The principle of the unsteady aerothermodynamics was theoretically investigated for the attached flow. Firstly, two simplified models with analytic solutions to the N-S equations were selected for the research, namely the compressible unsteady flows on the infinite flat plate with both time-varying wall velocity and time-varying wall temperature boundary conditions. The unsteady temperature field and the unsteady wall heat flux (heat flow) were analytically solved for the second model. Then, the interaction characteristic of the unsteady temperature field and the unsteady velocity field in the simplified models and the effects of the interaction on the transient wall heat transfer were studied by these two analytic solutions. The unsteady heat flux, which is governed by the energy equation, is directly related to the unsteady compression work and viscous dissipation which originates from the velocity field governed by the momentum equation. The main parameters and their roles in how the unsteady velocity field affects the unsteady heat flux were discussed for the simplified models. Lastly, the similarity criteria of the unsteady aerothermodynamics were derived based on the compressible boundary layer equations. Along with the Strouhal number Stu, the unsteadiness criterion of the velocity field, StT number, the unsteadiness criterion of the temperature field was proposed for the first time. Different from the traditional method used in unsteady aerodynamics which measures the flow unsteadiness only by the Stu number, present results show that the flow unsteadiness in unsteady aerothermodynamics should be comprehensively estimated by comparing the relative magnitudes of the temperature field unsteadiness criterion StT number with the coefficients of other terms in the dimensionless energy equation.
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