Analytical determination of the law of temperature distribution along the radius of metallic-polymeric holder for intramedullary osteo-synthesis at sterilization (Q2768806)

This paper deals with the temperature distribution along the radius of a metallic-polymeric holder consisting of two concentric cylinders (the inner is polymeric and the external metallic). The mathematical model is the following: to construct a bounded solution in the domain NEWLINE\[NEWLINED=\{(t,r):\;t\in(0,\infty);\;r\in(0,R_1)\cup(R_1,R_2),\;R_2<\infty\}NEWLINE\]NEWLINE of the system of heat equations NEWLINE\[NEWLINE\partial T_{j}/\partial t-a_{j}^2(\partial^2/\partial r^2+r^{-1}\partial/\partial r)T_{j}(t,r)=0,\quad j=1,2,NEWLINE\]NEWLINE with zero initial conditions, boundary conditions NEWLINE\[NEWLINE\partial T_{1}/\partial r|_{r=0}=0,\quad T_2(t,r)|_{r=R_2}=\omega,NEWLINE\]NEWLINE and conjunction conditions NEWLINE\[NEWLINE[(b_{1}\partial T_{1}/\partial r+T_1)-T_2]|_{r=R_1}=0,\quad (\partial T_{1}/\partial r-e_1\partial T_{2}/\partial r)|_{r=R_1}=0.NEWLINE\]NEWLINE Here \(a_{j}^2\) is a temperature conduction coefficient, \(b_1\) is a heat resistance coefficient, \(e_1=\lambda_1/\lambda_2\), and \(\lambda_{j}\) is a heat conduction coefficient. The solution is constructed by the method of the first kind Hankel integral transform.