A one dimensional heat transfer

A one-dimensional heat transfer assumption is reasonable for both the metal plate and the imitative material, and their governing equations take the same formwhere , and are density, specific heat capacity and thermal conductivity, respectively. As shown in Fig. 1, the boundary conditions of metal plate and imitative material are identical. Their top boundary conditions can be similarly expressed asand the bottom boundary conditions are both adiabatic. In Eq. (2), is the net heat flux into the top boundary, is the solar irradiation absorbed by the top surface, is the b-raf inhibitors heat flux between top surface and sky, and is the convection heat flux between top surface and air. is equal to , where represents the solar absorptance and represents the solar irradiation. is equal to , where , , and represent infrared emissivity, Stefan–Boltzmann constant, top surface temperature and effective sky temperature. is equal to , where represents the convection coefficient estimated by [9] ( is the wind speed), and represents the temperature of air flow. The correlation used here for computing convection coefficient is selected according to the recommendation of a survey of wind convection coefficient correlations in Ref. 9 which is commonly used to calculate the convection coefficient over a flat plate by taking both the natural and force convections into account. And its reliability has been commonly accepted. To develop the false target which has the same infrared characteristics as the metal plate, the radiative properties of metal plate and imitative material, i.e., and , are set to be the same, which can be realized by the same coating. The contact resistance between the coating and the metal plate or the imitative material can both be neglected, and the coating can be very thin so that its influence on the surface temperature can also be neglected. The material properties are assumed to be constant. This assumption was adopted because the metal plate and the imitative material are both not specified, and there are no general variation laws of their properties with temperature so that the variation of properties with temperature is difficult to be considered. Hence, we did not consider the temperature dependencies of the related thermal properties of metal plate and imitative material. However, the results below can be taken as a reasonable approximation.
Results and discussion
Conclusions The influences of the imitative material\'s thermophysical properties on the STD were analyzed when subjected to periodical ambient conditions, and the key factors were found to be its dimensionless thickness () and thermal inertia (). When is more than 1.0, the STD is invariable as long as is a constant. And if the dimensionless thickness of metal plate () is also larger than 1.0, the STD approaches to zero as long as is the same as the thermal inertia of metal plate. When is between 0.08 and 1, the STD varies irregularly with and . However, if is also in the range of 0.08–1, the STD approaches to zero for and . When is below 0.08, the STD is unchanged when is a constant. And if is also smaller than 0.08, the STD approaches to zero as long as . Besides, the application of PCMs leads to a lighter and thinner false target for a preset STD.
Acknowledgment The work was funded by the National Natural Science Foundation of China (No. 51576188).
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