Your management has recently become aware that not only office spaces require heating during the winter but also open areas such as lobbies, waiting areas, and hallways. As a junior engineer, you have identified an opportunity to utilize the residual heat in the condensate from heating the offices to warm these open spaces before it is eventually reheated in the boiler. Based on your calculations, these areas need to be raised from an average temperature of 18°C to 45°C to ensure human comfort. You plan to use a working fluid at a flow rate of 21.4 kg/s and with a specific heat capacity of 2.3 kJ/kg oC in a one-shell-pass and six-tube-pass heat exchanger, given that these spaces are relatively larger than offices. The hot condensate enters the shell side at 102°C and exits at 68°C, while you estimate the overall heat transfer coefficient to be approximately 1040 W/m2 oC. The working fluid, which requires heating from 18°C to 45°C, flows through the tube side, and the hot condensate flows through the shell side.

With the provided conditions, your task is to determine the heat transfer rate and the required heat transfer area using the log mean temperature difference method to ensure that the desired heating level can be achieved. The correction factor (F) must relate the log mean temperature difference of the counterflow to the shell and tube heat exchanger flow arrangements