scholarly journals Numerical Study of the Unique Solvability of the Showalter - Sidorov Problem for a Mathematical Model of the Propagation of Nerve Impulses in the Membrane

2021 ◽  
Vol 8 (3) ◽  
pp. 32-48
Author(s):  
O.V. Gavrilova ◽  
Keyword(s):  
Mathematical Model ◽  
Unique Solvability ◽  
Numerical Study ◽  
Nerve Impulses

NUMERICAL STUDY FOR THAILAND: MATHEMATICAL MODEL OF PRODUCTION AND LOGISTIC PLANNING FOR SUGARCANES USED IN BIOFUEL PRODUCTION

2013 ◽  
Author(s):  
Pancheewa Benjamasutin ◽  
◽  
Ponthong Rijana ◽  
Phongchayont Srisuwan ◽  
Aussadavut Dumrongsiri
Keyword(s):  
Mathematical Model ◽  
Numerical Study ◽  
Biofuel Production ◽  
Logistic Planning

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Solidification of a Binary Solution (NH4Cl+H2O) under Shear Flow: A Numerical Study

2014 ◽  
Vol 217-218 ◽  
pp. 174-181
Author(s):  
Akshaya Kumar Nayak ◽  
Nilkanta Barman ◽  
Himadri Chattaopadhyay
Keyword(s):  
Mathematical Model ◽  
Shear Flow ◽  
Numerical Study ◽  
Binary Solution ◽  
Species Conservation ◽  
Solidification Process ◽  
Bulk Solution ◽  
Computational Domain ◽  
Simpler Algorithm ◽  
Slurry Layer

In the present work, the solidification behaviour of a metal analogues transparent binary solution (8 wt% of NH4Cl in H2O) under shear flow is investigated numerically. The shear flow in the mush is developed due to flow over an inclined cooling plate. The dendrites formed during solidification are fragmented under the shear flow and transported into the bulk solution. The suspended dendrites form a slurry layer in the domain. Consequently, a suitable mathematical model is considered to study the transport phenomena. In the mathematical model, the free surface of the solution is represented by the volume-of-fluid (VOF) method. The solidification process is modelled by a set of volume-averaged-single-phase mass, momentum, energy and species conservation equations. A separate equation is considered for the solid velocity based on Stokes model. The governing equations are solved based on the pressure-based semi-implicit finite volume method according to the SIMPLER algorithm using TDMA solver along with the enthalpy update scheme. Finally, the simulation predicts temperature, velocity, solid fraction and the species distributions in the computational domain. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

scholarly journals Implementation of a Mathematical Model to Improve Sustainability in the Handling of Transport Costs in a Distribution Network

2019 ◽  
Vol 12 (1) ◽  
pp. 63
Author(s):  
José Manuel Velarde ◽  
Susana García ◽  
Mauricio López ◽  
Alfredo Bueno-Solano
Keyword(s):  
Mathematical Model ◽  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Numerical Study ◽  
Distribution Network ◽  
Transport Cost ◽  
Mixed Integer ◽  
Distribution Area ◽  
Use Of Resources

This work considers the application of a mathematical model using mixed-integer linear programming for the vehicle routing problem. The model aims at establishing the distribution routes departing from a distribution center to each customer in order to reduce the transport cost associated with these routes. The study considers the use of a fleet of different capacities in the distribution network, which presents the special characteristic of a star network and which must meet different efficiency criteria, such as the fulfillment of each customer’s demand, the vehicle carrying capacity, work schedule, and sustainable use of resources. The intention is to find the amount of equipment suitable to satisfy the demand, thus improving the level of customer service, optimizing the use of both human and economic resources in the distribution area, and leveraging maximum vehicle capacity usage. The MILP mixed-integer linear programming mathematical model of the case study is presented, as well as the corresponding numerical study.

scholarly journals Development of a mathematical model for the numerical study of a thermal control system fluid circuit

2019 ◽  
Vol 537 ◽  
pp. 022003
Author(s):  
F V Tanasienko ◽  
Yu N Shevshenko ◽  
M G Melkozerov ◽  
A A Kishkin ◽  
A V Delkov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Numerical Study ◽  
Thermal Control ◽  
Thermal Control System

A Numerical Study on Integral Solar Air Collector

2013 ◽  
Vol 860-863 ◽  
pp. 146-150
Author(s):  
Fu Sheng Dong ◽  
Ming Fu Hu ◽  
Xiao Chun Huang
Keyword(s):  
Mathematical Model ◽  
Solar Radiation ◽  
Thermal Efficiency ◽  
Radiation Intensity ◽  
Numerical Study ◽  
One Dimension ◽  
Inlet Temperature ◽  
Solar Radiation Intensity ◽  
Solar Air Collector ◽  
Matlab Programming

A mathematical modeling method was devoted to study the thermal performance of integral solar air collector. A mathematical model of heat transfer was set up based on one-dimension assumptions at first, and then numerical solution was brought out by using finite-difference method under one-dimension steady heat exchange. Through the MATLAB programming, the approximate solutions for the local air temperature and thermal efficiency were obtained at the quasi-steady state. After calculation, the influence of air inlet velocity, inlet temperature, solar radiation intensity and height of flow channel on the performance of collector was analyzed. It is discovered that the mathematical model is reasonable, the thermal efficiency decreases with temperature of inlet air increasing and increases with air velocity increasing, on which the solar radiation intensity have little influence. Depth of the channel and optimum flow both have a best value.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

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