Conjugate heat transfer in an inclined slab with an array of horizontal circular channels

Effects of buoyancy on thermal characteristics of conjugate heat transfer across an inclined slab with an array of horizontal, circular channels inside are investigated numerically. Results are presented for Prandtl numbers of 0.7 and 4 over wide ranges of values of Grashof number Gr and thermal conductivity ratio, with the angle of inclination phi ranging from 0 degrees to 180 degrees from the horizontal. It is found that higher heat transfer rates can be obtained when the slab is inclined with phi = 60 degrees-90 degrees. For some particular cases, a 30% increase in heat transfer, bat only 8% increase in friction factor, may by obtained by changing the inclination angle. In general, the secondary fluid flow exhibits a single-cell pattern in the channel within the inclined slab with the exception of the cases at phi = 180 degrees and 0 degrees. For phi = 180 degrees (hot top) and phi = 0 degrees (hot bottom), a symmetric four-cell secondary flow pattern may be observed at lower Gr. However, for the hot-bottom cases, when Gr exceeds a threshold value, the secondary flow resumes the single-cell pattern and a significant increase in the Nusselt number is clearly observed For the parameter ranges considered in this study, the threshold value is located within Gr = 10(4)-10(5), dependent on the physical and geometric parameters.