Interdisciplinary Applied Mathematics

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(M2Ml) 7M2M2n ‘



(4.11)



+


4fx = 1+]_ to + VM2)


D 27 °ge |_M2(l + ^±M2n)


The variation of Mach number in the channel as a function of the inlet Mach number and MfT is found by plotting equation (4.11) for specified Min values. Once the Mach number variation in the channel is known, the corresponding pressure ratio (-p~) and the density ratio    variations


along the channel can be calculated by using the following relations:


p Min


Лп M


(1 +V M2)


P Min


-(l+7_iM2)


Pin M


(1 + ^M2J


FIGURE 4.7. Pressure ratio (-p—) variation along the channel as a function of j-for inlet conditions of Table 4.2.


(4.12)


The Mach    number    variation    along    the    channels    is    given    in    Figure    4.6


(left) as a function of |) for three different inlet conditions reported in (Harley, 1993). Very steep variation of the Mach number is observed toward the exit of the channel. This variation becomes steeper as the inlet Mach


TABLE 4.2. Experimental data in microchannels from (Harley, 1993). DH is the hydraulic diameter, and all the f and f factors denote Fanning friction factors as noted. Also, Po is the Poiseuille number; see Section 1.2.


Case


JP9


JH6


JH6


Width pm


92.40


96.60


96.60


Depth pm


4.44


0.51


0.51


DHpm


8.47


1.01


1.01


Length mm


10.90


10.90


10.90


Gas


n2

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