Experimental Validation of Analytical Solutions for Vertical Flat Plate of Finite Thickness Under Natural-Convection Cooling

The analytical solution for a vertical heated plate subjected to conjugate heat transfer due to natural convection at the surface and conduction below is presented. The heated surface is split into two regions; the uniform heat flux region toward upstream and remaining fraction as the uniform wall temperature region. The fractional areas under the two regions are considered variable. Adopting thermally thin wall regime approximation, the possible solutions were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in the transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The ranges for Rayleigh number and heat conduction parameter $(α)$ during various test conditions were $2×108–6×108$⁠, and 0.001–1, respectively. The limiting solutions for stipulated conditions are analyzed and compared with experimental data. Reasonable agreement is observed between the experimental and analytical results.