|
Exact solution of boundary value problemdescribing the convective heat transfer in fully-developedlaminar flow through a circular conduit |
|---|---|
| รหัสดีโอไอ | |
| Creator | 1. Ali Belhocine 2. Wan Zaidi Wan Omar |
| Title | Exact solution of boundary value problemdescribing the convective heat transfer in fully-developedlaminar flow through a circular conduit |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2561 |
| Journal Title | Songklanakarin Journal of Science and Technology |
| Journal Vol. | 40 |
| Journal No. | 4 |
| Page no. | 840 |
| Keyword | Graetz problem, Sturm-Liouville problem, partial differential equation, dimensionless variable |
| URL Website | http://rdo.psu.ac.th/sjstweb/index.php |
| ISSN | 0125-3395 |
| Abstract | This paper proposes anexact solution in terms of an infinite series to the classical Graetz problem represented by anonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. Themathematical derivation is based on the method of separation of variables whose several stages are elaborated to reach thesolution of the Graetz problem. MATLAB was used to compute the eigenvalues of the differential equation as well as thecoefficient series. However, both the Nusselt number as an infinite series solution and the Graetz number are based on the heattransfer coefficient and the heat flux from the wall to the fluid. In addition, the analytical solution was compared to the numericalvalues obtained by the same author using a FORTRAN program, showing that the orthogonal collocation method gave betterresults. It is important to note that the analytical solution is in good agreement with published numerical data. |
