Experimental assessment of the similarity law for a heat conduction problem

Abstract

Similarities are mathematical laws, which are based on the dimensionless formulation of the governing equation of a physical phenomenon. Consequently, a set of characteristic dimensionless numbers is obtained. Similarities aim, via these numbers, to find equivalences between particular configurations. This approach is widely adopted, especially in fluid and aerodynamic problems. In the building context, the phenomena of heat and mass transfer in porous media occur with slow kinetics. Thus, similarities can be employed to reduce the duration of experimental campaigns to characterize material properties. These laws were investigated here in the case of a heat transfer problem through an experimental campaign. Two equivalent configurations were submitted to a heat stress. Temperatures inside materials were measured and compared to assess the validity of thermal similarity. A complete evaluation of uncertainty propagation was then carried out. Uncertainties related to the sensor position, its response time, the omission of mass transfer, the sensor systematic accuracy, the random measurement aspect, the one-dimensional transfer hypothesis and the boundary condition modeling were evaluated. The comparison of both configurations was carried out based on the confidence interval of both measurements. The results showed a good agreement between the reference and reduced experiment. On the basis of these findings, similarities were experimentally verified within a margin of discrepancy that was justified. Thus, they can be adopted in heat transfer experiments in order to identify equivalent configurations that are easier to conduct.