This special solution for cylindrical symmetry can be similarly generalized and

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This special solution for cylindrical symmetry can be similarly generalized and adapted so boundary conditions, as for the spherical case. Finally, the z-dependence can be factored in, because z separates from the plane polar radial variable rho. For a homogenous spherical solid with constant thermal diffusivity, K, and no heat source, the equation of heat conduction becomes Assume a solution of the form T = R(r)T(t) and separate variables. Show that the radial equation may take on the standard form r2 d2 R/dr2 + 2r dR/dr + alpha2r2 R = 0. and that sin alpha r/r and cos alpha r/r are its solutions. Separate variables in the thermal diffusion equation of Exercise 9.7.1 in circular cylindrical coordinates. Assume that you can neglect end effects and take T = T(rho, t). Solve the PDE

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