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 Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Shooting Method ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Stagnation Point Flow ◽  
Stretching Surfaces

Abstract In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

Unsteady Chemically Reacting Casson Fluid Flow in an Irregular Channel with Convective Boundary

2015 ◽  
Vol 70 (8) ◽  
pp. 583-591
Author(s):  
Muhammad Nasir ◽  
Adnan Saeed Butt ◽  
Asif Ali
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mass Concentration ◽  
Perturbation Technique ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Wavy Wall ◽  
Convective Boundary ◽  
Grashof Number ◽  
Chemically Reacting

AbstractA mathematical model has been performed for momentum, temperature, and mass concentration of a time-dependent Casson fluid flow between a long vertical wavy wall and a parallel wavy wall subject to convective boundary conditions. Perturbation technique is used to convert the coupled partial differential equations for velocity, temperature, and mass concentration to systems of ordinary differential equations. Analytical results for these differential equations are computed. The effects of various physical parameters such as thermal conductivity, thermal Grashof number, solutal Grashof number, heat absorption parameter, and Biot number are analysed graphically.

Unsteady MHD Rear Stagnation-Point Flow of a Hybrid Nanofluid with Heat Generation/Absorption Effect

2021 ◽  
Vol 87 (1) ◽  
pp. 41-51
Author(s):  
Nurul Amira Zainal ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Absorption Effect ◽  
Suction Parameter ◽  
The Impact ◽  
Rear Stagnation Point

The study of unsteady flow is essential in various engineering systems, for instance, the periodic fluid motion and start-up process. Therefore, this numerical study focuses on examining the unsteady magnetohydrodynamics (MHD) rear stagnation-point flow in Al2O3-Cu/H2O hybrid nanofluid past a permeable stretching/shrinking surface with the impact of heat generation/absorption. By choosing a suitable similarity transformation, partial differential equations are transformed into a system of nonlinear ordinary differential equations and solved using the bvp4c function in the MATLAB package. The effects of the solution domain’s operating parameters are analysed, and dual solutions are observable as the sheet shrinks. It is found that the addition of the suction parameter escalates the heat transfer efficiency. Eventually, the existence of the unsteadiness parameter and the heat generation/absorption effect significantly encourage heat transfer deterioration.

scholarly journals Influences of Slip Velocity and Induced Magnetic Field on MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Ahmed A. Afify
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Slip Velocity ◽  
Casson Fluid ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Casson Fluid Model

The steady MHD boundary layer flow near the stagnation point over a stretching surface in the presence of the induced magnetic field, viscous dissipation, magnetic dissipation, slip velocity phenomenon, and heat generation/absorption effects has been investigated numerically. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The governing partial differential equations using appropriate similarity transformations are reduced into a set of nonlinear ordinary differential equations, which are solved numerically using a shooting method with fourth-order Runge-Kutta integration scheme. Comparisons with the earlier results have been made and good agreements were found. Numerical results for the velocity, induced magnetic field, temperature profiles, skin friction coefficient, and Nusselt number are presented through graphs and tables for various values of physical parameters. Results predicted that the magnetic parameter with α<1 has the tendency to enhance the heat transfer rate, whereas the reverse trend is seen with α>1. It is also noticed that the rate of heat transfer is a decreasing function of the reciprocal of a magnetic Prandtl number, whereas the opposite phenomenon occurs with the magnitude of the friction factor.

Stability analysis of triple solutions of Casson nanofluid past on a vertical exponentially stretching/shrinking sheet

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110596
Author(s):  
Hazoor Bux Lanjwani ◽  
Salman Saleem ◽  
Muhammad Saleem Chandio ◽  
Muhammad Imran Anwar ◽  
Nadeem Abbas
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Temperature Profiles ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Casson Nanofluid ◽  
Exponential Stretching

The MHD two dimensional boundary layer flow of Casson nanofluid on an exponential stretching/shrinking sheet is considered with effects of radiation parameter, nanoparticles volume fractions (i.e. Fe3O4 and Ti6Al4V) and thermal convective boundary condition. The partial differential equations are transformed into ordinary differential equations by means of similarity transformations. The solutions of the transferred equations are achieved numerically with the help of shooting technique in Maple software. At different ranges of involved physical parameters, triple solutions are found. Therefore, stability analysis is performed by bvp4c in MATLAB to find the stable and physically reliable solution. Impacts of the physical parameter are presented through graphs and tables. Mainly, it is found that an increase in Casson and suction parameters decrease the corresponding velocity profiles while increase in Prandtl number, stretching/shrinking, and suction parameter decrease the temperature profiles. Furthermore, an increase in nanoparticles volumetric fraction, radiation and magnetic parameters as well as Biot number increase the temperature profiles and their thermal boundary layer thicknesses.

scholarly journals MHD Flow and Heat Transfer of a Jeffrey Fluid over a Porous Stretching/Shrinking Sheet with a Convective Boundary Condition

2021 ◽  
Vol 39 (3) ◽  
pp. 885-894
Author(s):  
Dondu Harish Babu ◽  
Nainaru Tarakaramu ◽  
Panyam Venkata Satya Narayana ◽  
Ganganapalli Sarojamma ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Flow Characteristics ◽  
Mhd Flow ◽  
Jeffrey Fluid ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Dimensionless Numbers ◽  
Convective Boundary ◽  
Suction Parameter ◽  
The Impact

This work explores the heat transfer flow characteristics of an incompressible non-Newtonian Jeffrey fluid over a stretching/shrinking surface with thermal radiation and heat source. The sheet is linearly stretched in the presence of a transverse magnetic field with convective boundary conditions. Appropriate similarity variables are used to transform the basic governing equations (PDEs) into ODEs. The resulting equations are solved by utilizing MATLAB bvp4c. The impact of distinctive physical parameters and dimensionless numbers on the flow field and heat transfer is analysed graphically. It is noticed that the measure of heat raised with increasing the Biot number and opposite effect with the rise of the suction parameter.

INFLUENCE OF HEAT TRANSFER ON THE MHD STAGNATION POINT FLOW OF A POWER LAW FLUID WITH CONVECTIVE BOUNDARY CONDITION

2015 ◽  
Vol 77 (20) ◽  
Author(s):  
Shah Jahan ◽  
Hamzah Sakidin
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Stagnation Point ◽  
Power Law ◽  
Convective Boundary Condition ◽  
Stagnation Point Flow ◽  
Power Law Fluid ◽  
Convective Boundary ◽  
The Impact

In this article, we examined the impact of heat transfer on the magnetohydrodynamic (MHD) stagnation point flow of a non-Newtonian power- law fluid with convective boundary condition. By using suitable similarity transformations, coupled nonlinear partial differential equations are transformed to ordinary differential equations. Then solved the resulting equations with Homotopy analysis method.  Interesting flow parameters such as MHD , stagnation parameter  convective parameter  are discussed graphically. Convergence is checked at 20th order of approximation. Numerical values of physical interested parameter such as local Nusselt number are also tabulated.

Peristaltic flow of a Jeffery fluid over a porous conduit in the presence of variable liquid properties and convective boundary conditions

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
G. Manjunatha ◽  
C. Rajashekhar ◽  
K. V. Prasad ◽  
Hanumesh Vaidya ◽  
Saraswati
Keyword(s):  
Boundary Conditions ◽  
Frictional Force ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Velocity Slip ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Closed Form Solutions

The present article addresses the peristaltic flow of a Jeffery fluid over an inclined axisymmetric porous tube with varying viscosity and thermal conductivity. Velocity slip and convective boundary conditions are considered. Resulting governing equations are solved using long wavelength and small Reynolds number approximations. The closed-form solutions are obtained for velocity, streamline, pressure gradient, temperature, pressure rise, and frictional force. The MATLAB numerical simulations are utilized to compute pressure rise and frictional force. The impacts of various physical parameters in the interims for time-averaged flow rate with pressure rise and is examined. The consequences of sinusoidal, multi-sinusoidal, triangular, trapezoidal, and square waveforms on physiological parameters are analyzed and discussed through graphs. The analysis reveals that the presence of variable viscosity helps in controlling the pumping performance of the fluid.

Thermo-Solutal Convection of a Nanofluid Utilizing Fourier’s-Type Compass Conditions

2020 ◽  
Vol 9 (4) ◽  
pp. 362-374
Author(s):  
J. C. Umavathi ◽  
Ali J. Chamkha
Keyword(s):  
Brownian Motion ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Surface Boundary ◽  
Perturbation Scheme ◽  
Runge Kutta ◽  
The Impact

Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a vertical duct containing nanofluid. Numerical scrutiny for the double-diffusive free and forced convection within a duct encumbered with nanofluid is performed. Buongiorno’s model is deployed to define the nanofluid. Robin boundary conditions are used to define the surface boundary conditions. Thermal and concentration equations envisage the viscous, Brownian motion, thermosphores of the nanofluid, Soret and Dufour effects. Using the Boussi-nesq approximation the solutal buoyancy effect as a result of gradients in concentration are incorporated. The conservation equations which are nonlinear are numerically estimated using fourth order Runge-Kutta methodology and analytically ratifying regular perturbation scheme. The mass, heat, nanoparticle concentration and species concentration fields on eight dimensionless physical parameters such as thermal and mass Grashof numbers, Brownian motion parameter, thermal parameter, Prandtl number, Eckert number, Schmidt parameter, and Soret parameter are calculated. The impact of these parameters are outlined pictorially. The velocity and temperature fields are boosted with the thermal Grashof number. The Soret and the Schemidt parameters reduces the nanoparticle volume fraction but it heightens the momentum, temperature and concentration. At the cold wall thermal and concentration Grashof numbers reduces the Nusselt values but they increase the Nusselt values at the hot wall. The reversal consequence was attained at the hot plate. The perturbation and Runge-Kutta solutions are equal in the nonappearance of Prandtl number. The (E. Zanchini, Int. J. Heat Mass Transfer 41, 3949 (1998)). results are restored for the regular fluid. The heat transfer rate is high for nanofluid when matched with regular fluid.

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