http://orcid.org/0000-0002-2954-1869
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ABSTRACT
A new approach for solving nonlinear integro-differential equations in conductive-radiative heat transfer has been developed. The method relies on eigenfunctions expansions for the unknown potentials, following the hybrid analytical-numerical framework provided by the generalized integral transform technique. The problem of conjugated conduction–radiation in a finned-tube radiator is selected for illustrating the method, and a traditional numerical solution of the problem is performed for comparing the proposed approach. A thorough error analysis demonstrates that the proposed scheme is very effective for handling integro-differential problems. Finally, a parametric analysis is provided, demonstrating the effects of the dimensionless groups in the temperature distribution.
Nomenclature
| 𝒜s | = | surface area |
| A, B, C, D | = | integral coefficients |
| F | = | configuration factor |
| h | = | height |
| i, j | = | summation indices |
| k | = | thermal conductivity |
| L | = | length |
| N | = | norm |
| = | radiation–conduction parameter | |
| r | = | radius |
| t | = | thickness |
| T | = | temperature |
| W | = | width |
| x, y | = | coordinates components |
| X, Y | = | dimensionless coordinates components |
| Greek symbols | = | |
| α1, α2 | = | constants |
| β | = | configuration parameter |
| δ | = | thickness |
| δij | = | kronecker delta |
| θ | = | homogenized dimensionless temperature |
| Θ | = | dimensionless temperature |
| κ | = | aspect ratio |
| λ | = | configuration parameter |
| μ | = | eigenvalues |
| σ | = | Stefan–Boltzmann constant |
| ϕ | = | filter |
| φ | = | angle |
| Ψ | = | eigenfunctions |
| ω | = | ratio between length and width |
| Subscripts | = | |
| b | = | base |
| c | = | conduction |
| max | = | maximum |
| r | = | radiation |
| Superscripts | = | |
| ∗ | = | dimensionless quantity |
| Overscripts | = | |
| ¯ | = | transformed quantity |
Nomenclature
| 𝒜s | = | surface area |
| A, B, C, D | = | integral coefficients |
| F | = | configuration factor |
| h | = | height |
| i, j | = | summation indices |
| k | = | thermal conductivity |
| L | = | length |
| N | = | norm |
| = | radiation–conduction parameter | |
| r | = | radius |
| t | = | thickness |
| T | = | temperature |
| W | = | width |
| x, y | = | coordinates components |
| X, Y | = | dimensionless coordinates components |
| Greek symbols | = | |
| α1, α2 | = | constants |
| β | = | configuration parameter |
| δ | = | thickness |
| δij | = | kronecker delta |
| θ | = | homogenized dimensionless temperature |
| Θ | = | dimensionless temperature |
| κ | = | aspect ratio |
| λ | = | configuration parameter |
| μ | = | eigenvalues |
| σ | = | Stefan–Boltzmann constant |
| ϕ | = | filter |
| φ | = | angle |
| Ψ | = | eigenfunctions |
| ω | = | ratio between length and width |
| Subscripts | = | |
| b | = | base |
| c | = | conduction |
| max | = | maximum |
| r | = | radiation |
| Superscripts | = | |
| ∗ | = | dimensionless quantity |
| Overscripts | = | |
| ¯ | = | transformed quantity |