Analysis of stress functions in a circular plate due to a partially distributed heat supply. (Q2783588)

\textit{W. Nowacki} [Bull. Acad. Polon. Sci., Ser. Tech., 5, 227 ff (1957)] obtained an axially symmetric solution of linear homogeneous isotropic thermoelastostatics for a thin circular disk subject to a temperature depending on the radial coordinate \(r\) of the cylindrical frame \((r,\phi, z)\). The authors generalize Nowacki's result to include an axially symmetric time-dependent temperature \(T= T(r,z,t)\), \(0\leq r\leq a\), \(| z|\leq b/2\), \(t\geq 0\) produced by a heat flux at \(z=- b/2\), \(0< r< a\), and subject to the heat exchange conditions for \(z= b/2\), \(0< r< a\), and for \(r= a\), \(| z|< b/2\). Meaning of the generalization is not clear since the governing equation (1.1) in which \(U\) is to be identified with a two-dimensional thermoelastic displacement potential and not with a radial displacement, has been obtained for a two-dimensional thermoelasticity. In addition, the radial stress obtained by the authors does not vanish at \(r= a\), \(| z|< b/2\), \(t> 0\).