Steady heat conduction with generalized boundary conditions

Kevin D. Cole, Filippo De Monte, Robert L. McMasters, Keith A. Woodbury, A. Haji-Sheikh, James V. Beck

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Heat transfer in solids provides an opportunity for students to learn of several boundary conditions: the first kind for specified temperature, the second kind for specified heat flux, and the third kind for specified convection. In this paper we explore the relationship among these types of boundary conditions in steady heat transfer. Specifically, the normalized third kind of boundary condition (convection) produces the first kind condition (specified temperature) for large Biot number, and it produces the second kind condition (specified flux) for small Biot number. By employing a generalized boundary condition, one expression provides the temperature for several combinations of boundary conditions. This combined expression is presented for several simple geometries (slabs, cylinders, spheres) with and without internal heat generation. The bioheat equation is also treated. Further, a number system is discussed for each combination to identify the type of boundary conditions present, which side is heated, and whether internal generation is present. Computer code for obtaining numerical values from the several expressions is available, along with plots and tables of numerical values, at a web site called the Exact Analytical Conduction Toolbox. Classroom strategies are discussed regarding student learning of these issues: the relationship among boundary conditions; a number system to identify the several components of a boundary value problem; and, the utility of a web-based resource for analytical heat-transfer solutions.

Original languageEnglish (US)
Title of host publicationEducation and Globalization
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791850572
StatePublished - 2016
EventASME 2016 International Mechanical Engineering Congress and Exposition, IMECE 2016 - Phoenix, United States
Duration: Nov 11 2016Nov 17 2016

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)


OtherASME 2016 International Mechanical Engineering Congress and Exposition, IMECE 2016
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Mechanical Engineering


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