Critical insulation thickness of a rectangular slab embedded with a periodic array of isothermal strips

Marios M. Fyrillas, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We address the problem of two-dimensional heat conduction in a solid slab embedded with a periodic array of isothermal strips. The surfaces of the slab are subjected to a convective heat transfer boundary condition with a uniform heat transfer coefficient. Similar to the concept of critical insulation radius, associated with cylindrical and spherical configurations, we show that there exists a critical insulation thickness, associated with the slab, such that the total thermal resistance attains a minimum, i.e. a maximum heat transfer rate can be achieved. This result, which is not observed in one-dimensional heat conduction in a plane wall, is a consequence of the non-trivial coupling between conduction and convection that results in a 2D temperature distribution in the slab, and a non-uniform temperature on the surface of the slab. The findings of this work offer opportunities for improving the design of a broad range of engineering processes and products.

Original languageEnglish (US)
Pages (from-to)180-185
Number of pages6
JournalInternational Journal of Heat and Mass Transfer
Issue number1-3
StatePublished - Jan 15 2011

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


  • Critical insulation thickness
  • Heat conduction/convection
  • Laplace equation
  • Overall heat transfer coefficient
  • Shape factor
  • Solid slab with periodic array of isothermal strips
  • Total thermal resistance


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