Operational Principle of Thermal Bubble Jet injected droplet

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

Satellite Droplets Inkjet Droplet injection sequence

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

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

1 -D, steady Heat Transfer in Cylindrical Coordinate qr+dr=qr+(dqr/dr)dr qr=-k. Ar(d. T/dr) Radial direction

Cylindrical Heat Conduction

Heat Loss from a Cylindrical Pipe (no insulation) r 1=1 cm r 2=1. 25 cm Steam at 300°C flow in a cast iron circular pipe (k=80 W/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) Rconv, 2 T R R cond conv, 1 T

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.

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. Rconv, 1 T Rcond Rinsulation Rconv, 2 T Assume the fiber thickness is t r 3=r 2+t Rconv, 1 and Rcond stay the same, unchanged r 1 r 2 r 3 r 1=1 cm r 2=1. 25 cm

Insulation-2 • Plot this function in the following slide

Critical thickness Critical Radius of Insulation • Heat loss increases initially when one adds insulation (why? ) • Maximum heat loss at critical radius of insulation that rcritical =kinsul/houtside • In the present case, rcritical=0. 5/20=0. 025 • Its critical thickness is t=0. 025 -0. 0125=0. 0125(m) Note: similar derivation can be made for a spherical container. The critical radius for a spherical shell is rcritical=2 k/h