You are asked to design a heating system for a swimming

pool that is $2$ m deep, $25$ m long, and $25$ m wide. Your

client desires that the heating system be large enough to raise

the water temperature from $20$C to $30$C in $3$ h$.$ The heater

must also be able to maintain the pool at $30$C at the outdoor

design conditions of $15$C$,1$ atm, $35$ percent relative humidity,

$40$ mph winds, and effective sky temperature of $10$C$.$

Heat losses to the ground are expected to be small and can

be disregarded. The heater considered is a natural gas furnace

whose efficiency is $80$ percent. What heater size $($in Btu$/$h

input$)$ would you recommend that your client buy?

consider convection, radiation and evaporation.