The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximat...The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.展开更多
Lunar equatorial regolith temperature profiles were simulated using the half-limited solid heat conduction model. Based on the infrared data measured using the Diviner radiometer on the Lunar Reconnaissance Orbiter la...Lunar equatorial regolith temperature profiles were simulated using the half-limited solid heat conduction model. Based on the infrared data measured using the Diviner radiometer on the Lunar Reconnaissance Orbiter launched by the United Sates in June 2009, three factors influencing temperature profiles were analyzed. The infrared brightness temperature data from Diviner channel 7 were used to retrieve surface temperature. In simulating regolith temperature profiles, the retrieved temperature, rather than temperatures calculated from solar radiance at the lunar surface, were used as the input for surface temperature in solving the heat-conductive equation. The results showed that the bottom-layer temperature at depths of 6 m approached almost 246 K after 10000 iterations. The temperature was different to the temperature of 250 K at the same depth encountered in simulations using solar radiance. Simulations from both methods of surface temperatures over a lunar day gave similar variations. At lunar night, the temperature difference between the two was about 2 K; the main differences occurred when the solar elevation angle was very low when surface temperatures are largely affected by terrain topography. With no certainty in lunar temperature profiles at present, the advantage of the retrieval method using infrared sensor data as input to the boundary conditions in solving the lunar heat conduction equation is that simulations of surface temperature variations are more accurate. This is especially true in areas with large variations in terrain topography, where surface temperatures vary greatly because of shading from the sunlight.展开更多
文摘The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.
文摘Lunar equatorial regolith temperature profiles were simulated using the half-limited solid heat conduction model. Based on the infrared data measured using the Diviner radiometer on the Lunar Reconnaissance Orbiter launched by the United Sates in June 2009, three factors influencing temperature profiles were analyzed. The infrared brightness temperature data from Diviner channel 7 were used to retrieve surface temperature. In simulating regolith temperature profiles, the retrieved temperature, rather than temperatures calculated from solar radiance at the lunar surface, were used as the input for surface temperature in solving the heat-conductive equation. The results showed that the bottom-layer temperature at depths of 6 m approached almost 246 K after 10000 iterations. The temperature was different to the temperature of 250 K at the same depth encountered in simulations using solar radiance. Simulations from both methods of surface temperatures over a lunar day gave similar variations. At lunar night, the temperature difference between the two was about 2 K; the main differences occurred when the solar elevation angle was very low when surface temperatures are largely affected by terrain topography. With no certainty in lunar temperature profiles at present, the advantage of the retrieval method using infrared sensor data as input to the boundary conditions in solving the lunar heat conduction equation is that simulations of surface temperature variations are more accurate. This is especially true in areas with large variations in terrain topography, where surface temperatures vary greatly because of shading from the sunlight.
