In this case, finding A isn't the problem, U is. Is the condensation / evaporation on the inside or the outside? I presume you are referring to a system like an air conditioner, where you're heating or cooling air, rather than an air separation plant, where you would be condensing or evaporating air.

A is the surface are where the heat rate is passing through. If the surface area is the surface of the coil then the perimeter of the coil * coil length gives you A. A = pi * D * L.

Dear Salehi,

                    actually your question is not clear where you are just solving a problem or you are modeling a condenser/evaporator. if it is a modeling then please assume some suitable value of U from data book and then you can calculate the surface area required to transfer the heat duty of evaporator. then selecting the radius and length for without fin condition you can  apply iteration method  to minimize standard deviation and then you got best combination of length and radius of tube. if you are using fin then please assume suitable value by applying the condition mL=5 and effectiveness greater than 2 for this you can repeat same iteration process to find suitable value.