Theoretical treatment of bio-convective Maxwell nanofluid over an exponentially stretching sheet

2020 ◽  
Vol 98 (8) ◽  
pp. 732-741 ◽  
Author(s):  
Muhammad Naveed Khan ◽  
Sohail Nadeem
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Theoretical Treatment ◽  
Shooting Technique ◽  
Maxwell Nanofluid ◽  
Exponentially Stretching Sheet ◽  
Two Dimensional Flow ◽  
Exponentially Stretching

The heat and mass transfer of unsteady two-dimensional flow of a bio-convective non-Newtonian Maxwell nanofluid past an exponentially stretching sheet is presented. A viscous dissipation and external magnetic field along multiple slip conditions and chemical reactions are incorporated. The governing partial differential equations are reduced to the system of ordinary differential equations by applying suitable transformations. Using the bvp4c -shooting technique, we were able to solve the boundary value problem. The influence of the obtained parameters are deliberated graphically on the velocity, concentration, temperature, and microorganism profile. The tabulated values of skin friction, Nusselt number, mass flux rate, and microorganism rate along various parameters are computed and examined. The findings show that the value of the skin friction, Nusselt number, Sherwood number, and microorganism number decline due to enhancement in the time relaxation parameter.

scholarly journals Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
I. Swain ◽  
S. R. Mishra ◽  
H. B. Pattanayak
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Mass Transfer Effect ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching ◽  
Source Sink

An attempt has been made to study the heat and mass transfer effect in a boundary layer MHD flow of an electrically conducting viscous fluid subject to transverse magnetic field on an exponentially stretching sheet through porous medium. The effect of thermal radiation and heat source/sink has also been discussed in this paper. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. Graphical results are displayed for nondimensional velocity, temperature, and concentration profiles while numerical values of the skin friction local Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system.

scholarly journals Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3291
Author(s):  
Abdul Samad Khan ◽  
He-Yong Xu ◽  
Waris Khan
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Skin Friction ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Slip Parameter ◽  
Nanofluid Flow ◽  
Slip Conditions ◽  
Exponentially Stretching ◽  
The Impact

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

MHD Three Dimensional Flow of Casson Fluid over an Unsteady Exponentially Stretching Sheet with Slip Conditions

2018 ◽  
Vol 388 ◽  
pp. 77-95 ◽  
Author(s):  
M. Krishna Murthy
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Slip Conditions ◽  
Exponentially Stretching Sheet ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Exponentially Stretching

Magnetohydrodynamic (MHD) three dimensional boundary layer flow of Casson fluid over an unsteady exponentially stretching sheet with slip conditions is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and are solved numerically using shooting technique. The effects of pertinent parameters on velocity and temperature distributions are shown in graphically. The skin friction coefficient and the Nusselt number are computed numerically. We noticed that Casson parameter increases then the velocities and temperature decrease.

scholarly journals MHD Flow of a Viscous Fluid over an Exponentially Stretching Sheet in a Porous Medium

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Iftikhar Ahmad ◽  
Muhmmad Sajid ◽  
Wasim Awan ◽  
Muhammad Rafique ◽  
Wajid Aziz ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Transfer Problem ◽  
Heat Transfer Analysis ◽  
Physical Parameters ◽  
Exponentially Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

Radiation effects on magnetohydrodynamic (MHD) boundary-layer flow and heat transfer characteristic through a porous medium due to an exponentially stretching sheet have been studied. Formulation of the problem is based upon the variable thermal conductivity. The heat transfer analysis is carried out for both prescribed surface temperature (PST) and prescribed heat flux (PHF) cases. The developed system of nonlinear coupled partial differential equations is transformed to nonlinear coupled ordinary differential equations by using similarity transformations. The series solutions for the transformed of the transformed flow and heat transfer problem were constructed by homotopy analysis method (HAM). The obtained results are analyzed under the influence of various physical parameters.

scholarly journals Influence of Thermal Radiation on Magnetohydrodynamic (MHD) Boundary Layer Flow of a Viscous Fluid Over an Exponentially Stretching Sheet

2016 ◽  
Vol 21 (3) ◽  
pp. 581-592 ◽  
Author(s):  
A.S. Idowu ◽  
S. Usman
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Exponentially Stretching Sheet ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Exponentially Stretching ◽  
Mhd Boundary Layer Flow

Abstract Radiation on a magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was considered together with its effects. The new technique of homotopy analysis method (nHAM) was used to obtain the convergent series expressions for velocity and temperature, where the governig system of partial differential equations was transformed into ordinary differential equations. The interpretation of these expressions is shown physically through graphs. We observed that the effects of the Prandtl and magnetic number act in opposite to each other on the temperature.

scholarly journals Heat and mass transfer of steady magnetohydrodynamics mixed convection of dusty fluid flow with chemical reaction past an exponentially stretching sheet

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Siti Nur Haseela Izani ◽  
Anati Ali
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Dusty Fluid ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching

An analysis has been carried out to study a problem of the chemical reaction effects on magnetohydrodynamics (MHD) mixed convective boundary layer flow with a fluid-particle suspension due to an exponentially stretching sheet. The effects of magnetic field and mass transfer are taken into account for the first time in the dusty fluid over the exponentially stretching sheet. The governing partial nonlinear differential equations corresponding to the momentum, energy and concentration are converted into a system of ordinary differential equations by using similarity transformations. The relevant dimensionless equations are then solved numerically using Runge-Kutta-Fehlberg fourth fifth order method (RKF45) with the help of Maple symbolic software. The influence of physical parameters on the velocity, temperature and concentration distributions for both phases were discussed numerically and presented in details through plotted graphs and tables. Also, the numerical values of skin friction coefficient, Nusselt and Sherwood number of the governing parameters are analyzed and discussed in details. The outcomes show that the reaction parameter affects the fluid flow whereas the magnetic field retards the fluid flow. A comparative study of the present results with the previous study provides an excellent agreement.

scholarly journals Unsteady Tangent Hyperbolic Fluid on Radiated Exponentially Porous Surface

2019 ◽  
Vol 9 (1S5) ◽  
pp. 230-234
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Governing Equations ◽  
Shooting Technique ◽  
Runge Kutta Method ◽  
Tangent Hyperbolic Fluid ◽  
Porosity Effect ◽  
Exponentially Stretching ◽  
Parameter Values

This analysis refers the radiation and porosity effects on unsteady hyperbolic tangent fluid over exponentially stretching sheet. Using similarity transformation the governing equations which are partial differential equations in nature have been modified into nonlinear differential equations (ODE), and then we obtained the solution by shooting technique along with Runge-Kutta method. The dimensional less velocity and temperature have been represented graphically. We have found local Nusselt number and friction factor for distant dimensional less physical parameter values, and they displayed in table. At the end of the analysis we conclude that magnetic field decreases velocity of hyper tangent fluid and porosity effect decreases velocity of hyper tangent fluid. Further the radiation enriches temperature profile in injection case than suction case. This conclusion tells us injection case is useful in temperature transportation than suction case.

scholarly journals Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 249-259 ◽  
Author(s):  
Stanford Shateyi ◽  
Gerald T. Marewo
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Deborah Number ◽  
Exponentially Stretching Sheet ◽  
Non Linear ◽  
Exponentially Stretching

Abstract We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

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