scholarly journals MHD Flows of Second Grade Fluid Through the Moving Porous Cylindrical Domain

2019 ◽  
Vol 12 (3) ◽  
pp. 1149-1175 ◽  
Author(s):  
Muhammad Jamil ◽  
Muhammad Zafarullah
Keyword(s):  
Outer Cylinder ◽  
Hankel Transform ◽  
Newtonian Fluids ◽  
Circular Cylinders ◽  
Second Grade ◽  
Convolution Product ◽  
Shear Stresses ◽  
Cylindrical Domain ◽  
Second Grade Fluid ◽  
Grade Fluid

The flows of Magnetohydrodynamics(MHD) second grade fluid between two infinite porous coaxial circular cylinders are studied. At time t=0^+, the inner cylinder begins to rotate around its axis and to slide along the same axis due to torsional and longitudinal time dependent shear stresses and the outer cylinder is also rotate around its axis and to slide along the same axis with acceleration. The exact solutions obtained with the help of discrete Laplace and finite Hankel transform, satisfy all imposed initial and boundary conditions. The solution presented in convolution product of Laplace transform . The corresponding solutions for second grade and Newtonian fluids are also obtained as limiting cases with and without MHD effect. Finally, the influence of pertinent parameters on the velocity components and shear stresses, as well as a comparison among, second grade and Newtonian fluids with and without MHD  is also analyzed by graphical illustrations.

scholarly journals Oscillating Flows of Fractionalized Second Grade Fluid

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Muhammad Jamil ◽  
Najeeb Alam Khan ◽  
Abdul Rauf
Keyword(s):  
Fluid Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Classical Solutions ◽  
Second Grade Fluid ◽  
New Exact Solutions ◽  
Special Cases ◽  
Transient Solutions ◽  
In Series ◽  
Grade Fluid

New exact solutions for the motion of a fractionalized (this word is suitable when fractional derivative is used in constitutive or governing equations) second grade fluid due to longitudinal and torsional oscillations of an infinite circular cylinder are determined by means of Laplace and finite Hankel transforms. These solutions are presented in series form in term of generalized Ga,b,c(⋅,t) functions and satisfy all imposed initial and boundary conditions. In special cases, solutions for ordinary second grade and Newtonian fluids are obtained. Furthermore, other equivalent forms of solutions for ordinary second grade and Newtonian fluids are presented and written as sum of steady-state and transient solutions. The solutions for Newtonian fluid coincide with the well-known classical solutions. Finally, by means of graphical illustrations, the influence of pertinent parameters on fluid motion as well as comparison among different models is discussed.

SECOND‐GRADE FLUID FLOW WITH POWER‐LAW HEAT FLUX AND A HEAT SOURCE

2013 ◽  
Vol 44 (8) ◽  
pp. 687-702 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir A. Shehzad ◽  
Muhammad Qasim ◽  
F. Alsaadi ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Flux ◽  
Fluid Flow ◽  
Heat Source ◽  
Power Law ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Power Law Heat Flux

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

Flow of Second Grade Fluid in a Scraped Surface Heat Exchanger

2016 ◽  
Vol 40 (2) ◽  
pp. e12393 ◽  
Author(s):  
A. Imran ◽  
M.A. Rana ◽  
A.M. Siddiqui ◽  
M. Shoaib
Keyword(s):  
Heat Exchanger ◽  
Surface Heat ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Scraped Surface Heat Exchanger ◽  
Grade Fluid ◽  
Surface Heat Exchanger

scholarly journals Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall

2016 ◽  
Vol 21 (2) ◽  
pp. 359-376
Author(s):  
N.A. Khan ◽  
F. Naz
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Three Dimensional ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Grade Fluid ◽  
Suction Or Injection

AbstractThis investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid

Meccanica ◽  
2008 ◽  
Vol 43 (5) ◽  
pp. 495-504 ◽  
Author(s):  
S. Nadeem ◽  
S. Asghar ◽  
T. Hayat ◽  
Mazhar Hussain
Keyword(s):  
Stokes Problem ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

Stability analysis on dual solutions of second- grade fluid flow with heat and mass transfers over a stretching sheet

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
D. Dey ◽  
R. Borah
Keyword(s):  
Fluid Flow ◽  
Stability Analysis ◽  
Lorentz Force ◽  
Drag Force ◽  
Dual Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Independent Case ◽  
Grade Fluid ◽  
Mass Transfers

Stability on dual solutions of second-grade fluid flow over a stretching surface with simultaneous thermal and mass diffusions has been studied. The fluid flow is governed by Lorentz force and energy dissipation due to viscosity. Lorentz force is generated due to the application of magnetic field along the transverse direction. In methodology, suitable similarity transformation and MATLAB built-in bvp4c solver technique have been adopted. Effects of some flow parameters are exhibited through figures and tables and a special emphasis is given on the existence of dual solutions. A stability analysis is executed to determine the stable and physically achievable solutions. For the laminar flow, the drag force on the surface for the time-independent case is reduced due to amplifying values of But, it enhances the drag force for the time-dependent case. This shows the effectiveness of the first solution (during steady case) over the unsteady case.

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