2.2. Mathematical analysis:
An equation that describes how TH varies in time can be obtained by solving Eq. (1) as
With the appropriate modifications, it can be used for obtaining expressions to calculate ton and toff. However, exponential equations are not very convenient to use. Alternatively, one can derive linear expressions for ton and toff. This can be done by replacing dTH by Thigh-Tlow (Tlow - Thigh) in Eq. (1) when the EWH is ON (OFF) and dt by ton (toff). Besides, TH is
assumed equal to Td in order to calculate the average heat losses to the ambient and due to inlet cold water replacing the water drawn from the tank. In this case