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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2016015459
pages 147-161

INTEGRAL TRANSFORM SOLUTION FOR THERMALLY DEVELOPING SLIP-FLOW WITHIN ISOTHERMAL PARALLEL PLATES

Daniel Chalhub
Universidade do Estado do Rio de Janeiro
Leandro A. Sphaier
Department of Mechanical Engineering – PGMEC, Universidade Federal Fluminense, Rua Passo da Patria 156, bloco E, sala 216, Niteroi, RJ, 24210-240, Brazil
Leonardo Alves
Departamento de Engenharia Mecânica - TEM Universidade Federal Fluminense - UFF

ABSTRAKT

This paper presents an analytical solution for an extended version of the Graetz problem for slip-flow in parallelplates channels. The problem formulation includes axial heat diffusion in a semi-infinite channel with a given inlet condition and isothermal walls. The solution methodology is based on the Generalized Integral Transform Technique, in which the sought temperature profile is written in terms of an orthogonal eigenfunction basis, stemming from a Sturm-Liouville type problem. Although the transformation of the original problem leads to a coupled ODE system, a closedform solution is obtained in terms of eigenvalues and eigenvectors of a matrix involving the ODE system's coupling coefficients. The solution is properly verified through comparisons with previous literature results and a numerical solution by finite differences. A convergence analysis of the results shows that better convergence rates are obtained for larger values of the Péclet and Knudsen numbers, even in the near-entrance region. Finally, a parametric analysis shows that the local Nusselt number increases with the Péclet number, and this increase is stronger for upstream positions. Nevertheless, for larger values of the Knudsen number, the dependence of the Nusselt number values on the Péclet number is shown to be weaker.


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