An x-ray "monochrometer" is a mirror that reflects only a single wavelength from a broadband beam of x-rays. Over 99% of the beam's energy arrives on other wavelengths and is absorbed creating a high heat flux on part of the surface of the monochrometer. Consider a monochrometer made from a silicon block 10 mm long and 3 mm by 3 mm in cross-section which absorbs a flux of 12.5 W/mm2 over an area of 6 mm2 on one face (a heat load of 75 W). To control the temperature, it is proposed to pump liquid nitrogen through a circular channel bored down the center of the silicon block. The channel is 10 mm long and 1 mm in diameter. LN2 enters the channel at 80 K and a pressure of 1.6 MPa (Tsat = 111.5 K). The entry to this channel is a long, straight, unheated passage of the same diameter.
a. For what range of mass flow rates will the LN2 have a bulk temperature rise of less than 1.5 K over the length of the channel?
b. At your minimum flow rate, estimate the maximum wall temperature in the channel.
As a first approximation, assume that the silicon conducts heat well enough to distribute the 75 W heat load uniformly over the channel surface. Could boiling occur in the channel?
Discuss the influence of entry length and variable property effects.