A fluid passes through a double pipe heat exchanger and changes phase but does not change temperature. A warm fluid at a temperature of $104\mathrm{.}4C$ enters a double pipe heat exchanger and leaves still at a temperature of $104\mathrm{.}4C.$ A cooler fluid enters the exchanger at $37\mathrm{.}8C$ and is heated to $65\mathrm{.}6C.$ Determine the LMTD for $($a$)$ counterflow and for $($b$)$ parallel flow.