Heat Transfer in a Rarefied Gas Enclosed Between Parallel Plates: Role of Boundary Conditions

The influence of boundary conditions of accomodation coefficients and Maxwellian diffuse specular reflection on heat transfer through a rarefied gas enclosed between two parallel plates is examined. An exact expression for heat transfer for accomodation coefficient boundary conditions and the Bhatnagar–Gross–Krook (BGK) model is constructed by using results of Cercignani and Pagani and Thomas, Chang, and Siewert. These results are compared with some variational results of Cipolla and Cercignani and some exact results of Thomas, Chang, and Siewert and Thomas for the BGK model and Maxwellian diffuse specular reflection boundary conditions. It is concluded that the two boundary conditions provide results that agree within about 3% for a range of Knudsen numbers and boundary parameters. It is found that the variational results are remarkably accurate for the BGK model and both types of boundary conditions. Further, it is noted that the heat transfer between parallel plates with different accommodation coefficients at the two surfaces can be calculated exactly by using a harmonic mean for each surface.