You are designing an operating room heat exchange device to cool blood (bypassed from a patient) from 40 to 30°C by passing the fluid through a coiled tube sitting in a vat of water-ice mixture. The volumetric flow rate (∀) is 10-4 m3 /min; the tube diameter (D) is 2.5 mm; and Tm,j and Tm,o represent the inlet and outlet temperatures of the blood. Neglect heat transfer enhancement associated with the coiling.

(a) At what temperature would you evaluate the fluid properties in determining Ii for the entire tube length?

(b) If the properties of blood evaluated at the temperature for part (a) are p = 1000 kg/m3, J) = 7 x 10-7m2/s ∙ k = 0.5 W/m ∙ K, and c p = 4.0 kJ/kg ∙ K, what is the Prandtl number for the blood?

(c) Is the blood flow laminar or turbulent?

(d) Neglecting all entrance effects and assuming fully developed conditions, calculate the value of Ii for heat transfer from the blood.

(e) What is the total heat rate loss from the blood as it passes through the tube?

(f) When free convection effects on the outside of the tube are included, the average overall heat transfer coefficient V between the blood and the ice-water mixture can be approximated as 300 W/m2 ∙ K. Determine the tube length L required to obtain the outlet temperature Tm.o