scholarly journals Numerical investigation of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110198
Author(s):  
Kamran Ahmed ◽  
Tanvir Akbar
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Exponential Order ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching ◽  
Porous Stretching Surface ◽  
Order Surface

This research work describes the investigation of a magnetohydrodynamic flow of Williamson nanofluid over an exponentially porous stretching surface considering two cases of heat transfer i.e., prescribed exponential order surface temperature (PEST), and prescribed exponential order heat flux (PEHF). As a result of this infestation, a mathematical model of the problem based on conservation of linear momentum and law of conservation of mass and energy is developed. Whereas governing nonlinear partial differential equations (PDEs) are converted to nonlinear ordinary differential equations (ODEs). Subsequently, the velocity, concentration, and temperature profiles are developed by using the method of similarity transformation. Furthermore, the effects of various physical parameters of engineering interests are demonstrated graphically. It is highlighted that both the magnetic parameter [Formula: see text] and Williamson parameter [Formula: see text] causes to reduce the boundary layer thickness.

Three-dimensional flow of Eyring Powell nanofluid over an exponentially stretching sheet

2015 ◽  
Vol 25 (3) ◽  
pp. 593-616 ◽  
Author(s):  
Tasawar Hayat ◽  
Bilal Ashraf ◽  
Sabir Ali Shehzad ◽  
Elbaz Abouelmagd
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching ◽  
Made In

Purpose – The purpose of this paper is to analyze the Eyring Powell fluid over an exponentially stretching surface. Heat and mass transfer effects are taken into account with nanoparticles. Design/methodology/approach – Appropriate transformations are employed to reduce the boundary layer partial differential equations into ordinary differential equations. Series solutions of the problem are obtained and impacts of physical parameters on the velocities, temperature and concentration profiles are discussed. Findings – Numerical values of local Nusselt and Sherwood numbers for all the involved physical parameters are computed and analyzed. A comparative study between the present and previous results is made in a limiting sense. Local Nusselt number −′(0) increases by increasing ε, Pr, λ and N while it decreases for δ, N_{t{, N_{b} and Sc. Originality/value – This analysis has not been discussed in the literature yet.

Darcy–Forchheimer flow of a magneto-radiated couple stress fluid over an inclined exponentially stretching surface with Ohmic dissipation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
S. Das ◽  
Akram Ali ◽  
R.N. Jana
Keyword(s):  
Couple Stress ◽  
Couple Stress Fluid ◽  
Temperature Profiles ◽  
Stretching Surface ◽  
Ohmic Dissipation ◽  
Content Type ◽  
Exponential Order ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching ◽  
Forchheimer Flow

Purpose In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing. Design/methodology/approach The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables. Findings As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case. Practical implications The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc. Originality/value From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

scholarly journals Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

2013 ◽  
Vol 18 (4) ◽  
pp. 1151-1164 ◽  
Author(s):  
G.V.R. Reddy ◽  
B.A. Reddy ◽  
N.B. Reddy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Flow ◽  
Physical Parameters ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

scholarly journals MHD boundary layer slip flow of a casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction

2016 ◽  
Vol 13 (2) ◽  
pp. 165-177 ◽  
Author(s):  
P. Bala Anki Reddy
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Casson Fluid ◽  
Stretching Surface ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

An analysis is carried out to investigate the steady two-dimensional magnetohydrodynamic boundary layer flow of a Casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction. Velocity, thermal and solutal slips are considered instead of no-slip conditions at the boundary. Stretching velocity, wall temperature and wall concentration are considered in the exponential forms. The non-linear partial differential equations are converted into a system of non-linear ordinary differential equations by similarity transformations. The resultant non-linear ordinary differential equations are solved numerically by fourth order Runge-Kutta method along with shooting technique. The influence of various parameters on the fluid velocity, temperature, concentration, wall skin friction coefficient, the heat transfer coefficient and the Sherwood number have been computed and the results are presented graphically and discussed quantitatively. Comparisons with previously published works are performed on various special cases and are found to be in excellent agreement.  

Influence of partial slip flow and thermal jump on mixed convection from an exponentially stretching surface

2018 ◽  
Vol 28 (10) ◽  
pp. 2324-2341 ◽  
Author(s):  
Prabhugouda Mallanagouda Patil ◽  
Geeta Hadimani ◽  
Shashikant A. ◽  
P.S. Kulkarni ◽  
Mukesh Kumar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Velocity Ratio ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Partial Slip ◽  
Partial Differential ◽  
Content Type ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Purpose This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of suction/blowing, volumetric heat source/sink and velocity ratio parameter will be studied in this analysis. Design/methodology/approach The modeled governing equations for the assumed problem are dimensional nonlinear partial differential equations in nature. To reduce these equations, non-similar transformations are used to get the dimensionless nonlinear partial differential equations. Then, quasi-linearization technique is used to linearize these non-dimensional nonlinear partial differential equations. Finally, an implicit finite difference scheme is used to discretize the resulting equations. Findings The physical explanations are provided for the variations of various non-dimensional governing parameters over the velocity and temperature profiles. Also, the effects of these dimensionless parameters on skin friction coefficient and heat transfer rate are scrutinized in a manner which highlights their physical interpretation. The detailed discussion exhibits the fact that the streamwise co-ordinate velocity ratio parameter, partial slip parameter and the thermal jump parameter have significant influence over the flow and thermal fields. Originality/value This work has not been reported in the literature to the authors’ best of knowledge.

Boundary Layer Flow of Casson Fluid on Exponentially Stretching Porous Surface with Radiative Heat Transfer

2020 ◽  
Vol 26 ◽  
pp. 112-125
Author(s):  
Ibrahim Yakubu Seini ◽  
Golbert Aloliga ◽  
Baba Ziblim ◽  
Oluwole Daniel Makinde
Keyword(s):  
Differential Equations ◽  
Shooting Method ◽  
Radiative Heat ◽  
Fluid Model ◽  
Casson Fluid ◽  
Transformation Process ◽  
Stretching Surface ◽  
Exponentially Stretching Surface ◽  
Layer Flow ◽  
Exponentially Stretching

An analysis of aCasson fluid flowing over a porous exponentially stretching surface with radiation has been studied. A non-Newtonian fluid model was developed for the flow and similarity analysis used in the transformation process. The model of partial differential equations was transformed into ordinary differential equations and reduced into a system of first order differential equations which was then solved using the Fourth-order Runge-Kutta algorithm alongside the Newton Raphson shooting method. The results have been presented graphically and in tabular form for various controlling parameters of the problem. It is observed that general control can be achieved by the permeability of the surface and the value of the Casson parameter.

Thermal and chemically reactive features of Casson nanofluid flow with thermophoresis and Brownian effect over an exponentially stretching surface

2021 ◽  
pp. 095440892110644
Author(s):  
Muhammad Naveed Khan ◽  
Rifaqat Ali ◽  
Hijaz Ahmad ◽  
Nadeem Abbas ◽  
Abd Allah A. Mousa ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Transfer Rate ◽  
Casson Fluid ◽  
Stretching Surface ◽  
Casson Nanofluid ◽  
Fluid Parameter ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Heat and mass transfer of the MHD flow of Casson nanofluid by an exponential stretching sheet discussed in this analysis. The MHD with joule heating effects for Casson nanofluid numerically investigated. To characterize the transport property of heat and mass, we considered the thermophoresis and Brownian effect along with thermal radiation and thermophoretic effects. Additionally, we consider the microorganism theory to analyze the suspended nanoparticles by bio-convection. The mathematical model developed on the base of boundary layer flow of casson nanofluid at exponentially stretching surface in term of partial differential equations. The partial differential equations are transformed into nonlinear ordinary differential equations by means of similarity variable transformations. The non-dimensionalized differential equations have numerically tackled by using the Bvp4c MATLAB technique. The graphical outcomes are obtained against the various parameters. Moreover, physical quantities are examined graphically and tabulating data. It is reviewed that resistance of fluid flow improves by the higher estimation of the Casson fluid parameter. Therefore, the axial and transverse velocities are reduced. Further, it is noticed from the tabulated data that more vital values of the Casson fluid parameter diminishes the skin friction and mass transfer rate but enhances the heat transfer rate.

Unsteady MHD mixed convection along an exponentially stretching surface

2018 ◽  
Vol 28 (12) ◽  
pp. 2769-2783 ◽  
Author(s):  
Prabhugouda Mallanagouda Patil ◽  
Shashikant A. ◽  
Ebrahim Momoniat
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Mixed Convection ◽  
Stretching Surface ◽  
Partial Differential ◽  
Content Type ◽  
Buoyancy Flow ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Purpose This paper aims to investigate the unsteady mixed convection along an exponentially stretching surface in presence of transverse magnetic field applied at the wall and the opposing buoyancy flow. Design/methodology/approach The dimensional partial differential equations governing the flow field are transformed to non-dimensional coupled partial differential equations with the aid of suitable non-similar transformations. The resulting equations are then solved by the coalition of quasilinearization technique and the finite difference method. Findings Effects of volumetric heat source/sink, suction/blowing and other dimensionless parameters on velocity and temperature profiles are examined numerically. This investigation reveals that in presence of opposing buoyancy flow, the suction and volumetric heat source enhances the skin-friction coefficient, while the rise in the MHD increases the momentum boundary layer. Originality/value To the best of the authors’ knowledge, no such investigation has been carried out in the literature.

Three-dimensional mixed convection flow of viscoelastic nanofluid over an exponentially stretching surface

2015 ◽  
Vol 25 (2) ◽  
pp. 333-357 ◽  
Author(s):  
Tasawar Hayat ◽  
Bilal Ashraf ◽  
Sabir Ali Shehzad ◽  
A. Alsaedi ◽  
N. Bayomi
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Content Type ◽  
Viscoelastic Nanofluid ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Purpose – The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface. Design/methodology/approach – Similarity transformations are utilized to reduce the partial differential equations into the ordinary differential equations. The corresponding non-linear problems are solved by homotopy analysis method. Findings – The authors found that an increase in thermophoresis and Brownian motion parameter enhance the temperature. Here thermal conductivity of fluid is enhanced due to which higher temperature and thicker thermal boundary layer thickness is obtained. Practical implications – Heat and mass transfer effects in mixed convection flow over a stretching surface have numerous applications in the polymer technology and metallurgy. Such flows are encountered in metallurgical processes which involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid and that in the process of drawing, these strips are sometimes stretched. Originality/value – Three-dimensional flows over an exponentially stretching surface are very rare in the literature. Three-dimensional flow of viscoelastic nanofluid due to an exponentially stretching surface is first time investigated.

Sign in / Sign up

Export Citation Format

Share Document