# Question:Can't solve the linear pde problem of "two composite cylinder" of Carslaw and Jeager's book (link in description)

## Question:Can't solve the linear pde problem of "two composite cylinder" of Carslaw and Jeager's book (link in description)

Maple

Hello,

I am trying to recover with maple the analytical solution of the problem of conduction within two composite cylinders given in Carslaw and Jeager's book: "Conduction of heat in solids" (link here). Here is my take on the problem

```restart;
with(PDEtools);
C := diff_table(c(rho, t));
E := diff_table(e(rho, t));
PDE1 := diff(C[], t) - K_1*(diff(diff(C[], rho), rho) - diff(C[], rho)/rho) = 0;
PDE2 := diff(E[], t) - K_2*(diff(diff(E[], rho), rho) - diff(E[], rho)/rho) = 0;

ic1 := eval(C[], t = 0) = V;
ic2 := eval(E[], t = 0) = 0;

bc_1 := eval(C[], rho = a) = eval(E[], rho = a);
bc_2 := K_1*eval(diff(C[], rho), rho = a) = K_2*eval(diff(E[], rho), rho = a);
bc_3 := eval(E[], rho = infinity) = 0;
bc_4 := (diff(C[]/rho, rho), rho = 0) = 0;
pdsolve([PDE1, PDE2],[ic1,ic2, bc_1,bc_2,bc_3,bc_4]); ```

Unfortunately I end up with the following errors:

```Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{c(rho, t), e(rho, t)}, [c(rho, 0) = V, e(rho, 0) = 0, c(a, t) = e(a, t), K_1*(diff(c(a, t), a)) = K_2*(diff(e(a, t), a)), e(infinity, t) = 0, ((diff(c(rho, t), rho))/rho-c(rho, t)/rho^2, rho = 0) = 0]]
```

If I call pdsolve without any initial and boundary conditions, I have the general form of the equation which is correct (product of exponential function in time with Bessel functions for space) but I don't know how to determine the coeficients with maple from there.

Note also that the boundary condition "bc_2" does not seem to be correcty evaluated (it is supposed to specify the continuity of the flux ar r=a). Instead it just evaluate the expression with r swapped with a. If one write the same line of code with r=0 instead of r=a then the evaluation seems correct.

Any help would be very appreciated,

Cheers ﻿