Designing an experimental apparatus requires considerable amount of planning. Despite proper planning, one can easily overlook a design such as the standard uniform temperature boundary condition applied to all or portion of a wall of an experimental apparatus. Although this boundary condition is mathematically simple and precise, achieving it physically may not be that simple. This paper addresses one such three-dimensional natural convection heat transfer apparatus that was designed to measure benchmark Nusselt numbers at various Rayleigh numbers with uniform temperatures specified at two walls of the enclosure. It was found that the effect of thermal spreading/constriction resistance on one wall where this uniform temperature condition was prescribed was significant, and as a result, the uniform temperature profile based on the initial design was not physically achieved. In support of this non-uniform temperature observation, this paper presents a thermal resistance model of a plate (which is a portion of this overall heat transfer apparatus) to explain the observed temperature non-uniformity. The results obtained from the current model are validated with measured data, and in terms of a temperature difference between two locations on the plate, the approximate analytical solution is well within the experimental error of 0.03K.
C. Lee, P. Y. and Leong, W. H.
Physically-Realizable Uniform Temperature Boundary Condition Specification on a Wall of an Enclosure: Part I – Problem Investigation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
1, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss1/3