Validation of Local Similarity Solutions to Conjugate Free Convection for Vertical Plate

摘要

The paper presents the local similarity solution for a vertical heated plate subjected to conjugate free convection. A part of the surface is subjected to uniform heat flux and rest under uniform wall temperature conditions. The fractional areas under uniform heat flux and uniform wall temperature conditions are considered variable. The possible solutions based on thermally thin wall regime approximation were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in a transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The approximate range of the Rayleigh number during various test conditions was 2.7 × 10~8 to 5.4 × 10~8, and the order of magnitude of the heat conduction parameter (α) was between 10~(-3) and 1. Limiting solutions under considered thermal and geometric conditions are analyzed in detail, and comparison with experimental data is presented. Reasonable agreement is observed between the experimental and analytical results.