scholarly journals Fractional model of second grade fluid induced by generalized thermal and molecular fluxes with constant proportional caputo

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 207-212
Author(s):  
Yu-Ming Chu ◽  
Mushtaq Ahmad ◽  
Muhammad Asjad ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Vertical Plate ◽  
Flow Model ◽  
Second Grade ◽  
Dimensionless Form ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Research Article ◽  
Grade Fluid ◽  
Molecular Profiles

In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.

Transient Free Convection Mass Transfer of Second-grade Fluid Flow with Wall Transpiration

CFD Letters ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 35-52
Author(s):  
Mohamad Alif Ismail ◽  
Mohamad Hidayad Ahmad Kamal ◽  
Lim Yeou Jiann ◽  
Anati Ali ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Schmidt Number ◽  
Second Grade ◽  
Concentration Profiles ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Wall Suction ◽  
Viscoelastic Parameter ◽  
Grade Fluid ◽  
Wall Injection

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

Advanced Implicit Meshless Approaches for the Rayleigh–Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

2018 ◽  
Vol 15 (05) ◽  
pp. 1850032 ◽  
Author(s):  
Xiaolei Bi ◽  
Shanjun Mu ◽  
Qingxia Liu ◽  
Quanzhen Liu ◽  
Baoquan Liu ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Bounded Domain ◽  
Stokes Problem ◽  
Second Order ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Discrete Scheme ◽  
First Order ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

To solve the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative in a bounded domain is important in the research for diffusion processes. In this paper, novel implicit meshless approaches based on the moving least squares (MLS) approximation for spatial discretization and two different time discrete schemes, which are the first-order semi-discrete scheme and the second-order semi-discrete scheme for time, are developed for the numerical simulation of the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative in a bounded domain. Based on these two time discretization schemes, the newly developed meshless approaches will have the first-order and the second-order accuracy in time, respectively. The stability and convergence of the implicit MLS meshless approaches are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approaches. It has found that the newly developed meshless approaches are accurate and convergent for fractional partial differential equations (FPDEs). Most importantly, the meshless approaches are robust for arbitrarily distributed nodes and complex domains.

scholarly journals On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝ N

2021 ◽  
Vol 11 (1) ◽  
pp. 580-597
Author(s):  
Jia Wei He ◽  
Yong Zhou ◽  
Li Peng ◽  
Bashir Ahmad
Keyword(s):  
Fractional Derivative ◽  
Blow Up ◽  
Stokes Problem ◽  
Second Grade ◽  
Laplacian Operator ◽  
Well Posedness ◽  
Second Grade Fluid ◽  
Liouville Fractional Derivative ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract We are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝ N , which is derived from a non-Newtonain fluid for a generalized second grade fluid with Riemann-Liouville fractional derivative. We show that a solution operator involving the Laplacian operator is very effective to discuss the proposed problem. In this paper, we are concerned with the global/local well-posedness of the problem, the approaches rely on the Gagliardo-Nirenberg inequalities, operator theory, standard fixed point technique and harmonic analysis methods. We also present several results on the continuation, a blow-up alternative with a blow-up rate and the integrability in Lebesgue spaces.

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