### Abstract

We present the mathematical equations that govern heat transfer in a polymer melt flowing in a circular tube with constant ambient temperature, taking into account the viscous dissipation effects. This leads to a nonlinear parabolic partial differential equation. It is shown that the exact solution of a linearized version of the governing equation can be presented in terms of the Whittaker function. A finite difference scheme is used to produce an approximate solution of the linearized problem. The numerical solution is shown to be a good approximation to the exact solution found in terms of the Whittaker function. The finite difference scheme is then modified to approximate the nonlinear parabolic partial differential equation using nonlinear a iterative technique, and is compared to the results found using the finite element method.

Original language | English |
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Title of host publication | Society of Plastics Engineers - International Polyolefins Conference - FLEXPACKCON 2008 |

Pages | 791-796 |

Number of pages | 6 |

Volume | 2 |

Publication status | Published - 2008 |

Externally published | Yes |

Event | International Polyolefins Conference - FLEXPACKCON 2008 - Houston, TX, United States Duration: 24 Feb 2008 → 27 Feb 2008 |

### Other

Other | International Polyolefins Conference - FLEXPACKCON 2008 |
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Country | United States |

City | Houston, TX |

Period | 24/2/08 → 27/2/08 |

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### ASJC Scopus subject areas

- Chemical Engineering(all)
- Chemistry(all)
- Polymers and Plastics

### Cite this

*Society of Plastics Engineers - International Polyolefins Conference - FLEXPACKCON 2008*(Vol. 2, pp. 791-796)