Shown is a large scale model (model larger than prototype) of a high temperature fastener to be used to connect materials that are essentially insulators.
The model has a circular cross-section of radius, r, which varies with axial position, x, according to the relation
The model is constructed of two materials having thermal conductivities k1
and k2. During a recent test of our scale model, the temperature of the large end was measured as 1000oF, while that of the small end was 100oF.
Assuming heat conduction only in the axial (x) direction, determine for these end temperatures:
(a) The temperature profile in material 1.
(b) The temperature Ti where the two materials join.
(c) The heat flux across the end at the position x = 6 ft.
(d) The heat flow in Btu/h across the junction at x = 3 ft.