An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates

Prashant K. Jain, Suneet Singh, Rizwan-uddin

Research output: Contribution to journalArticle

Abstract

Analytical series solution is proposed for the transient boundary-value problem of multilayer heat conduction in r-θ spherical coordinates. Spatially non-uniform, but time-independent, volumetric heat sources may exist in the concentric layers. Proposed solution is valid for any combination of homogenous boundary conditions of the first or second kind in the θ -direction. However, inhomogeneous boundary conditions of the first, second or third kind may be applied at the inner and outer radial boundaries of the concentric layers. It is noted that the proposed solution is "free" from imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of radial eigenvalues on those in the θ-direction. Solution is shown to be relatively simple for the most common spherical geometries-(multilayer) hemisphere and full sphere. An illustrative problem of heat conduction in a three-layer hemisphere is solved. Results along with the isotherms are shown graphically and discussed.

Original languageEnglish (US)
Pages (from-to)2133-2142
Number of pages10
JournalInternational Journal of Heat and Mass Transfer
Volume53
Issue number9-10
DOIs
StatePublished - Apr 2010

Fingerprint

Dysostoses
Micelles
conductive heat transfer
eigenvalues
Heat conduction
Multilayers
Cholestenones
spherical coordinates
hemispheres
boundary conditions
Boundary conditions
Almanacs
Cholesterol Side-Chain Cleavage Enzyme
Genetic Engineering
Hot Temperature
Escherichia coli
Geometry
heat sources
boundary value problems
isotherms

Keywords

  • Analytical
  • Conduction
  • Cones and wedges
  • Hemisphere
  • Multilayer
  • Spherical
  • Transient

ASJC Scopus subject areas

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

Cite this

An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates. / Jain, Prashant K.; Singh, Suneet; Rizwan-uddin.

In: International Journal of Heat and Mass Transfer, Vol. 53, No. 9-10, 04.2010, p. 2133-2142.

Research output: Contribution to journalArticle

Jain, Prashant K.; Singh, Suneet; Rizwan-uddin / An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates.

In: International Journal of Heat and Mass Transfer, Vol. 53, No. 9-10, 04.2010, p. 2133-2142.

Research output: Contribution to journalArticle

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