A heatline approach on the analysis of the heat transfer enhancement in a square enclosure with an internal conducting solid body

• Heatlines were used to study the conjugate heat transfer in the enclosure.
• The effects of the solid on the Nusselt number can be predicted by the heatlines.
• The heat transfer approaches the conduction limit for large sizes of the solid.
• For small solids heat transfer is a function of the Rayleigh number only.

In this article, conjugate heat transfer in a square enclosure heated and cooled at the adjacent walls with an internal conducting solid body is studied. The effect of a square body on the steady state heat transfer in the enclosure is investigated for a Prandtl number of 7.0 in a range of Rayleigh number from 103 to 106, the ratio of the enclosure and body dimensions (ζ) from 0.1 to 0.9 and the ratio of the thermal conductivities of the solid and fluid (k*) from 0.01 to 100. A heatline approach is used on the analysis of the conjugate heat transfer in the enclosure. The heat transfer process in the enclosure is governed by the Rayleigh number, the size of the solid and thermal conductivity. For dimensionless body sizes of ζ < 0.3, the heat transfer in the enclosure is not affected by the body and the Nusselt number remains a function of the Rayleigh number. As the body size increases, the Nusselt number also becomes dependent on the size of the body and its thermal conductivity. In the range of ζ > 0.8 and k* > 10, the dependence of the Nusselt number on the Rayleigh number weakens and the heat transfer in the enclosure approaches the limit of pure conduction.