Unsteady Mhd Stagnation-point Flow of Fractional Oldroyd-b Fluid Over a Stretching Sheet with Modified Fractional Fourier's Law

2021 ◽  
Author(s):  
Yu Bai ◽  
Sa Wan ◽  
Yan Zhang
Keyword(s):  
Stagnation Point ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Momentum Equation ◽  
Stagnation Point Flow ◽  
Governing Equations ◽  
Fourier’S Law ◽  
Relaxation Parameters ◽  
Memory Characteristic ◽  
Fourier's Law

Abstract The aim of the article is to research the unsteady magnetohydrodynamic stagnation-point flow of fractional Oldroyd-B fluid over a stretched sheet. According to the distribution characteristics of pressure and magnetic field near the stagnation point, the momentum equation based on fractional Oldroyd-B constitutive model is derived. Moreover, the modified fractional Fourier's law considering thermal relaxation-retardation time is proposed, which applies in both the energy equation and the boundary condition of convective heat transfer. New finite difference scheme combined with L1 algorithm is established to solve the governing equations, whose convergence is confirmed by constructing the exact solution. The results indicate that the larger relaxation parameters of velocity block the flow, yet the retardation parameters of velocity show the opposite trend. It is particularly worth mentioning that all the temperature profiles first go up slightly to a maximal value and then descend markedly, which presents the thermal retardation characteristic of Oldroyd-B fluid. Additionally, under the effects of temperature's retardation and relaxation parameters, the intersection of the profiles far away from stretching sheet demonstrates the thermal memory characteristic.

Impact of Cattaneo–Christov Heat Flux Model on Stagnation-Point Flow Toward a Stretching Sheet with Slip Effects

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Fayeza Al Sulti
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Fourier’S Law ◽  
Slip Effects ◽  
Flux Model ◽  
Fourier's Law ◽  
Heat Flux Model

Stagnation-point flow toward a stretching sheet with slip effects has been investigated. Unlike most classical works, Cattaneo–Christov heat flux model is utilized for the formulation of the energy equation instead of Fourier's law of heat conduction. A similarity transformation technique is adopted to reduce partial differential equations into a system of nonlinear ordinary differential equations. Numerical solutions are obtained by using shooting method to explore the features of various parameters for the velocity and temperature distributions. The obtained results are graphically presented and analyzed. It is found that fluid temperature has a converse relationship with the thermal relaxation time. A comparison of Cattaneo–Christov heat flux model and Fourier's law is also presented.

scholarly journals MHD stagnation point flow of micro nanofluid towards a shrinking sheet with convective and zero mass flux conditions

2017 ◽  
Vol 65 (2) ◽  
pp. 155-162 ◽  
Author(s):  
A. Rauf ◽  
S. A. Shehzad ◽  
T. Hayat ◽  
M. A. Meraj ◽  
A. Alsaedi
Keyword(s):  
Stagnation Point ◽  
Mass Flux ◽  
Numerical Technique ◽  
Convective Boundary Condition ◽  
Momentum Equation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Convective Boundary ◽  
Electrically Conducting ◽  
Zero Mass

AbstractIn this article the stagnation point flow of electrically conducting micro nanofluid towards a shrinking sheet, considering a chemical reaction of first order is investigated. Involvement of magnetic field occurs in the momentum equation, whereas the energy and concentrations equations incorporated the influence of thermophoresis and Brownian motion. Convective boundary condition on temperature and zero mass flux condition on concentration are implemented. Partial differential equations are converted into the ordinary ones using suitable variables. The numerical technique is utilized to discuss the results for velocity, microrotation, temperature, and concentration fields.

Stagnation-Point Flow over an Exponentially Shrinking/Stretching Sheet

2011 ◽  
Vol 66 (12) ◽  
pp. 705-711 ◽  
Author(s):  
Sin Wei Wong ◽  
Abu Omar Awang ◽  
Anuar Ishak
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Free Stream ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Heat Transfer Characteristics ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
Box Method

The steady two-dimensional stagnation-point flow of an incompressible viscous fluid over an exponentially shrinking/stretching sheet is studied. The shrinking/stretching velocity, the free stream velocity, and the surface temperature are assumed to vary in a power-law form with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations before being solved numerically by a finite difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.

scholarly journals Fractional order stagnation point flow of the hybrid nanofluid towards a stretching sheet

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anwar Saeed ◽  
Muhammad Bilal ◽  
Taza Gul ◽  
Poom Kumam ◽  
Amir Khan ◽  
...  
Keyword(s):  
Stagnation Point ◽  
Fractional Order ◽  
Transition Rate ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Fractional Order Differential Equations ◽  
Classical Calculus ◽  
Electric And Magnetic Fields ◽  
Heat Transition

AbstractFractional calculus characterizes a function at those points, where classical calculus failed. In the current study, we explored the fractional behavior of the stagnation point flow of hybrid nano liquid consisting of TiO2 and Ag nanoparticles across a stretching sheet. Silver Ag and Titanium dioxide TiO2 nanocomposites are one of the most significant and fascinating nanocomposites perform an important role in nanobiotechnology, especially in nanomedicine and for cancer cell therapy since these metal nanoparticles are thought to improve photocatalytic operation. The fluid movement over a stretching layer is subjected to electric and magnetic fields. The problem has been formulated in the form of the system of PDEs, which are reduced to the system of fractional-order ODEs by implementing the fractional similarity framework. The obtained fractional order differential equations are further solved via fractional code FDE-12 based on Caputo derivative. It has been perceived that the drifting velocity generated by the electric field E significantly improves the velocity and heat transition rate of blood. The fractional model is more generalized and applicable than the classical one.

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