Comparison between the Linear and Nonlinear Steady-State Behavior of a Heated Tube

The range of applicability for the solution of the linearized diffusion equation is discussed for a particular case—heating of a homogeneous tube by internal energy generation. The range is defined by comparisons of series solutions of the linear and nonlinear diffusion equations (constant material properties vs variable material properties). Two sources of errors in the constant-property solution are evaluated and a criterion for the limits of applicability of the linear solution is derived.