scholarly journals On the MHD Casson Axisymmetric Marangoni Forced Convective Flow of Nanofluids

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1087 ◽  
Author(s):  
Anum Shafiq ◽  
Islam Zari ◽  
Ghulam Rasool ◽  
Iskander Tlili ◽  
Tahir Saeed Khan
Keyword(s):  
Differential Equations ◽  
Convective Flow ◽  
Flow Behavior ◽  
Marangoni Effect ◽  
Casson Fluid ◽  
Linear Ordinary Differential Equations ◽  
Metallic Particles ◽  
Flow Parameters ◽  
Forced Convective Flow ◽  
The Impact

The proposed investigation concerns the impact of inclined magnetohydrodynamics (MHD) in a Casson axisymmetric Marangoni forced convective flow of nanofluids. Axisymmetric Marangoni convective flow has been driven by concentration and temperature gradients due to an infinite disk. Brownian motion appears due to concentration of the nanosize metallic particles in a typical base fluid. Thermophoretic attribute and heat source are considered. The analysis of flow pattern is perceived in the presence of certain distinct fluid parameters. Using appropriate transformations, the system of Partial Differential Equations (PDEs) is reduced into non-linear Ordinary Differential Equations (ODEs). Numerical solution of this problem is achieved invoking Runge–Kutta fourth-order algorithm. To observe the effect of inclined MHD in axisymmetric Marangoni convective flow, some suitable boundary conditions are incorporated. To figure out the impact of heat/mass phenomena on flow behavior, different physical and flow parameters are addressed for velocity, concentration and temperature profiles with the aid of tables and graphs. The results indicate that Casson fluid parameter and angle of inclination of MHD are reducing factors for fluid movement; however, stronger Marangoni effect is sufficient to improve the velocity profile.

scholarly journals Ohmic and Viscous Dissipation Effect on Free and Forced Convective Flow of Casson Fluid in a Channel

2021 ◽  
Vol 12 (1) ◽  
pp. 132-148
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Convective Flow ◽  
Casson Fluid ◽  
Pictorial Representation ◽  
Physical Parameters ◽  
Partial Differential ◽  
Buoyancy Parameter ◽  
Forced Convective Flow

Analytical study of the free and forced convective flow of Casson fluid in the existence of viscous dissipation, ohmic effect and uniform magnetic field in a porous channel to the physical model. The nonlinear coupled partial differential equations are converted to linear partial differential equations using similarity transformation and the classical perturbation method. The physical parameters such as Prandtl number (Pr), viscous dissipation (Vi), Schmidt number (Sc), Reynolds number (R), thermal buoyancy parameter (λ), Ohmic number (Oh), Casson fluid parameter (β), Darcy number (Da), Hartmann number (M2), the concentration of buoyancy parameter (N), chemical reaction rate (γ) effect on velocity, temperature and concentration have been studied with pictorial representation. For the particular case, the present paper analysis is compared with the previous work and is found good agreement.

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.

scholarly journals Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1238 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stagnation Point ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Three Solutions ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Stretching Surfaces ◽  
The Impact

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

scholarly journals Slip Effects on Unsteady Oblique Stagnation Point Flow of Nanofluid in a View of Inclined Magnetic Field

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Rizwana Rizwana ◽  
Azad Hussain ◽  
S. Nadeem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stagnation Point ◽  
Flow Behavior ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Working Fluid ◽  
Petroleum Reservoir ◽  
Metallic Nanoparticle ◽  
The Impact

This study may be applicable in heavy power engine and cooling of a nuclear reactor, insulation for buildings, petroleum reservoir operations, and magnetic material processing solar energy collectors. In this manuscript, the slip results are evaluated for the non-Newtonian fluid on the oblique stagnation point flow of induced magnetic field over the oscillating surface. The valuation of heat flux is examined through the Fourier law of heat transfer. The metallic nanoparticle Copper Cu is within the base fluid, and water is utilized in the analysis. Nanofluids have benefits such as steadiness of the working fluid, decreasing blockage, clogs, decreasing prices, decreasing the friction coefficient, and decreasing the size of the heat transfer system. Similarity variables are utilized to convert the developed flow into higher nonlinear coupled ordinary differential equations (ODE) which are tackled numerically using a mathematical technique such as the bvp4c method in Maple and Matlab software. According to the present geometry, the flow behavior of the operating nanofluid has analyzed by stream lines. Disparities in velocity and temperature profile are demonstrated by graphs to describe the effects of controlling parameters. The Casson fluid parameter enhances the velocity of the fluid. The system heats up by the impact of Joule heating and dissipation.

scholarly journals Heat Transport Phenomena for the Darcy–Forchheimer Flow of Casson Fluid over Stretching Sheets with Electro-Osmosis Forces and Newtonian Heating

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2525
Author(s):  
Xianqin Zhang ◽  
Dezhi Yang ◽  
Muhammad Israr Ur Rehman ◽  
Aamir Hamid
Keyword(s):  
Differential Equations ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Similarity Transformations ◽  
Governing System ◽  
Electro Osmosis ◽  
The Impact ◽  
Osmotic Effects ◽  
Forchheimer Flow ◽  
Good Agreement

In this study, an investigation has been carried out to analyze the impact of electro-osmotic effects on the Darcy–Forchheimer flow of Casson nanofluid past a stretching sheet. The energy equation was modelled with the inclusion of electro-osmotic effects with viscous and Joule dissipations. The governing system of partial differential equations were transformed by using the suitable similarity transformations to a system of ordinary differential equations and then numerically solved by using the Runge–Kutta–Fehlberg method with a shooting scheme. The effects of various parameters of interest on dimensionless velocity and temperature distributions, as well as skin friction and heat transfer coefficient, have been adequately delineated via graphs and tables. A comparison with previous published results was performed, and good agreement was found. The results suggested that the electric and Forchheimer parameters have the tendency to enhance the fluid velocity as well as momentum boundary layer thickness. Enhancements in temperature distribution were observed for growing values of Eckert number. It was also observed that higher values of electric field parameter diminished the wall shear stress and local Nusselt number.

scholarly journals Dual solutions for radiative MHD forced convective flow of a nanofluid over a slendering stretching sheet in porous medium

2015 ◽  
Vol 12 (2) ◽  
pp. 115-124 ◽  
Author(s):  
C. Sulochana ◽  
N. Sandeep
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Convective Flow ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Navier Slip ◽  
Matlab Package ◽  
Forced Convective Flow

In this study we analyzed the magnetohydrodynamic forced convective flow of a nanofluid over a slendering stretching sheet in porous medium in presence of thermal radiation and slip effects. We presented dual solutions for no-slip and Navier slip conditions. Using self similarity transformation, the governing partial differential equations are transformed into nonlinear ordinary differential equations and solved numerically using bvp5c Matlab package. The effects of dimensionless governing parameters on velocity and temperature profiles of the flow are discussed with the help of graphs. Numerical computations are carried out and discussed for skin friction coefficient and local Nusselt number. We found an excellent agreement of the present results with the existed results under some special conditions. Results indicate that the dual solutions exist only for certain range of velocity slip parameter. It is also found that the heat transfer performance is high in presence of velocity slip effect.

Melting heat transfer analysis of non-Newtonian Casson fluid due to moving plate

2018 ◽  
Vol 35 (3) ◽  
pp. 1301-1313 ◽  
Author(s):  
Mahantesh M. Nandeppanavar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Casson Fluid ◽  
Heat Transfer Analysis ◽  
Moving Plate ◽  
Content Type ◽  
Melting Heat ◽  
Linear Ordinary Differential Equations ◽  
Melting Heat Transfer ◽  
Non Linear

Purpose This paper aims to investigate laminar boundary layer flow and heat transfer from a warm laminar Casson liquid to a melting sheet moving parallel to a melting stream. The governing equations, i.e. continuity, momentum and heat transfer, are coupled non-linear partial differential equations. These equations are reduced to non-linear ordinary differential equations by means of similarity transformations, converted into first-order differential equations, and are solved numerically using the Runge–Kutta–Felhberg method with an efficient shooting technique. The velocity and temperature profiles are plotted for various values of the governing parameters, such as the moving parameter, Prandlt number, melting parameter and Casson parameter. It is found that the problem admits multiple solutions. The results of this study are validated by comparing them with the earlier published studies’ results. Thus, a good agreement is obtained. Design/methodology/approach This study carries out numerical solution of melting heat transfer analysis. Findings The findings of this study show the analysis of flow and melting heat transfer characteristics. Research limitations/implications In this study, analysis of dual solution is carried out. Originality/value In this paper, the melting heat transfer analysis on Blasius flow of a Casson fluid is taken into consideration. To the best of the author’s knowledge, no investigations have been reported on this topic.

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.

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.  

Radiation Absorption and Viscous-Dissipation on MHD Flow of Casson Fluid over a Vertical Plate Filled with Porous Layers

2017 ◽  
Vol 11 ◽  
pp. 43-56 ◽  
Author(s):  
S. Venkateswarlu ◽  
S.V.K. Varma ◽  
R.V.M.S.S. Kiran Kumar ◽  
Chakravarthula S.K. Raju ◽  
Putta Durga Prasad
Keyword(s):  
Viscous Dissipation ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Infinite Plate ◽  
Casson Fluid ◽  
Radiation Absorption ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Casson Fluid Model ◽  
The Impact

The present study aims to analyze the radiation absorption and viscous dissipation effects on MHD free convective Casson fluid flow over a vertical permeable semi-infinite plate in the presence of first order homogeneous chemical reaction. The time-dependent wall suction is assumed to occur at the permeable surface. The non-Newtonian fluid behavior is characterized by using the Casson fluid model. The coupled non-linear ordinary differential equations (ODE’s) are solved by perturbation technique. The impact of sundry parameters on the velocity, temperature, species concentration as well as the friction factor coefficient, the rate of heat and mass transfer coefficients are computed and analyzed through graphs.

Sign in / Sign up

Export Citation Format

Share Document