Steady temperature in rectangular rod (different BC)

This function computes T (x,y) in the cross-section of a multi-layer rectangular rod. Edge-emitting laser with untypical boundary condition.

This function is a variation of T_rect_rod uploaded by me earlier. The difference lies in the top boundary condition: convection has been replaced by isotherm at the upper surface.

Originally the problem was considered in the context of heat flow in the semiconductor laser of edge-emitting geometry. The details of the model, schematic view of the system as well as discussion of results can be found in [M. Szymański, Two-Dimensional Model of Heat Flow in Broad-Area Laser Diode: Discussion of the Upper Boundary Condition, Microelectron. J., vol. 38, no. 6-7, (2007), pp. 771–776].

Short review of the model is presented below.

T_rect_rod_isotup 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;
- isothermal condition at the upper surface (UNTYPICAL for edge – emitting lasers).

The heat source is assumed to be an infinitely thin stripe o width w placed between layers nos. 1 and 2.

Example structure of GaAs/AlGaAs/GaAsP laser chip (without heat sink) consisting of 17 layers is entered.