Use of the Alternating Directions Method in Cylindrical Coordinates, Applied to the Two-Dimension Unsteady Conduction Heat Transfer

Finding analytical solutions for the unsteady conduction heat transfer equation is generally very difficult due to the intrinsic complexity of the problem. In most cases, the equation has no analytical solutions. A numerical approach that surmounts these difficulties consists of the finite difference technique. The alternate directions finite-difference technique especially suits to the two-dimension heat conduction. The paper considers a hollow cylinder consisting of a conduction heat transfer medium, and the two-direction unsteady heat propagation within this medium is studied by means of the alternate directions method. The approach simulates the heat conduction process during a charge-discharge cycle of a single borehole heat storage.