching sheet. The governing partial differential equations of the defined problem are reduced into a set of nonlinear ordinary differential equations using adequate similarity transformations. Obtained set of similarity equations are then solved with the help of efficient numerical method fourth fifth order Runge-Kutta-Fehlberg method. The effects of different flow pertinent parameters on the flow fields like velocity, temperature, and concentration are shown in the form of graphs and tables. The detailed analysis of the problem is carried out based on the plotted graphs and tables. It is observed that an increase in the radiation parameter, temperature ratio parameter, Brownian motion parameter and thermophoretic parameter lead to increase in the thermal boundary layer thickness but quite opposite phenomenon can be seen for the effect of Prandtl number.

Thermal and solutal transport analysis in swirling flow of Maxwell fluid subject to Cattaneo–Christov theory

2021 ◽  
pp. 095440892110365
Author(s):  
Masood Khan ◽  
Awais Ahmed ◽  
Ayesha Maqbool ◽  
Zahoor Iqbal ◽  
Muhammad Yousaf Malik ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mass Transport ◽  
Ordinary Differential Equations ◽  
Chemical Reaction ◽  
Energy Transport ◽  
Swirling Flow ◽  
Maxwell Fluid ◽  
Partial Differential ◽  
Heat And Mass Transport

In this article, the thermal and solutal analysis are carried out in the swirling flow of Maxwell fluid over a stretchable rotating cylinder in the perspective of Cattaneo–Christov double diffusion theory instead of classical Fourier’s and Fick’s law for heat and mass transport phenomena. The constant rotation of the cylinder and axial-dependent stretching produced the flow under the influence of the magnetic field. The heat sink/source and chemical reaction in flow work as a controlling agent for energy transportation. The problem of thermal and solutal transport in flow under certain suppositions is modeled in the form of partial differential equations. Furthermore, the partial differential equations are converted to ordinary differential equations using flow similarities. To calculate the numerical computation of similar ordinary differential equations is performed through the bvp4c MATLAB technique. The flow phenomenon and energy distribution in flow are examined by using graphs. The key findings of this study reveal that increase in relaxation time parameters for heat and mass transport, both temperature and concentration profiles decline. Moreover, the energy transport increases for the higher heat source and chemical reaction parameters.

Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

2021 ◽  
pp. 095440892110670
Author(s):  
Zahoor Iqbal ◽  
Awais Ahmed ◽  
Amina Anwar ◽  
Sivanandam Sivasankaran ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Flow Problem ◽  
Fluid Motion ◽  
Retardation Time ◽  
Linear Ordinary Differential Equations ◽  
Fluid Parameter ◽  
Burgers Fluid ◽  
Time Parameters ◽  
The Impact

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

Effect of Radiation on MHD Free Convective Flow over a Stretching Sheet in the Presence of Heat Source/Sink

2017 ◽  
Vol 378 ◽  
pp. 1-15
Author(s):  
S. Baag ◽  
S.R. Mishra ◽  
B. Nayak ◽  
M.R. Acharya
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Linear Ordinary Differential Equations ◽  
Electrically Conducting ◽  
Flow Phenomena ◽  
Flow Heat ◽  
Layer Flow ◽  
Source Sink

In this analysis, effects of viscous dissipation and thermal radiation on an electrically conducting boundary layer flow, heat and mass transfer of a fluid through a porous medium over a stretching sheet in the presence of heat source/sink is considered. The symmetry groups admitted by the corresponding boundary value problem are obtained by using symmetric transformations. These transformations are used to convert the partial differential equations of the governing equations into self-similar non-linear ordinary differential equations. These transformed ODEs are solved by employing Runge-Kutta fourth order with shooting method. Numerical results obtained for different thermo-physical parameters characterizes the flow phenomena are drawn graphically and effects of various physical parameters on velocity, temperature and concentration profiles are discussed. Numerical computation for skin friction, Nusselt number and Sherwood number are also obtained and presented in Tables.

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