For PCM, when it is in the solid phase, The above equations are approximated using fully-implicit finite difference equations. It turns out that the PCM equation becomes explicit for PCM temperature or quality when it is written in finite difference form. Here, i and n refer to the location of the node under consideration and the time step, respectively. Using the finite difference equation for the PCM in the finite difference form of Equation (1) yields the equation for the fluid temperature as Equations (8)—(12) are a set of simultaneous equations, the solution of which provides the temperatures of the fluid, PCM, and the quality of the PCM at each time step. This set of equations is tri-diagonal in matrix form. The scheme used in this study restricts the size of the time step so that only one node changes phase at a time. This time step is found using iteration.
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