Fluids flow in porous media are usually affected by multiphysics domains. Thermal, mass transfer, and hydraulic domain will all significantly affect the features of fluids flow in porous media. Thermal fluids coupling problems occur almost in every area of reservoir engineering such as geothermal energy development, and heavy oil recovery. Mass transfer is another important mechanism that should be considered in solvent based heavy oil recovery and unconventional enhance oil recovery methods. This research focuses on using analytical source and sink function method applied in heat transfer and mass transfer to simulate two domain coupling model. Based on thermal source and sink function derived in this thesis, convective heat is treated as a simple special form of source and sink function. The calculation of transient convective heat amount in Laplace domain problem has also been solved innovatively in this dissertation. Sensitivity analysis on segment size from computing prospect, thermal diffusivity and velocity from system prospect are analyzed to help understand the heat transfer process integrating conduction and convection mechanism. Secondly, this convective source function methodology is applied in a 2D model of geothermal energy recovery process. A typical geothermal energy recovery well pair is simulated by the innovative coupling methodology. Different well pair locations and fractured wells are examined through this model referring to the enhanced geothermal system technology for hot dry rock reservoir. Big jumps from heat transfer to mass transfer are made to analytically model the solvent injection process for heavy oil recovery. Multi-mechanisms including diffusion and dispersion, viscosity reduction, oil swelling are considered analytically and integrated into the two domain coupling model. Solvent-based Post Cold Heavy Oil Production with Sand (CHOPS) with single fracture structure is also modeled by this methodology. The mass transfer proves to have significant influence on fluids flow in porous media. Heavy oil thermal based recovery methods such as SAGD have complicated interactions phenomenon between thermal domain and pressure domain. Viscosity reduction, fluids thermal expansion and heat loss to caprock will significantly affect the operation energy efficient and environment footprint. Sensitivity analysis of key parameters affecting the thermal injection process are also conducted.