Numerical Solution of the Three-Dimensional Diffusion Equation in Solids with Arbitrary Geometry for the Convective Boundary Condition: Application in Drying

2013 ◽  
Vol 334-335 ◽  
pp. 149-154 ◽  
Author(s):  
V.S.O. Farias ◽  
Wilton Pereira Silva ◽  
C.M.D.P. Silva e Silva ◽  
L.D. Silva ◽  
F.J.A. Gama ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Convective Boundary Condition ◽  
Finite Cylinder ◽  
Transport Parameters ◽  
Time Step ◽  
Convective Boundary

In this work, a numerical solution for the diffusion equation applied to solids with arbitrary shape considering convective boundary condition is presented. To this end, the diffusion equation, written in generalized coordinates, was discretized by the finite-volume method with a fully implicit formulation. The transport parameters and the dimensions of the solids are considered constant during all process. For each time step, the system of equations obtained for a given non-orthogonal structured mesh was solved by the Gauss-Seidel method. One computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (parallelepiped and finite cylinder). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. In order to verify the potential of the proposed numerical solution, we used experimental data of the drying of ceramic roof tiles for the following temperature: T = 55.6 °C. The analysis of the results and the statistical indicators enables to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature for the convective boundary condition.

Three-Dimensional Diffusion in Arbitrary Domain Using Generalized Coordinates for the Boundary Condition of the First Kind: Application in Drying

2012 ◽  
Vol 326-328 ◽  
pp. 120-125 ◽  
Author(s):  
V.S.O. Farias ◽  
Wilton Pereira Silva ◽  
C.M.D.P. Silva e Silva ◽  
Antônio Gilson Barbosa de Lima
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Transient State ◽  
Arbitrary Domain ◽  
Time Step ◽  
Generalized Coordinates ◽  
Computational Code

This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. For this end, the diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. The computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (orthogonal and non-orthogonal meshes). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. The developed computational code was applied in the simulation of the drying of ceramic roof tiles for the following temperature: 55.6 °C. The analysis of the results makes it possible to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature.

Effect of convective boundary condition on unsteady flow of CNT-H2O nanofluid towards a stagnation-point on a shrinking/expanding flat sheet

2021 ◽  
pp. 095440892110546
Author(s):  
Sohita Rajput ◽  
Amit Kumar Pandey ◽  
Krishnendu Bhattacharyya ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Boundary Condition ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Convective Boundary Condition ◽  
Dual Solutions ◽  
Convective Boundary ◽  
Walled Carbon Nanotubes

A model study of unsteady stagnation-point flow of most important nanoparticles, that is, carbon nanotubes suspended nanofluid towards shrinking/expanding sheet with convective boundary condition is demonstrated. Two types of carbon nanotubes, namely, single-wall and multi-wall nanotubes are carefully considered. Numerical solutions of converted equations from governing equation of the problem are obtained and those are graphically presented. Similar to without carbon nanotubes case, dual and unique solutions in specific ranges of velocity ratio parameter are achieved. Analysis disclosures that the condition on range where dual solutions exist is unaltered with solid-volume fraction and type of carbon nanotubes. The surface drag-force and heat transfer rate from wall are larger for single-walled carbon nanotubes nanofluid than multi-walled carbon nanotubes nanofluid. An increment in the parameter related to convective boundary condition generates high rate of heat transfer. After stability analysis, it is identified that in case of dual solutions, upper branch is stable and lower branch is unstable, while unique solution is always stable.

Numerical Investigation of Two-Phase Mixed Convection Flow of Particulate Oldroyd-B Fluid with Non-Linear Thermal Radiation and Convective Boundary Condition

2018 ◽  
Vol 388 ◽  
pp. 204-222 ◽  
Author(s):  
Bijjanal Jayanna Gireesha ◽  
Basavarajappa Mahanthesh ◽  
Koneri L. Krupalakshmi
Keyword(s):  
Boundary Condition ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Numerical Solutions ◽  
Convective Boundary Condition ◽  
Dust Particles ◽  
Convection Flow ◽  
Nonlinear Thermal Radiation ◽  
Two Phase ◽  
Convective Boundary

The present investigation addresses the mixed convection two-phase flow of dusty Oldroyd-B fluid towards a vertical stretching surface in the presence of convective boundary condition and nonlinear thermal radiation. The fluid and dust particles motion is coupled only in the course of drag and heat transfer between them. The Stokes linear drag theory is employed to model the drag force. The numerical solutions based on the Runge-Kutta-Fehlberg 45 scheme with shooting method are presented for both fluid and particle phase velocity and temperature fields. Further, numerical results are obtained for skin friction factor and local Nusselt number of prescribed values of pertinent parameters. The results are presented graphically and the physical aspects of the problem are analyzed. The obtained results are validated with existing results and found to be in good agreement. It is found that the mass concentration of the dust particle parameter plays a key role in controlling flow and thermal behaviour of non-Newtonian fluids.

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