Steady temperature in rectangular rod(different heat source)

This function computes T (z,y) in the cross-section of a multi-layer rectangular rod. Longitudinal section of edge-emitting laser.

This function is a variation of T_rect_rod uploaded by me earlier. The difference lies in the heat source. Now it ranges from one side wall to another and consists of three segments: long one in the middle (ga) and short (gm's) in the vicinity of rod's side walls.

Originally the problem was considered in the context of heat flow in semiconductor laser of edge-emitting geometry [M. Szymański, A. Kozlowska, A. Maląg, A. Szerling, Two-dimensional model of heat flow in broad-area laser diode mounted to a non-ideal heat sink, (2007), Journal of Physics D: Applied Physics, vol. 40, p. 924-929]. The rod's cross-section was parrallel to mirror planes. Now we rotate the rod so its cross-section coincides with plane y-z, where z is the laser axis. Expressions derived for T(x,y) are valid after replacing x by z. These seemingly strange modifications are aimed at enabling temperature calculations of the entire device including the most susceptible for thermal runaway region, namely the vicinity of the joint of mirrors and active layer. The concept will be published soon [M. Szymański, A. Kozlowska, A. Maląg, P. Hoser, Two-dimensional model of heat flow in edge-emitting laser revisited: a new and more versatile approach]. However, if you find the code helpful at this stage (without additional explanations), please cite article as indicated below.

Short review of the model is presented below.

T_rect_rod_axial is based on analytical solution of 2D heat conduction equation obtained by separation of variables approach.

T [K] - relative temperature (the temperature exceeding the ambient temperature) in the cross-section of a multi-layer rectangular rod.

The boundary conditions assumed:
- isothermal condition at the bottom of the rod;
- thermally insulated side walls;
- convectively cooled upper surface.

The heat source g(-L/2 < z < L/2, y = 0) = gm, ga, gm, i.e. is assumed to be an infinitely thin, placed between layers nos. 1 and 2 and consisted of three flat segments.

Example structure of InGaAs/GaAs/AlGaAs laser chip is entered.