## Abstract

The thermally developing forced convection heat transfer in a micro-channel filled with a porous material in the slip-flow regime is analyzed. Channel walls are subjected to a constant heat flux. The local thermal non-equilibrium (LTNE) condition is considered and both the fluid and solid phases in the porous region are assumed to have internal heat generation. According to a perturbation analysis assuming small temperature difference between the two phases obtained by the scale analysis, we show that there is no need to apply a thermal boundary condition model at the channel wall. Thus, we obtained an analytical solution for the thermally developing Nusselt number (

*Nu*) using no model. Thermal boundary condition models (A and B) are also used to find the temperature jump at the wall. Comparing*Nu*of models A and B with the pure perturbation analysis (using no model) and with the solution under local thermal equilibrium (LTE) condition reveals that model B cannot predict the LTE condition when a temperature jump exists on the wall. Hence, model A may be the only valid scenario in the slip-flow regime. In addition, expressions for the thermal entry length (*x*) are proposed. An increase in_{developing}*β*as well as a decrease in the thermal conductivity ratio (*k*) decrease*x*._{developing}Original language | English |
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Pages (from-to) | 446-454 |

Number of pages | 10 |

Journal | Applied Thermal Engineering |

Volume | 99 |

Early online date | 19 Jan 2016 |

DOIs | |

Publication status | Published - 25 Apr 2016 |

Externally published | Yes |