A new efficient and accurate procedure for solving heat condution problems

The half-boundary method (HBM) which reduces the order of partial differential equations, is extended with detailed formula derivations to solve heat transfer problems. The method has a comparable accuracy with analytical solution even when a few nodes are involved in calculation. And it also saves more time than finite volume method (FVM). HBM can separately calculate the field variables at any point of interest in the domain without uniform mesh or dimensional length. Variables at any node within the domain are associated with those on one of the two boundaries. For one-dimensional problems, only two-order matrices are calculated in HBM instead of huge-order matrices required in FMV. Therefore, this method shows great potential in accurate and efficient calculating multi-dimensional heat transfer and fluid flow problems with complex geometries and huge grids. In this paper, we introduce the fundamental theory and test the applicability, accuracy and efficiency of HBM by solving six simple one-dimensional problems, one two-dimensional problem and one practical problem of the temperature field simulation of double vessels in China Experimental Fast Reactor (CEFR), which can give a universal sense for more complex problems. ANSYS simulation is also utilized to verify the accuracy of HBM. Matlab codes are used.