Moisture evaporation - CELL based approach
 

The phenomenon of moisture evaporation is a part of work in my main problem. The problem is simple, a rectangular 1D channel is considered where right end is symmetry, left end (wall) is with the temperature of 1050deg, other faces are empty (1D problem). With supply of heat (temperature) from the left wall end, the moisture inside the channel will be evaporated, and the heat is slowly propagated from left to right end.

As shown in the attachment, there found a heating wall with the boiling plane defined at the certain position (distanced xb from the wall). A cell with two nodes (1 and 2) - where one node is high temperature (-) near the heated wall and other with lower temperature (+). Initially the heat from the wall reaches the plane 1, the calculations at plane 1 is based on high (-) and low temperature (+) nodes. As defined, the moisture content on high temp side (-) is kept zero and on lower temp side (+), the moisture content and density changed need to be evaluated. The plane tends to move towards right notated as dxb/dt. With movement of plane, the calculations are made for (-) and (+), depending on it mass and heat balances are evaluated.

Here in my work, the moisture evaporation seems to be CELL-BASED approach based on sign changes (+, -). Is there any existing code structure for such kind of problem?

Kindly guide me, please.
Thank you