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ABSTRACT
In this article, the differential transform method (DTM) and the double-decomposition method (DDM) are used to solve the annular hyperbolic profile fins with variable thermal conductivity. Both DTM and DDM are used to derive the analytic solutions of nonlinear problems. As the thermal conductivity parameter ε is relatively large, the numerical solution using DDM becomes incorrect. For the terms of DDM more than seven, the numerical solution using DDM is also very complicated. However, DTM can be easily calculated as the number of terms is more than seven and has more precise numerical solutions.
Nomenclature
| Ar | = | cross-section area of the fin, m2; |
| As | = | local surface area, m2; |
| cm, n | = | integral constant; |
| ds | = | variation of the surface length; |
| g | = | source term heat transfer coefficient; |
| k | = | thermal conductivity, Wm−1K−1; |
| Q | = | heat transfer rate,; |
| Qideal | = | ideal heat transfer rate, W; |
| R | = | dimensionless radius, r/r0; |
| r | = | local radius of fin, m; |
| T | = | temperature, K. |
Nomenclature
| Ar | = | cross-section area of the fin, m2; |
| As | = | local surface area, m2; |
| cm, n | = | integral constant; |
| ds | = | variation of the surface length; |
| g | = | source term heat transfer coefficient; |
| k | = | thermal conductivity, Wm−1K−1; |
| Q | = | heat transfer rate,; |
| Qideal | = | ideal heat transfer rate, W; |
| R | = | dimensionless radius, r/r0; |
| r | = | local radius of fin, m; |
| T | = | temperature, K. |