# Interdisciplinary Applied Mathematics

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Figure 5.2 shows the flow field for early times as well as for a steady-state behavior. A uniform flow is obtained in the channels initially (past the end of the aforementioned first process). As more fluid is introduced into the hot tank, the pressure there increases while the pressure at the cold tank decreases. Initially, the pressure built up by this process is not sufficient to reverse the flow in the middle of the channel, and more fluid is being transported into the hot tank (see Figure 5.2 (a)). When the pressure in the hot tank is sufficiently high to overcome the flow due to thermal creep, the

T=300 K    T=400 K

 Knav= 0.365 3 : = = 3 ^ = g== = = = = = = = = = = = 3 = 3 Early Times (a) , , , , i , , , , T=300 K T=400 K и i :< Knav=0.365 i: : : : Steady State (b)

FIGURE 5.2. Demonstration of the thermal creep effects: Flow field for early times (a), and steady-state solution (b) (Kn = Knav = 0.365).

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a

Conductive Material

Array of Micro Channels

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G

Conductive Material

Tank 1

Tank 2

Hot Liquid

Cold Liquid

Pressure release valve