Analytical method for definition of transient temperatures in brake mechanisms. (Q2743062)

Analytical method for calculating of transient axisymmetric temperature field inside a cavity in the homogeneous brake disk based on the Bessel functions is offered. Heat conduction equation in cylindrical coordinate system for this case has the form NEWLINE\[NEWLINE \frac{\partial^2T}{\partial r^2}+ \frac1{r}\frac{\partial T}{\partial r}+ \frac{\partial^2 T}{\partial z^2}=\frac1{k}\frac{\partial T}{\partial t}, \quad r\in(r_a,r_b),\,z\in(-l,l), NEWLINE\]NEWLINE heat exchange on the boundary is taken according to the Newton law \(\lambda\frac{\partial T}{\partial n}+\alpha(T-T_a)=P\) and \(T(r,z,0)=T_a\) is the initial value condition. Adequacy of the calculation results to the actual process on a concrete example is shown.