Question

Homework problem Microfluidics. KT Mean free path, L: where k is Boltzmann's constant k=1.38x10-2)/K V2.P2 Knudsen number: - 1. You are required to model the heat transfer from a new type of hard disk where the gap between a reader and a disk is 25nm and the pressure is kept at 1.5 atmospheres with air molecules 0.7nm in diameter. The temperature is 303K.

(i) Calculate the Knudsen number.

(ii) Can you use continuum computational fluid dynamics for this and why?

(iii) Repeat (i) and (ii) for the case when air is replaced by argon at 5 atm with a molecular diameter of 1.5nm.

Answer 1

Answer is in the attached images,please do go through the same.

-23 Ke 1.38×10 Mean free Path J ax Pd² Knudsen Number : L ; L =) Characteristic length. Given T= 303k P = 105 atm = 1.5x co 1.013 x 103 pa d=o7nm =oTx10 m. -> L KT - 1.38 x102** 303 J2 APP 52 x 3.14 x 1.5x1 .013 x 105 x - 23 2 7x109) 2 -10 -> L = 126.403 X 10 m - 10 Kn 126.403 x 10 25x10-9 - kn = 05056 * 01 0110 Continuum. Transition flow regime Glip Our As ol k n = 10 = It free molecular form. is under Transition Le regime. dynamics cannot Therefore, continuum computational fluid

to free molecular more nearing as it is be flow applied . P= 5 x 100 13 x 105 pa. d = 1.5x109 m. T= 303K 2 - 1.38 X10-20 X 303 (2x 3.14 x 5 x 100 13 x 105 1.5x10-9² :> L - 2.258 x16-10 kn = 8.258 810 I = 8 26 x 10-9 = 33 > Ko -033 As .01€ kn sol , The flow is slip e flow which is nearing continuum Hence here continuum Computational Flurd dynamics can be applied in this range. You Thank Please hit the like button

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