18.24 Drug formulations contain an active drug dissolved in a nontoxic solution to facilitate its delivery into the body. They are often packaged into sterile syringes so that the patient can

inject the drug formulation directly into the body and then throw the syringe away. Often the drug-loaded syringes are shipped by air freight to customers. There is a concern that the low temperatures associated with air freight cargo holds might promote the precipitation of the drug from solution. A certain monoclonal antibody is known to precipitate from its delivery solution at 2 C. The cargo hold in the airplane used by the air freight company is maintained at 0 C. Initially, the syringe is at a uniform tempera- ture of 25 C. Within the current packaging environment of the syringe, the convective heat-transfer coefficient of air surround- ing the syringe is 0.86 W/m² K. The barrel of the syringe containing the liquid is 0.70 cm inner diameter and 8 cm in length. The thermal conductivity of the solution is 0.3 W/m. K, the density is 1 g/cm³, and heat capacity is 2000 J/kg. K. The syringe wall is very thin. If the air flight is 3.5 h in length, will the drug completely precipitate and ruin the product? Note: 0.86 W/m²-K is an extremely low value for h (see WRF Table 15). Please work this problem out using 43 W/m²-K instead. Additionally, find the temperature at the surface and at center of the syringe after the 3.5 hr flight.