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The nasal airway is an extremely complex structure, therefore grid generation for numerical prediction of airflow in the nasal cavity is time-consuming. This paper describes the development of a voxel-based model with a Cartesian structured grid, which is characterized by robust and automatic grid generation, and the simulation of the airflow and air-conditioning in an individual human nasal airway. Computed tomography images of a healthy adult nose were used to reconstruct a virtual three-dimensional model of the nasal airway. Simulations of quiet restful inspiratory flow were then performed using a Neumann boundary condition for the energy equation to adequately resolve the flow and heat transfer. General agreements of airflow patterns, which were a high-speed jet posterior to the nasal valve and recirculating flow that occupied the anterior part of the upper cavity, and temperature distributions of the airflow and septum wall were confirmed by comparing in-vivo measurements with numerical simulation results.