IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n684293.html

A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

Author

Listed:
  • Ryoichi Chiba

Abstract

A two‐dimensional differential transform method is applied to solve one‐dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other. In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature. A series solution is derived for the temperature profile in the melting or solidifying slab with temperature‐dependent thermal conductivity and volumetric heat capacity. The latent heat effect of the phase change is incorporated into the temperature‐dependent heat capacity. Numerical results demonstrate the effects of the temperature‐dependent parameters on the transient temperature profile of the slab.

Suggested Citation

  • Ryoichi Chiba, 2014. "A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:684293
    DOI: 10.1155/2014/684293
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/684293
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/684293?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Torabi, Mohsen & Aziz, Abdul & Zhang, Kaili, 2013. "A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities," Energy, Elsevier, vol. 51(C), pages 243-256.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kundu, Balaram & Lee, Kwan-Soo, 2014. "Analytical tools for calculating the maximum heat transfer of annular stepped fins with internal heat generation and radiation effects," Energy, Elsevier, vol. 76(C), pages 733-748.
    2. Torabi, Mohsen & Zhang, Kaili, 2014. "Classical entropy generation analysis in cooled homogenous and functionally graded material slabs with variation of internal heat generation with temperature, and convective–radiative boundary conditions," Energy, Elsevier, vol. 65(C), pages 387-397.
    3. Sousa, J. & Villafañe, L. & Paniagua, G., 2014. "Thermal analysis and modeling of surface heat exchangers operating in the transonic regime," Energy, Elsevier, vol. 64(C), pages 961-969.
    4. Hazarika, Saheera Azmi & Bhanja, Dipankar & Nath, Sujit & Kundu, Balaram, 2015. "Analytical solution to predict performance and optimum design parameters of a constructal T-shaped fin with simultaneous heat and mass transfer," Energy, Elsevier, vol. 84(C), pages 303-316.
    5. Torabi, Mohsen & Zhang, Kaili & Yang, Guangcheng & Wang, Jun & Wu, Peng, 2014. "Temperature distribution, local and total entropy generation analyses in asymmetric cooling composite geometries with multiple nonlinearities: Effect of imperfect thermal contact," Energy, Elsevier, vol. 78(C), pages 218-234.
    6. Torabi, Mohsen & Zhang, Kaili, 2014. "Temperature distribution and classical entropy generation analyses in an asymmetric cooling composite hollow cylinder with temperature-dependent thermal conductivity and internal heat generation," Energy, Elsevier, vol. 73(C), pages 484-496.
    7. P. V. Ananth Subray & B. N. Hanumagowda & S. V. K. Varma & A. M. Zidan & Mohammed Kbiri Alaoui & C. S. K. Raju & Nehad Ali Shah & Prem Junsawang, 2022. "Dynamics of Heat Transfer Analysis of Convective-Radiative Fins with Variable Thermal Conductivity and Heat Generation: Differential Transformation Method," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    8. Hsiao, Kai-Long, 2013. "Energy conversion conjugate conduction–convection and radiation over non-linearly extrusion stretching sheet with physical multimedia effects," Energy, Elsevier, vol. 59(C), pages 494-502.
    9. Saedodin, Seyfolah & Motaghedi Barforoush, Mohammad Sadegh, 2015. "Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields," Energy, Elsevier, vol. 90(P1), pages 652-662.
    10. Uddin, Md. Jashim & Bég, O. Anwar & Uddin, Md. Nazir, 2016. "Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions," Energy, Elsevier, vol. 115(P1), pages 1119-1129.
    11. Xia, H.H. & Tang, G.H. & Shi, Y. & Tao, W.Q., 2014. "Simulation of heat transfer enhancement by longitudinal vortex generators in dimple heat exchangers," Energy, Elsevier, vol. 74(C), pages 27-36.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:684293. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.