Implementation of p-version Finite Element Formulation for combined heat and mass transfer

In a refrigeration and air conditioning equipment, if the cooling surface temperature is lower than the dew point temperature of incoming moist air then the condensation of water vapor occurs on the cooling surface; thus heat and mass transfer occurs simultaneously. The analytical solutions for such systems are feasible only for the simple geometry, material and thermal loading cases. Otherwise, a numerical solution must be used. Finite element method is suitable to account for complexities caused by geometry, material or loading conditions. Nevertheless, the convergence of the finite element solution must be verified for its acceptance and further use for analysis or design purpose. The convergence of the finite element solution depends on mesh refinement. The most widely used method is h-refinement, where the mesh is refined by decreasing the size of the element while keeping the same order of polynomial of the shape functions. The main advantage of this approach is that the mathematical formulation is convenient to implement it in a Finite Element code. The disadvantage is that the each new solution is obtained from scratch and the preceding solution with the coarse mesh cannot be utilized. This also leads to considerable effort in model preparation for attaining a reasonable fine mesh. The second method of refinement is called p-refinement, where the size of the element (or mesh size) is kept the same while the refinement is achieved by increasing the order of the shape function polynomial. The advantage is that the model preparation efforts are decreased because a single coarse mesh is used even for those problems that contain singularity. Nevertheless, the main challenge is its implementation in a Finite Element code due to complex data structure and mathematical formulation caused by the higher order polynomial shape functions. In the proposed study, the p-version finite element formulation having the capability of heat and mass transfer will be implemented in a Finite Element code. The implemented formulation will be validated through some test case of studies by comparing them with experimental/numerical or analytical results.