![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
The paper analyzes the transient heat conduction problem with the irregular geometry using the meshless weighted least-square method (MWLS). The MWLS as a meshless method is fully independent of mesh, a discrete function is used to construct a series of linear equations, which avoided the troublesome task of numerical integration. First, irregular geometries are represented by the signed distance field. Then sampling the distance field, discrete nodes are obtained for MWLS analysis. The effectiveness and accuracy of the approach are illustrated by several numerical examples. Numerical cases show that a good agreement is achieved between the results obtained from the proposed meshless method and available analytical solutions or commercial software ANSYS.
Nomenclature
| a(x) | = | coefficient |
| A(x), B(x) | = | matrices of computation |
| c | = | specific heat |
| dmI | = | radius of the circular support domain |
| h | = | the heat transfer coefficient |
| I, J | = | node indices |
| k | = | thermal conductivity |
| kk | = | number of neighbor points |
| N | = | number of nodes |
| n | = | outward surface normal |
| N(x) | = | Shape functions |
| N1, N2, N3 | = | number of interior nodes in the boundary Γ1, Γ2, and Γ3 |
| p(x) | = | basis function |
| Q | = | heat source |
| q | = | normal heat flux |
| T | = | temperature |
| T∞ | = | ambient temperature |
| = | initial temperature | |
| Δt | = | time step |
| uI | = | the nodal parameter of the field variable at node I |
| u(x) | = | the moving least-square approximation function |
| xI | = | the positions of the nodes |
| Ω | = | fixed domain |
| Γ | = | closed boundary of Ω |
| Γ1 | = | Dirichlet boundary |
| Γ2 | = | Neumann boundary |
| Γ3 | = | Mixed boundary |
| ρ | = | mass density |
| ωI(x) | = | weight functions |
Nomenclature
| a(x) | = | coefficient |
| A(x), B(x) | = | matrices of computation |
| c | = | specific heat |
| dmI | = | radius of the circular support domain |
| h | = | the heat transfer coefficient |
| I, J | = | node indices |
| k | = | thermal conductivity |
| kk | = | number of neighbor points |
| N | = | number of nodes |
| n | = | outward surface normal |
| N(x) | = | Shape functions |
| N1, N2, N3 | = | number of interior nodes in the boundary Γ1, Γ2, and Γ3 |
| p(x) | = | basis function |
| Q | = | heat source |
| q | = | normal heat flux |
| T | = | temperature |
| T∞ | = | ambient temperature |
| = | initial temperature | |
| Δt | = | time step |
| uI | = | the nodal parameter of the field variable at node I |
| u(x) | = | the moving least-square approximation function |
| xI | = | the positions of the nodes |
| Ω | = | fixed domain |
| Γ | = | closed boundary of Ω |
| Γ1 | = | Dirichlet boundary |
| Γ2 | = | Neumann boundary |
| Γ3 | = | Mixed boundary |
| ρ | = | mass density |
| ωI(x) | = | weight functions |
Acknowledgment
The correlative members of the projects are hereby acknowledged.