An apparatus, used in an operating room to cool blood, consists of a coiled tube that is immersed in an ice bath. Using this apparatus, blood, flowing at 0.006 m³/h, is to be cooled from 40°C to 30°C. The inside diameter of the tube is 2.5 mm, and the surface coefficient between the ice bath and outer tube surface is 500 W/m² · K. The thermal resistance of the tube wall may be neglected.
Determine the required length of tubing to accomplish the desired cooling. Properties of blood are the following:

ρ = 1000 kg/m²

k = 0.5 W/m · K

c_p = 4.0 kJ/kg · K

v = 7 × 10^-7 m²/s

Determine the total heat transfer to the oil and its temperature at the heater exit.