1. Operational Principle of Thermal Bubble Jet injected droplet heater bubble Chamber neck liquid Current pulse heats up liquid Bubble as a pump pushes out droplet Refill by capillary force Boiling heat transfer

2. Satellite Droplets Inkjet Droplet injection sequence

3. Liquid Entrance Manifold Narrow heater Wide heater Nozzle Chamber Common line Electrode Liquid Micro-Machined Thermal Bubble Jet Heater Silicon Wafer

4. 1-D Heat Conduction with Generation Thin heater deposited on silicon can be modeled as heat generation Silicon Wafer thermal conductivity k T ,1, h 1 L TsTs T ,1 T ,2 1/(h 1 A) T T ,2, h 2 L/(kA) 1/(h 2 A) q1q1 q2q2 T

5. 1-D, steady Heat Transfer in Cylindrical Coordinate Radial direction q r =-kA r (dT/dr) q r+dr =qr+(dq r /dr)dr

6. Cylindrical Heat Conduction

7. Heat Loss from a Cylindrical Pipe (no insulation) Steam at 300°C flow in a cast iron circular pipe (k=80W/m.K). Determine the heat loss per unit length of the pipe to the surroundings at T  =20°C, with a combined (radiation & convection) heat transfer coefficient of h 2 =20 W/m 2.K). The convection coefficient inside the pipe is h 1 =50 W/m 2.K) r 1 =1 cm r 2 =1.25 cm R conv,1 R cond R conv,2 T TT

8. Heat Loss from a Cylindrical Pipe (no insulation) (cont.) Note: the cast iron pipe is a good conductor, therefore, it has a small thermal resistance. To prevent heat loss, it is recommended that insulation be used outside the pipe.

9. Insulation It is suggested that a thick layer of insulation (k=0.5 W/m.K) be wrapped outside the pipe. Determine the heat loss as a function of the thickness of the fiber glass wrap. R conv,1 R cond R conv,2 T TT R insulation r 1 =1 cm r 2 =1.25 cm Assume the fiber thickness is t r 3 =r 2 +t R conv,1 and R cond stay the same, unchanged r3r3 r2r2 r1r1

10. Insulation-2 Plot this function in the following slide

11. Critical Radius of Insulation Heat loss increases initially when one adds insulation (why?) Maximum heat loss at critical radius of insulation that r critical =k insul /h outside In the present case, r critical =0.5/20=0.025 Its critical thickness is t=0.025-0.0125=0.0125(m) Critical thickness Note: similar derivation can be made for a spherical container. The critical radius for a spherical shell is r critical =2k/h