Analytical Heat and Fluid Flow in Microchannels and Microsystems by Renato M. Cotta Diego C. Knupp & Carolina P. Naveira-Cotta

Author:Renato M. Cotta, Diego C. Knupp & Carolina P. Naveira-Cotta
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

P

Exact

Search interval [min, max]

Initial guess

Estimated

Confidence interval [min, max]

β v

1.5

[1.0, 5.0]

3

1.4731

[1.1014, 1.8649]

β t

3.88

[1.0, 5.0]

3

3.8908

[3.6886, 4.0770]

Bieff

0.8

[0.008, 8.0]

4.04

0.7992

[0.7923, 0.8068]

Figure 2.17 provides a direct comparison of the velocity distribution across the channel, as computed from the exact (solid line) and estimated (long dashed line) values of the slip coefficient, and also the velocity profiles as obtained from the lower (dotted line) and upper (dashed-dotted line) bounds of the 95 % confidence interval. In this case some slight changes in the velocity distribution are observable to the graph scale. As expected from the reasonably accurate estimation of the slip coefficient shown in Table 2.5, the two curves (exact and estimated) are essentially coincident.

Fig. 2.17Reconstructed velocity with estimated parameters (long dashes), with lower (dotted), upper (dashed-dotted) bounds of confidence interval, and exact (solid)

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