Derivation of minimum volume for underground cylindrical and spherical thermal energy stores

In this study, analytical solutions for the transient heat conduction problem outside underground cylindrical and spherical thermal energy stores are presented. It is proposed that minimum store volume is derived as a function of the other volume for the same energy inputs to these stores. Same initial and boundary conditions are taken for the both problems. Each problem for the stores are written by a partial differential equation, initial and boundary conditions and energy balance equation. The problems are solved separately. Finite Fourier technique and two other transformations are applied to the spherical store problem. Boundary conditions are transformed into homogeneous boundary conditions by using an expression to obtain eigen value problem. At the same time, the cylindrical store problem is obtained using different expressions to make homogeneous boundary conditions. The homogeneous problem is solved by applying Hankel transformation. In both solutions, water in the stores and surrounding temperatures are obtained as functions of readial distance and time. Analytical solution of the transient heat transfer problem of a store with minimum volume is the original ides of the thesis. Therefore, an analytical expression for the minimum store volume is obtained under the conditions of the same stores temperatures and energy inputs to the spherical and cylindrical stores. So, this study will be reference for the engineering applications regarding heating and cooling systems with energy store. As a result, type of energy store used in the heating and cooling systems is determined.