Inversion Method of Boundary Condition for a Class of Coupled Heat Flow Models
An inversion method for calculating the boundary conditions of heat flow coupled model in fractured rock mass is proposed.Based on single fracture heat flow coupled model and using partial temperature observation data,the temperature,temperature gradient,and convective heat transfer coefficients at the interface between the rock and fluid have been calculated.Firstly,the separation variable method is used to transform the boundary value problem of heat conduction into the first Fredholm integral equation,and then the integral equation is solved based on the regularization method to obtain the temperature and temperature gradient on the contact boundary between rock mass and fluid,and the local heat transfer coefficient is calculated.An unconstrained optimization problem is solved using the gradient descent method to determine the overall convective heat transfer coefficient.Finally,the heat flow coupled equation is numerically calculated.The numerical results show that the proposed method can overcome the uneasiness of the inversion problem and has high accuracy and stability.
heat-flow coupled modelheat transfer coefficientill-posednesssideways probleminversion computation
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