Journal of Zhejiang University SCIENCE A

, Volume 13, Issue 10, pp 768–781 | Cite as

An exact analytical solution for convective heat transfer in rectangular ducts

  • Mohammad Mohsen Shahmardan
  • Mahmood Norouzi
  • Mohammad Hassan Kayhani
  • Amin Amiri Delouei
Article

Abstract

An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time. This solution is valid for both H1 and H2 boundary conditions, which are related to fully developed convective heat transfer under constant heat flux at the duct walls. The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution. The local and mean Nusselt numbers are also obtained as functions of the aspect ratio. A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions. This is one of the major innovations of the current study. The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.

Key words

Exact analytical solution Convective heat transfer Straight duct Rectangular cross-section Constant heat flux 

CLC number

TK123 O35 

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Copyright information

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mohammad Mohsen Shahmardan
    • 1
  • Mahmood Norouzi
    • 1
  • Mohammad Hassan Kayhani
    • 1
  • Amin Amiri Delouei
    • 1
  1. 1.Department of Mechanical EngineeringShahrood University of TechnologyShahroodIran

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