scholarly journals Simulation and modeling of second order velocity slip flow of micropolar ferrofluid with Darcy–Forchheimer porous medium

2020 ◽  
Vol 9 (4) ◽  
pp. 7335-7340 ◽  
Author(s):  
M. Ijaz Khan ◽  
Faris Alzahrani ◽  
Aatef Hobiny
Keyword(s):  
Porous Medium ◽  
Slip Flow ◽  
Velocity Slip ◽  
Second Order ◽  
Simulation And Modeling

Modeling and theoretical investigation of curved parabolized surface of second-order velocity slip flow: Combined analysis of entropy generation and activation energy

2020 ◽  
Vol 34 (33) ◽  
pp. 2050383
Author(s):  
Sumaira Qayyum ◽  
M. Ijaz Khan ◽  
Wathek Chammam ◽  
W. A. Khan ◽  
Zulfiqar Ali ◽  
...  
Keyword(s):  
Activation Energy ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Slip Flow ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Second Order ◽  
Bejan Number ◽  
Biot Numbers ◽  
Chemical Reaction Parameter

Here our purpose is to explore the entropy generation in nanofluid MHD flow by curved stretching sheet; second-order slip is considered. Additional effects of viscous dissipation, Joule heating, and activation energy are taken. Temperature and concentration boundary conditions are considered convectively. For convergence of series solution NDSolve MATHEMATICA is used. Velocity, Bejan number, concentration, temperature, and entropy generation graphs are sketched for important parameters. For greater estimations of first- and second-order velocity slip parameters fluid velocity reduces. The thermal and solutal Biot numbers enhance the temperature and concentration, respectively. The concentration also has direct relation with activation energy. Entropy generation reduces for chemical reaction parameter and first- and second-order slip parameters.

scholarly journals MHD Flow of Nanofluid with Homogeneous-Heterogeneous Reactions in a Porous Medium under the Influence of Second-Order Velocity Slip

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 220 ◽  
Author(s):  
Fahd Almutairi ◽  
S.M. Khaled ◽  
Abdelhalim Ebaid
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Heterogeneous Reaction ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Heterogeneous Reactions

The influence of second-order velocity slip on the MHD flow of nanofluid in a porous medium under the effects of homogeneous-heterogeneous reactions has been analyzed. The governing flow equation is exactly solved and compared with those in the literature for the skin friction coefficient in the absence of the second slip, where great differences have been observed. In addition, the effects of the permanent parameters on the skin friction coefficient, the velocity, and the concentration have been discussed in the presence of the second slip. As an important result, the behavior of the skin friction coefficient at various values of the porosity and volume fraction is changed from increasing (in the absence of the second slip) to decreasing (in the presence of the second slip), which confirms the importance of the second slip in modeling the boundary layer flow of nanofluids. In addition, five kinds of nanofluids have been investigated for the velocity profiles and it is found that the Ag-water nanofluid is the lowest. For only the heterogeneous reaction, the concentration equation has been exactly solved, while the numerical solution is applied in the general case. Accordingly, a reduction in the concentration occurs with the strengthening of the heterogenous reaction and also with the increase in the Schmidt parameter. Moreover, the Ag-water nanofluid is of lower concentration than the Cu-water nanofluid. This is also true for the general case, when both of the homogenous and heterogenous reactions take place.

scholarly journals Oscillatory MHD Convective Flow of Second Order Fluid Through Porous Medium in a Vertical Rotating Channel in Slip-Flow Regime with Heat Radiation

2015 ◽  
Vol 20 (1) ◽  
pp. 33-52 ◽  
Author(s):  
B.P. Garg ◽  
K.D. Singh ◽  
A.K. Bansal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Convective Flow ◽  
Slip Flow ◽  
Closed Form Solution ◽  
Second Order ◽  
Slip Condition ◽  
Heat Radiation ◽  
Viscoelastic Parameter ◽  
Suction Parameter

Abstract An analysis of an oscillatory magnetohydrodynamic (MHD) convective flow of a second order (viscoelastic), incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented. The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature of the plate with no-slip condition is non-uniform and oscillates periodically with time and the temperature difference of the two plates is assumed high enough to induce heat radiation. The entire system rotates in unison about the axis perpendicular to the planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters of the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of the viscoelastic parameter γ, rotation parameter Ω, suction parameter λ , Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, radiation parameter N and the frequency of oscillation ω .

Entropy optimized magnetohydrodynamics Darcy–Forchheimer second order velocity slip flow of nanomaterials between two stretchable disks

2020 ◽  
Vol 234 (21) ◽  
pp. 4190-4199
Author(s):  
M Ijaz Khan ◽  
Faris Alzahrani
Keyword(s):  
Numerical Solutions ◽  
Ohmic Heating ◽  
Slip Flow ◽  
Velocity Slip ◽  
Second Order ◽  
Entropy Rate ◽  
Bejan Number ◽  
Rotating Disks ◽  
Different Types ◽  
Flow Variables

Here magnetohydrodynamics Darcy–Forchheimer second order velocity slip flow of nanomaterials is discussed between two stretchable surfaces of rotating disks, where the both disks are rotating with altered angular frequencies and rates. Flow in permeable medium is designated by implementing Darcy–Forchheimer relation. The energy expression is discussed and modeled subject to various effects like dissipation, Ohmic heating (Joule heating), and heat source/sink. Two different types of nanoparticles, i.e. graphene oxide (GO) and titanium dioxide (TiO2), are utilized and H2O as a base fluid. Total entropy rate which depends on five different types of irreversibilities (i.e., heat, mass fluid friction, Ohmic heating and Darcy–Forchheimer or porosity) is calculated via thermodynamics law (second). Furthermore, binary chemical reaction is accounted for the analysis of mass with activation energy. Numerical solutions are found out with the help of shooting method. Behaviors of flow variables on the skin friction coefficients, velocity field, Nusselt numbers, temperature distribution, entropy generation, concentration, and Bejan number are plotted graphically and discussed. The results are compared with previous literature and found good agreement with them. Our obtained results illustrate that the entropy rate is more subject to rising Brinkman number.

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