Abstract
The heat equation, for both steady and unsteady situations, is considered when the material parameters are spherically symmetric functions of position. Explicit separated solutions are derived when the material parameters are exponential functions; the radial part of these solutions is given in terms of confluent hypergeometric functions or Whittaker functions. In the steady case, explicit solutions are found when the conductivity k(r)= exp(−βrq), where β and q are parameters with q>0. The behaviour near the tip of a spherically-graded cone is also investigated.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.