| After several years of exploration,the research of heat transfer has evolved from experimental exploration and theretical calculation to numerical calculation with a great deal of numerical computational methods appearing.Numerical calculation can take full advantage of the computing power of the computer and solve the differential equation of heat conduction.In this paper,a new numerical calculation method proposed in recent years,the Half Boundary Method,is studied.The HBM has been applied in many fields including material structure science,heat conduction,convention heat transfer,etc.The new method shows the great advantages of high accuracy and efficency in calculation.The inverse heat transfer problem is a sub-problem of the inverse problem,which mainly foucuse on the solution of the inverse heat transfer problem(IHTP).Due to the lack of corresponding conditions required in solving the normal heat transfer problem,the normal numerical calculation method cannot be used for solving ITHP.The inverse heat transfer problem has the characteristics of nonlinearity,ill-posedness,large computational complexity,and often solved by iteration,which occupies a large amount of computing resources.For the case where the partial boundarys are unknown in the IHTP,the HBM can solve the result marching from one-side boundary to the other,which has advantages in solving IHTP.So the HBM is used to solve this kind of problems.This paper will introduce how the HBM deal with the differential equation of heat conduction,and compare the process with the finite volume method,thus highlighting the characteristics of the HBM.The paper calculates the theoretical results in the transient conditions and steady conditions,then do research in rectangular coordinates and cylindrical coordinates for each condition.The order of solving is as follows:normal heat transfer problem is solved first and compared with the analytical solution,and then the temperature obtained by solving the normal problem is used as the output data of the thermocouples supposing installed in the object to be study,and the partial boundary of the positive problem is set to unknown,then we combine other conditions to calculate the distribution of variables at unknown boundaries.From the calculation results,the accuracy of the distribution of variables on the boundary is very high by using the HBM.This high-precision solution provides a new idea for solving the inverse heat problem with unknown boundary conditions.In addition,the paper also studies the influence of the measurement error and installation position of the thermocouples on the calculation results.The paper also summarizes how the measurement error transfered in the calculation domain,so as to improve the accuracy of the inverse estimation.This paper provides a new idea for solving the IHTP,and also indicates a new application direction for the HBM. |
