Mathematical Model of Flow in a Doubly Constricted Permeable Channel with Effect of Slip Velocity

2019 ◽  
Vol 8 (4) ◽  
pp. 656-666
Author(s):  
P. Muthu ◽  
M. Varunkumar
Keyword(s):  
Mathematical Model ◽  
Slip Velocity ◽  
Permeable Channel

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Mathematical model for two-dimensional dry friction modified by dither

2016 ◽  
Vol 22 (10) ◽  
pp. 1936-1949 ◽  
Author(s):  
Adam Wijata ◽  
Jan Awrejcewicz ◽  
Jan Matej ◽  
Michał Makowski
Keyword(s):  
Mathematical Model ◽  
Dry Friction ◽  
Slip Velocity ◽  
Dimensional Space ◽  
Friction Model ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Friction Anisotropy ◽  
Stick Slip ◽  
Integrator Model

A new dynamic two-dimensional friction model is developed that is based on the bristle theory. Actually, it is the Reset Integrator Model converted into a two-dimensional space. Usually, two-dimensional friction models are in fact one-dimensional models that are rotated into a slip velocity direction. However, this common approach cannot be applied to the bristle model. That is why the idea of a two-dimensional bristle is presented. The bristle’s deformation is described using polar coordinates. The carried-out numerical simulation of a planar oscillator has proved that the new model correctly captures the mechanism of smoothing dry friction by dither applied in both a perpendicular and co-linear way regarding body velocity. Furthermore, the introduced mathematical model captures two-dimensional stick-slip behaviour. Cartesian slip velocity components are the only inputs to the model. In addition, our proposed model allows one to describe friction anisotropy using bristle parameters. The paper contains the results of an experimental verification of the new friction model, conducted with a special laboratory rig employed to investigate a two-dimensional motion in the presence of dither as well as to validate our numerical results.

A mathematical model of blood flow in a permeable channel: application to flat plate dialyzer

2020 ◽  
Vol 95 (4) ◽  
pp. 045202 ◽  
Author(s):  
Muhammad Kahshan ◽  
Dianchen Lu ◽  
Mohammad Rahimi-Gorji ◽  
Hoang-Thinh Do
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Flat Plate ◽  
Permeable Channel

scholarly journals Mathematical model of solute transfer in a permeable channel with effect of variable viscosity

2021 ◽  
Author(s):  
Varunkumar Merugu
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Osmotic Pressure ◽  
Variable Viscosity ◽  
Colloid Osmotic Pressure ◽  
Solute Transfer ◽  
Permeable Channel ◽  
Coupled Equations ◽  
Glomerular Capillary ◽  
The Difference

This paper describes a mathematical model of solute transfer in fluid flow across a permeable channel with variable viscosity, with applications to glomerular capillary blood flow. Solute transfer through the glomerular capillary wall is controlled by the difference in transcapillary hydrostatic pressure and the analogous difference in colloid osmotic pressure (Starling’s law). Using appropriate analytical and numerical approaches, the solutions of coupled equations regulating fluid flow and solute transport are found. The current study’s hydrostatic and osmotic pressure curves are qualitatively in excellent agreement with the experimental data. The effects of variable viscosity on velocity profiles, concentration profiles, and total solute clearance are seen to be substantial, and the findings are graphically depicted.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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