# The shape factor for conduction through the edge of adjoining

The shape factor for conduction through the edge of adjoining walls for which D > L/5, where D and L are the wall depth and thickness, respectively, the two-dimensional symmetrical element of the edge, which is represented by inset (a), is bounded by the diagonal symmetry adiabat and a section of the wall thickness over which the temperature distribution is assumed to be linear between T1 and T2.

(a) Using the nodal network of inset (a) with L = 40 mm, determine the temperature distribution in the element for T1 = 100Â°C and T2 = OÂ°C. Evaluate the heat rate per unit depth (D = 1 m) if k = 1 W/m ∙ K. Determine the corresponding shape factor for the edge and compare your result with that from Table 4.1.

(b) Choosing a value of n = 1 or n = 1.5, establish a nodal network for the trapezoid of inset (b) and determine the corresponding temperature field. Assess the validity of assuming linear temperature distributions across sections a-a and b-b.

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