ME 598 Electronics Cooling
Fall 2023
Homework 3
Problem #1 (10 points)
A nickel-coated heater element with a thickness of 15 mm and a thermal conductivity of
50 (W/m K) is exposed to saturated water at atmospheric pressure. A thermocouple is
attached to the back surface, which is well insulated. Measurements at a particular
operating condition yield an electrical power dissipation in the heater element of 6.950 x
107 W/m3 and a temperature of To = 266.4°C.
(a) From the foregoing data, calculate the surface temperature, Ts, and the heat flux
at the exposed surface.
(b) Using the surface heat flux determined in part (a), estimate the surface temperature
by applying an appropriate boiling correlation.
ME 598 Electronics Cooling
Fall 2023
Problem #2 (10 points)
A novel scheme for cooling computer chips uses a thermosyphon containing a saturated
fluorocarbon. The chip is brazed to the bottom of a cuplike container, within which heat is
dissipated by boiling and subsequently transferred to an external coolant (water) via
condensation on the inner surface of a thin-walled tube. The nucleate boiling constants and
the properties of the fluorocarbon are provided below:
Tsat = 57°C, cp,l = 1100 J/(kg K), hƒg = 84,400 J/kg, ρl = 1619.2 kg/m3, kl = 0.054 W/(m
K), ρv = 13.4 kg/m3, σ = 8.1x10-3 N/m, µl = 440x10-6 kg/(m s), and Prl = 9.01. In addition,
the nucleate boiling constants are Cs,ƒ = 0.005 and n = 1.7.
(a) If the chip operates under steady-state conditions and its surface heat flux is
maintained at 90% of the critical heat flux, what is its temperature T? What is the
total power dissipation if the chip width is Lc = 20 mm on a side?
(b) If the tube diameter is D = 30 mm and its surface is maintained at Ts = 25°C by the
water, what tube length L is required to maintain the designated conditions?
ME 598 Electronics Cooling
Fall 2023
Problem #3 (20 points)
A thermosyphon consists of a closed container that absorbs heat along its boiling section
and rejects heat along its condensation section. Consider a thermosyphon made from a thinwalled mechanically polished stainless steel cylinder of diameter D. Heat supplied to the
thermosyphon boils saturated water at atmospheric pressure on the surfaces of the lower
boiling section of length Lb and is then rejected by condensing vapor into a thin film, which
falls by gravity along the wall of the condensation section of length Lc back into the boiling
section. The two sections are separated by an insulated section of length Li. The top surface
of the condensation section may be treated as being insulated.
The thermosyphon dimensions are D = 20 mm, Lb = 20 mm, Lc = 40 mm, and Li = 40 mm.
(a) Find the mean surface temperature, Ts,b, of the boiling surface if the nucleate
boiling heat flux is to be maintained at 30% of the critical heat flux.
(b) Find the total condensation flow rate, 𝒎̇, and the mean surface temperature of
the condensation section, Ts,c.