Microfluidic　technology　has　been　increasingly　used　for　biochemical　synthesis　and　analysis,　allowing　for　automation,　integration　and　parallelization.　Numerical　modeling　and　simulation　can　improve　theoretical　understanding,　reduce　prototyping　consumption,　and　speed　up　development.　In　this　work,　we　set　up　a　3D　finite-element　COMSOL-based　model　to　analyze　the　multi-physical　dynamics　of　a　microfluidic　system.　The　hydrodynamics　of　single-phase　laminar　flow　in　the　microfluidic　system　with　variant　chamber　profiles,　fluid-structure　interaction　(FSI)　of　fluid　and　an　immobilized　single　cell　within　cell　trapping　component　have　been　studied.　Also,　the　process　of　on-chip　heat　transfer　has　been　investigated.　The　velocity　and　pressure　field　of　fluid　flow,　the　force　and　stress　on　cell　surface　and　the　temperature　distribution　of　the　integrated　device　have　been　presented　and　discussed.　The　reported　approach　is　able　to　optimize　microfluidic　design,　reveal　the　coupled　dynamics　in　complicated　multi-physical　field,　and　therefore　holds　the　potential　for　improving　microfluidics　application　in　fundamental　research　and　clinical　settings.