Heat flow in a solid bounded by two conical surfaces (Fig. 11B.9). A solid object has the
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Heat flow in a solid bounded by two conical surfaces (Fig. 11B.9). A solid object has the shape depicted in the figure. The conical surfaces θ1 = constant and θ2 = constant are held at temperatures T1 and T2, respectively. The spherical surface at r = R is insulated. For steady-state heat conduction, find
(a) The partial differential equation that T(θ) must satisfy.
(b) The solution to the differential equation in (a) containing two constants of integration.
(c) Expressions for the constants of integration.
(d) The expression for the O-component of the heat flux vector.
(e) The total heat flow (cal/sec) across the conical surface at θ = θ1.
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