Final Design Parameter Settings for a Physically-Realizable Uniform Temperature Boundary Condition Specification on a Wall of an Enclosure

Design parameters based on a three-dimensional internal natural convection heat transfer in a cubical apparatus are presented so that a uniform temperature boundary condition specification on a wall of the apparatus can be physically achieved. Preliminary temperature measurements based on the initial design of the apparatus where the uniform boundary condition was prescribed revealed that a temperature non-uniformity existed in the excess of 4% error. In order to complete the objective of the benchmark internal natural convection study, the apparatus had to be modified so that the temperature non-uniformity can be reduced to less than 1% error. It was decided that the original design be modified by simply adding two auxiliary heaters in the vicinity of the wall where the uniform temperature profile was desired. Before the implementation of the auxiliary heaters onto the apparatus, a detailed mathematical analysis was conducted to determine the position and the contact width of the heaters, and to establish an appropriate heat flux required to reduce the temperature non-uniformity to less than 1% along the wall of the apparatus. This analysis was achieved by using the approximate analytical temperature solution obtained from the boundary value problem of a plate (which is one part of the apparatus) with boundary conditions prescribed to model the auxiliary heaters. Previously, a specific set of design parameters were used that reduced the temperature non-uniformity to less than 1% along a wall of the modified cubical apparatus. As an extension to the previous work, this paper presents a generalized set of design parameters that can equally prescribe a physically-realizable uniform temperature setting along a wall of an enclosure to within 1% error. With the range of design parameters, this would enable any designer with the flexibility in choosing what parameters can be allocated based on their need.