### 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. This 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 and is compared with the results found using the finite element method.

Original language | English |
---|---|

Pages (from-to) | 289-294 |

Number of pages | 6 |

Journal | Journal of Applied Polymer Science |

Volume | 102 |

Issue number | 1 |

DOIs | |

Publication status | Published - 5 Oct 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Calculations
- Modeling
- Rheology
- Thermodynamics

### ASJC Scopus subject areas

- Polymers and Plastics

### Cite this

*Journal of Applied Polymer Science*,

*102*(1), 289-294. https://doi.org/10.1002/app.23780

**Finite difference solutions of the heat equation in a molten polymer flowing in a circular tube.** / Leong, C. H.; Mohr, D. G.; Elgindi, Mohamed; Langer, R. W.

Research output: Contribution to journal › Article

*Journal of Applied Polymer Science*, vol. 102, no. 1, pp. 289-294. https://doi.org/10.1002/app.23780

}

TY - JOUR

T1 - Finite difference solutions of the heat equation in a molten polymer flowing in a circular tube

AU - Leong, C. H.

AU - Mohr, D. G.

AU - Elgindi, Mohamed

AU - Langer, R. W.

PY - 2006/10/5

Y1 - 2006/10/5

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. This 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 and is compared with 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. This 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 and is compared with the results found using the finite element method.

KW - Calculations

KW - Modeling

KW - Rheology

KW - Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=33749492935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749492935&partnerID=8YFLogxK

U2 - 10.1002/app.23780

DO - 10.1002/app.23780

M3 - Article

VL - 102

SP - 289

EP - 294

JO - Journal of Applied Polymer Science

JF - Journal of Applied Polymer Science

SN - 0021-8995

IS - 1

ER -