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Computational Thermal Sciences: An International Journal

Publication de 6  numéros par an

ISSN Imprimer: 1940-2503

ISSN En ligne: 1940-2554

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

Volume 8, Numéro 2, 2016, pp. 147-161
DOI: 10.1615/ComputThermalScien.2016015459
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RÉSUMÉ

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.

CITÉ PAR
  1. Pinheiro I. F., Sphaier L. A., de B. Alves L. S., Integral transform solution of integro-differential equations in conduction-radiation problems, Numerical Heat Transfer, Part A: Applications, 73, 2, 2018. Crossref

  2. Corrêa Lívia M., Chalhub Daniel J. N. M., Application of an exact integral transform formulation for temperature estimation in solid-state electronics, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 4, 2021. Crossref

  3. Sphaier L.A., Braga N.R., Chalhub D.J.N.M., Analytical solutions for extended Graetz problem in infinite domains via integral transforms, International Journal of Thermal Sciences, 170, 2021. Crossref

  4. Su Liangbin, He Boshu, Wang Gang, Xiao Renzheng, Yu Wan, Simultaneously developing flow and heat transfer in circular and parallel-plates microchannels with velocity slip and temperature jump, International Journal of Thermal Sciences, 177, 2022. Crossref

  5. Chalhub Daniel J.N.M., Corrêa Lívia M., Teixeira Renan de S., Analytical solution for thermally developing laminar core-annular flow with two immiscible liquids considering axial diffusion in semi-infinite ducts, Chemical Engineering Research and Design, 178, 2022. Crossref

  6. Pinheiro Isabela F., Sphaier Leandro A., SEMI-ANALYTICAL METHOD FOR INTEGRAL TRANSFORM SOLUTION OF TRANSIENT DIFFUSION WITH VARIABLE COEFFICIENTS , Computational Thermal Sciences: An International Journal, 14, 4, 2022. Crossref

  7. Su Liangbin, He Boshu, Yu Wan, Analytical solution of thermally developing heat transfer in circular and parallel plates microchannels, Sādhanā, 47, 4, 2022. Crossref

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