Mathematical Model of Fluid Flow and Solute Transfer in a Permeable Channel with Slip Velocity at the Boundaries

2021 ◽  
Author(s):  
G. Radhakrishnamacharya ◽  
P. Muthu ◽  
M. Varunkumar
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Slip Velocity ◽  
Solute Transfer ◽  
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.

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.

Mathematical model of the hydrocyclone based on physics of fluid flow

AIChE Journal ◽  
1991 ◽  
Vol 37 (5) ◽  
pp. 735-746 ◽  
Author(s):  
K. T. Hsieh ◽  
R. K. Rajamani
Keyword(s):  
Mathematical Model ◽  
Fluid Flow

scholarly journals Spreading of chemical substance after its accidental spillage onto the soil surface under unsaturated conditions and variable porosity

2019 ◽  
pp. 41-44
Author(s):  
Olena Kozhushko ◽  
Petro Martyniuk
Keyword(s):  
Mathematical Model ◽  
Soil Moisture ◽  
Soil Profile ◽  
Moisture Transport ◽  
Soil Surface ◽  
Chemical Substance ◽  
High Concentration ◽  
Solute Transfer ◽  
Variable Porosity ◽  
The One

In this paper we study a mathematical model of soil moisture transport with variable porosity. The problem is set for the case of highly concentrated solute spilled onto soil surface. We investigate the way solute transfer, adsorption of contaminant by soil particles and variable porosity influence infiltration of solute into the soil profile. For that purpose, two models are used: a classical one and the one with consideration of mentioned factors. By comparing the results of both models, we established that high concentration of solute causes moisture transport to transpire more slowly, and the pollutant to remain on the soil surface for longer time. Numerical results indicate that porosity can vary considerably under the conditions of intensive contamination with salts.

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