Search

This study focused on the coupling heat transfer mechanism and the cooling efficiency of L-shaped two-phase closed thermosyphons (L-shaped TPCTs) in the wide subgrade of permafrost regions. Considering the fact that time–space dynamics change the effects of the air temperature, wind speed, and geotemperature, a coupled air temperature–L-shaped TPCT–subgrade soil heat transfer model was established using the ANSYS 15.0 software platform, and the rationality of the model was verified through measured data. The heat-transfer characteristics of the L-shaped TPCTs and the long-term thermal stability of the subgrade were studied under different inclination angles of the evaporator (α = 15°, 30°, 50°, 70°, and 90°). Then, the cooling effectiveness of a composite subgrade with TPCTs and an XPS insulation board was numerically calculated. The results show that the heat flux of the L-shaped TPCT was the greatest when α = 50°, and the heat flux reached the maximum value of 165.7 W·m−2 in January. The L-shaped TPCT had a relatively good cooling effect on the subgrade as a whole when α = 50° and 70°, but the thawing depth at the center of the subgrade with L-shaped TPCTs reached 9.0 m below the ground surface in the 30th year. The composite subgrade with L-shaped TPCTs/vertical TPCT/XPS insulation board is an effective method to protect the permafrost foundation and improve the long-term thermal stability of the wide subgrade. The maximum heat flux of evaporation section of the L-shaped TPCT is 18.8% higher than that of the vertical TPCT during the working period of the TPCTs of the composite subgrade. [ABSTRACT FROM AUTHOR]

In this paper, we shall present the quadratic convergence of Levenberg-Marquardt (L-M) method for solving general ill-posed nonlinear inverse problems including two parameters to be identified. As the Tikhonov regularized minimizations are non-convex due to the nonlinearity of the nonlinear inverse problems, the L-M method transforms them into convex minimizations. The quadratic convergence of the L-M method is rigorously demonstrated under some basic assumptions. An application of the L-M method for the simultaneous identification of the Robin coefficient and heat flux in an elliptic system is presented, and the surrogate functional technique is introduced to solve the convex but still strongly ill-conditioned minimizations, resulting in an explicit minimizer of the minimization at each L-M iteration. Numerical experiments are presented to illustrate the efficiency and accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper aims to solve an inverse heat conduction problem in two-dimensional space under transient regime, which consists of the estimation of multiple time-dependent heat sources placed at the boundaries. Robin boundary condition (third type boundary condition) is considered at the working domain boundary. The simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with Tikhonov regularization. The properties of the continuous and discrete optimization problem are studied. Differentiability results and the adjoint problems are established. The numerical estimation is investigated using a modified conjugate gradient method. Furthermore, to verify the performance of the proposed algorithm, obtained results are compared with results obtained from the well-known finite-element software COMSOL Multiphysics under the same conditions. The numerical results show that the proposed algorithm is accurate, robust and capable of simultaneously representing the time effects on reconstructing the time-dependent Robin coefficient and heat flux. [ABSTRACT FROM AUTHOR]

In this paper, we shall derive and propose an efficient algorithm for simultaneously reconstructing the Robin coefficient and heat flux in an elliptic system from part of the boundary measurements. The uniqueness of the simultaneous identification is demonstrated. The ill-posed inverse problem is formulated into an output least-squares nonlinear and non-convex minimization with Tikhonov regularization, while the regularizing effects of the regularized system are justified. The Levenberg–Marquardt method is applied to change the non-convex minimization into convex minimization, which will be solved by surrogate functional method so as to get the explicit expression of the minimizer. Numerical experiments are provided to show the accuracy and efficiency of the algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we aim to reconstruct the unknown Robin coefficient and unknown heat flux simultaneously in an elliptic system from Cauchy data on arbitrarily small portion of accessible boundary. A novel logarithmic type stability in terms of the negative Sobolev norms is established. [ABSTRACT FROM AUTHOR]