We want to cool a solution containing 100 mg/mL of a monoclonal antibody from an initial temperature of 25°C to 10°C by having the solution flow through a coil of stainless-steel tubing immersed in a water bath, which keeps the tube wall at 4°C. The inner diameter of the tube is 1.0 cm.

The solution flows at the rate of 10 kg/h and has a viscosity of 20 mPa s at 20°C. Assuming that the thermal conductivity of the solution is 0.40 W/m K, that the heat capacity is 4,000 J/kg K, and that the density is 1,030 kg/m³, determine the length of tubing required.