### 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 |

### Fingerprint

### 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)

**Temperatre balance of polymer flow through pipe.** / Elgindi, Mohamed.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Society of Plastics Engineers - International Polyolefins Conference - FLEXPACKCON 2008.*vol. 2, pp. 791-796, International Polyolefins Conference - FLEXPACKCON 2008, Houston, TX, United States, 24/2/08.

}

TY - GEN

T1 - Temperatre balance of polymer flow through pipe

AU - Elgindi, Mohamed

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=52649170263&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52649170263&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781605603438

VL - 2

SP - 791

EP - 796

BT - Society of Plastics Engineers - International Polyolefins Conference - FLEXPACKCON 2008

ER -