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An analysis of transient heat flow through a composite wall McDonald, James W.

Abstract

The object of this investigation was to examine the transient heat flow through a composite wall. This wall was chosen to represent the type used in house construction. It consisted of a fir frame, covered on one side with hardboard and on the other with cedar, and the space between the hardboard and cedar was filled with fibreglass insulation. A vapour barrier was not included as it would offer little resistance to heat flow. This structure, therefore, offered resistances to heat flow in series and parallel. The theoretical analysis was numerical owing to the anisotropic properties of the materials and to the composite structure of the wall. Two analyses were made of the transient heat flow, an exact analysis and an approximate analysis which neglected the effect of the frame. The heat flow was three dimensional in the first analysis owing to the difference in the magnitude of the parallel resistances and was one dimensional in the approximate analysis. The two theoretical solutions both showed exponential cooling rates and agreed within five percent of each other, which shows that the effect of the frame is negligible when its surface area is small as compared to the total surface area of the wall. The ratio of total wall surface area to frame area for the wall studied was 9.6 to 1.0. The wall was mounted in a guarded hot-box apparatus and experiments were performed in order to verify the results of the theoretical analysis. The experiments consisted of establishing a steady state temperature gradient across the wall and then eliminating the heat source. The ensuing transient temperatures were measured by thermocouples and were compared with those predicted by theory. The experimental results varied from the exact solution by 14 percent and from the approximate solution by 18 percent. The experimental results indicated that the tests were consistent. The difference between the theoretical and experimental results was attributed to: (1) contact resistances, (2) nonhomogeneous wall materials, (3) nonuniform surface coefficients of heat transfer, and (k) the effect of neglecting certain heat capacities which actually were not negligible. The results indicated that the transient temperatures varied according to the equation T = Ti e [formula omitted] where T represents temperature, t represents time, and [formula omitted] is the time constant. The results also showed that the method of analysis was acceptable and that the approximate analysis is suitable for walls with small frame areas.

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