a$.$ Assuming that T$1,$ T$2,$ and Se are known, perform a shell balance on the slab and utilizing Fourier$$s Law of conduction, write a second order differential equation that describes the variation of temperature with respect to position $($d$2$T$/$dx$2=?)$ and write

appropriate boundary conditions. You don$$t need to solve this differential equation. $(10$ pts$)$

b$.$ Using known values of Se$,$ T$1,$ and T$2,$ and applying the appropriate boundary conditions, the equation from part $($a$)$ can be solved to yield: T $[\backslash$deg C$]=20000$ x$2+3000$ x $+30\backslash$deg C where x has units of $[$m$],20000$ has units of $[\backslash$deg C$/$m$2],3000$ has units of $[\backslash$deg C$/$m$],$ and could be plotted as shown in the graph. What is the heat flux $[$W$/$m$2]$ and Temperature at x$=$L$?(10$ pts$)$

c$.$ Based on your answers to part b and the data in the figure, calculate T$4($the temperature at the blood and muscle interface$).$ Is the slab appropriate and therapeutic to put on my back? $($REMINDER: the end of the muscle layer should reach at least $40\backslash$deg C to relax my back muscles.$)(10$ pts$)$