Numerical Modeling of the Effect of the Ratio of Thermal Conductivity on the Thin Film Condensation in Forced Convection in a Canal Whose Walls are Covered with a Porous Material
Pape Tamsir Ndiaye *
Fluid Mechanics and Transfer Laboratory, Physics Department, Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal.
Omar Ngor Thiam
Fluid Mechanics and Transfer Laboratory, Physics Department, Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal and Research Group on Solar Energy and Transfers (GREST), Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal.
Momath Ndiaye
Fluid Mechanics and Transfer Laboratory, Physics Department, Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal and Department of the Ufr Hydraulics, Rural Engineering, Machinery and Renewable Energy, University of Sine Saloum Elhadji Ibrahima NIASS, Kaolack, Senegal.
Goumbo Ndiaye
The Water, Energy, Environment and Industrial Processes Laboratory of the Polytech Higher School, Cheikh Anta Diop University, Dakar, Senegal.
Mamadou Lamine Sow
Fluid Mechanics and Transfer Laboratory, Physics Department, Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal and Research Group on Solar Energy and Transfers (GREST), Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal.
Cheikh Mbow
Fluid Mechanics and Transfer Laboratory, Physics Department, Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal and Research Group on Solar Energy and Transfers (GREST), Sciences and Technologies Faculty, Cheikh Anta DIOP University, Dakar-Fann, Senegal.
*Author to whom correspondence should be addressed.
Abstract
A numerical modeling of the effect of the ratio of thermal conductivity on the thin film condensation in forced convection in a canal whose walls are covered with a porous material is presented. In this work, the generalized Darcy-Brinkman-Forchheimer (DBF) equations in the porous medium and the hydrodynamic and thermal boundary layer equations in the pure liquid, were used.
Rendered dimensionless and homotopically transformed into a new rectangular basis, we used a finite difference method to discretize them. The advection and the diffusion terms are discretized with respectively a backward-centered scheme and a centered scheme.
After validation, we find that a variation of the longitudinal velocity as a function of the ratio of thermal conductivity only for low values of the Peclet number. When the ratio of thermal conductivity increases, corresponding to an increasingly conductive medium, the longitudinal velocity, the temperature and the Nusselt number increase (even when the Peclet number is high for the thermal field). While the thickness of the liquid film decreases (disadvantaged condensation) and leads to an increase in the length of entry, increase almost linear. The sensitivity of condensation to variations in the ratio of thermal conductivity is constant, whatever its value.
The ratio of thermal conductivity is a very decisive and predictable physical quantity to properly examine the performance of condensation.
Keywords: Channel with porous wall, condensation thin film, generalized darcy-brinkman- forchheimer model, iterative gauss-seidel relaxation method, lengths of entry, ratio of thermal conductivity