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

作者：Jain Prashant K^*; Singh Suneet; Rizwan uddin

来源：International Journal of Heat and Mass Transfer, 2010, 53(9-10): 2133-2142.

DOI：10.1016/j.ijheatmasstransfer.2009.12.035

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

Analytical series solution is proposed for the transient boundary-value problem of multilayer heat conduction in r-theta 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 theta-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 oil those in the theta-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.

• 出版日期2010-4