*Article* **Dependence of Conjugate Heat Transfer in Ribbed Channel on Thermal Conductivity of Channel Wall: An LES Study**

**Joon Ahn 1,\*, Jeong Chul Song <sup>2</sup> and Joon Sik Lee <sup>2</sup>**


**\*** Correspondence: jahn@kookmin.ac.kr

**Abstract:** A series of large eddy simulations was conducted to analyze conjugate heat transfer characteristics in a ribbed channel. The cross section of the rib is square and the blockage ratio is 0.1. The pitch between the ribs is 10 times the rib height. The Reynolds number of the channel is 30,000. In the simulations, the effect of the thermal resistance of the solid wall of the channel on convective heat transfer was observed in the turbulent flow regime. The numerical method used was based on the immersed boundary method and the concept of effective conductivity is introduced. When the conductivity ratio between the solid wall and the fluid (*K*\*) exceeded 100, the heat transfer characteristics resembled those for an isothermal wall, and the cold core fluid impinging and flow recirculation mainly influenced the convective heat transfer. For *K*\* ≤ 10, the effect of the cold core fluid impinging became weak and the vortices at the rib corners strongly influenced the convective heat transfer; the heat transfer characteristics were therefore considerably different from those for an isothermal wall. At *K*\* = 100, temperature fluctuations at the upstream edge of the rib reached 2%, and at *K*\* = 1, temperature fluctuations in the solid region were similar to those in the fluid region. The rib promoted heat transfer up to *K*\* = 100, but not for *K*\* ≤ 10. The Biot number based on the channel wall thickness appears to adequately explain the variation of the heat transfer characteristics with *K*\*.

**Keywords:** ribbed channel; large eddy simulation; immersed boundary method; conjugate heat transfer; thermal conductivity ratio
