# Interdisciplinary Applied Mathematics

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1.685

1.873

2.014

0.1

1.4043

1.556

1.668

1.853

1.992

2.944

0.2

1.3820

1.523

1.627

1.806

1.931

0.4

1.3796

1.510

1.615

1.768

1.888

2.720

0.6

1.3982

1.523

1.621

1.772

1.888

2.691

0.8

1.4261

1.547

1.638

1.791

1.904

1.0

1.4594

1.578

1.668

1.818

1.930

2.706

2.0

1.6608

1.773

1.861

2.007

2.116

2.879

3.0

1.8850

1.994

2.081

2.227

2.336

3.096

4.0

2.1188

2.225

2.312

2.458

2.567

3.372

5.0

2.3578

2.461

2.548

2.694

2.803

3.565

6.0

2.5999

2.700

2.787

2.934

3.003

7.0

2.8440

2.942

3.029

3.167

3.285

8.0

3.0894

3.185

3.272

3.420

3.529

4.293

9.0

3.3355

3,430

3.517

3.664

3.778

10.0

3.5821

3.675

3.761

3.910

4.019

4.785

FIGURE 15.17. Thermal creep in a channel: Normalized flowrate versus the rarefaction parameter S = /тг/(2Кп).

###### 15-4-4 Nonisothermal Flows

Unlike isothermal flows, where the BGK model equations result in accurate approximations to the Boltzmann equation, in the case of heat transfer the BGK model is inadequate, since it gives the wrong Prandtl number. This is particularly evident in simulations of thermal creep, where the difference in solutions of the BGK and Boltzmann equations may be as high as 30%. This is shown in the Figure 15.17, where we plot the normalized flowrate in a channel due to thermal creep. The BGK solution, due to (Loy-alka, 1974), differs significantly from the solution of the Boltzmann equation obtained by (Ohwada et al., 1989a). The BGK solution can be improved if the assumption that states that the collision frequency is independent of the molecular velocity is relaxed.

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