The Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional time‐derivative approach on transient free convection flow between two vertical parallel plates: A semi‐analytical solution

Heat Transfer ◽  
2021 ◽  
Author(s):  
Basant K. Jha ◽  
Ismaila Olatoye Oyelade ◽  
Peter Malgwi
Keyword(s):  
Analytical Solution ◽  
Free Convection ◽  
Time Derivative ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Fractional Time Derivative

Shape Effect in Magnetohydrodynamic Free Convection Flow of Sodium Alginate-Ferrimagnetic Nanofluid

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Muhammad Saqib ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Sodium Alginate ◽  
Fluid Model ◽  
Dominant Factor ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Shape Effect ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Laplace Transform Technique

This article presents the generalization of the unsteady MHD free convection flow of non-Newtonian sodium alginate-ferrimagnetic nanofluid in two infinite vertical parallel plates. The different shape (blade, brick, cylinder, and platelet) ferrimagnetic nanoparticles are dissolved in the non-Newtonian sodium alginate (SA) as base fluid to form non-Newtonian nanofluids. The Jeffrey fluid model together with energy equation is considered to demonstrate the flow. The Atangana–Baleanu fractional operator is utilized for the generalization of mathematical model. The Laplace transform technique and Zakian's numerical algorithm are used to developed general solutions with a fractional order for the proposed model. The obtained results are computed numerically and presented graphically to understand the physics of pertinent flow parameters. It is noticed that the velocity and temperature profiles are significantly increased with the increasing values of the fractional parameter due to the variation in thermal and momentum boundary layers. In the case of the effect of different shapes of nanoparticles, density is a dominant factor as compared to thermal conductivity, which significantly affects the flow of non-Newtonian nanofluid.

scholarly journals Unsteady Free Convection Flow between Two Vertical Parallel Plates with Newtonian Heating

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 117-127
Author(s):  
Fasihah Zulkiflee ◽  
Ahmad Qushairi Mohamad ◽  
Sharidan Shafie ◽  
Arshad Khan
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Skin Friction ◽  
Approximate Solutions ◽  
Convection Flow ◽  
Parallel Plates ◽  
Newtonian Heating ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Incompressible Viscous Fluids

Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutionsfor velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.

scholarly journals Hydromagnetic free convection flow of viscous fluid between vertical parallel plates with damped thermal and mass fluxes

2019 ◽  
Vol 58 (3) ◽  
pp. 989-1000 ◽  
Author(s):  
Zehui Shao ◽  
Nehad Ali Shah ◽  
Iskander Tlili ◽  
Usman Afzal ◽  
M. Saqib Khan
Keyword(s):  
Free Convection ◽  
Viscous Fluid ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Mass Fluxes

Transient free convection flow between two vertical parallel plates

1996 ◽  
Vol 31 (5) ◽  
pp. 329-331 ◽  
Author(s):  
A. K. Singh ◽  
H. R. Gholami ◽  
V. M. Soundalgekar
Keyword(s):  
Free Convection ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow

scholarly journals Unsteady Free Convection Flow of Nanofluids between Vertical Oscillating Plates with Mass Diffusion

2020 ◽  
Vol 76 (2) ◽  
pp. 118-131
Author(s):  
Fasihah Zulkiflee ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad
Keyword(s):  
Free Convection ◽  
Schmidt Number ◽  
Volume Fraction ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Concentration Profiles ◽  
Parallel Plates ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Nanoparticles Volume Fraction

In this paper, free convection of nanofluids flow with oscillating vertical parallel plates and mass diffusion were considered. Obtained equations were converted into ordinary differential equations with appropriate transformations. Method of Laplace transform was used to find the exact solutions of velocity, temperature and concentration profiles from the dimensionless governing equations. Discussion of graph pertaining to different embedded parameters such as Prandtl number, Schmidt number, Grashof and mass Grashof number, oscillating parameter and nanoparticles volume fraction parameter was also added. Skin friction, Nusselt and Sherwood number were also discussed and deliberated.

Free convection flow with chemical reaction effect between oscillating parallel plates

2021 ◽  
Vol 2 (2) ◽  
pp. 52-59
Author(s):  
F. Zulkiflee ◽  
S. Shafie ◽  
A. Ali ◽  
A.Q. Mohamad
Keyword(s):  
Free Convection ◽  
Prandtl Number ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Schmidt Number ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Transform Method ◽  
Grashof Number

This research purpose is to investigate the exact solutions for unsteady free convection flow between oscillating parallel plates with mass diffusion and chemical reaction. The governing equations are modelled and reduced using non-dimensional variables. The method used is Laplace transform method. Solutions for velocity, temperature, and concentration fields as well as skin friction, Nusselt and Sherwood number are obtained. For physical understanding, analytical results for velocity, temperature and concentration profile are plotted graphically with respect to the Schmidt number, Prandtl number, oscillating parameter, Grashof number, mass Grashof number and chemical reaction parameter. Increasing Prandtl number and Schmidt number decreases the concentration, velocity, temperature, and skin friction but increases the Sherwood and Nusselt numbers.

Transient free convection flow between two vertical parallel plates

1996 ◽  
Vol 31 (5) ◽  
pp. 329-331
Author(s):  
A. K. Singh ◽  
Hamid R. Gholami ◽  
V. M. Soundalgekar
Keyword(s):  
Free Convection ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow
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