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.

The layout of Boussinesq couple-stress fluid flow over an exponentially stretching sheet with slip in porous space subject to a variable magnetic field

2020 ◽  
Vol 16 (5) ◽  
pp. 1131-1154
Author(s):  
S. Das ◽  
R.R. Patra ◽  
R.N. Jana
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Porous Medium ◽  
Couple Stress ◽  
Stretching Sheet ◽  
Couple Stress Fluid ◽  
Slip Effect ◽  
Content Type ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching

PurposeThe purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an electrically conducting Boussinesq couple-stress fluid induced by an exponentially stretching sheet embedded in a porous medium under the effect of the magnetic field of the variable kind. The heat transfer phenomenon is accounted for under thermal radiation, Joule and viscous dissipation effects.Design/methodology/approachThe governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations (ODEs) by using some appropriate dimensionless variables and then the consequential nonlinear ODEs are solved numerically by making the use of the well-known shooting iteration technique along with the standard fourth-order Runge–Kutta integration scheme. The impact of emerging flow parameters on velocity and temperature profiles, streamlines, local skin friction coefficient and Nusselt number are described comprehensively through graphs and tables.FindingsResults reveal that the velocity profile is observed to diminish considerably within the boundary layer in the presence of a magnetic field and slip condition. The enhanced radiation parameter is to decline the temperature field. The slip effect is favorable for fluid flow.Originality/valueTill now, slip effect on Boussinesq couple-stress fluid over an exponentially stretching sheet embedded in a porous medium has not been explored. The present results are validated with the previously published study and found to be highly satisfactory.

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.

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.

Unsteady mixed convection along a permeable exponentially stretching surface

2018 ◽  
Vol 28 (9) ◽  
pp. 1994-2011 ◽  
Author(s):  
Prabhugouda Mallanagouda Patil ◽  
Shashikant A.
Keyword(s):  
Fluid Flow ◽  
Mixed Convection ◽  
Skin Friction Coefficient ◽  
Governing Equations ◽  
Stretching Surface ◽  
Content Type ◽  
Linear Partial Differential Equations ◽  
Unsteady Mixed Convection ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Purpose The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially stretching surface. It is also intended to explore the influence of suction/injection and volumetric heat source/sink on the fluid flow. Design/methodology/approach The assumed problem is modelled into governing equations which are dimensional non-linear partial differential equations in nature. To obtain solutions, initially the governing equations were made non-dimensional by the suitable non-similar transformations. Then, the dimensionless non-linear partial differential equations are linearized with the aid of Quasilinearization technique. The so obtained equations are discretized by the implicit finite difference method. Findings The detailed analysis of the considered problem displays that the non-similarity variable reduces the velocity and temperature profiles. For higher values of mixed convection parameter, the magnitude of velocity profile as well as the Nusselt number increase. The unsteady variable diminishes the fluid flow. The higher values of velocity ratio parameter reduce the skin-friction coefficient. Further, the magnitude of skin-friction coefficient and heat transfer rate are to minimize for increasing values of partial slip and thermal jump parameters, respectively. Volumetric heat source and injection parameters are to rise the flow behavior within the momentum and thermal boundary layers significantly. Originality/value To the best of authors’ knowledge, no such investigation has been found in the literature.

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