Computational Fluid Dynamics Questions and Answers – General Transport Equation

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This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “General Transport Equation”.

1. The general equation applicable to all the properties is called the general transport equation. What does this term ‘transport’ signify?
a) The equation is applicable to all properties
b) The equation can be transformed easily
c) The equation includes various transport processes
d) The equation is general

Explanation: The general transport equation involves all the transport processes which are responsible for the transfer of mass, energy or other properties.

2. What are the terms included in the transport equation?
a) Rate of change term, advective term, convective term, source term
b) Advective term, diffusive term, convective term, source term
c) Rate of change term, diffusive term, convective term, advective term
d) Rate of change term, diffusive term, convective term, source term

Explanation: Transport equation involves four terms which are rate of change, diffusion, convection and source of properties.

3. What does the term $$\frac{\partial(\rho\Phi)}{\partial t}$$ mean?
a) Rate of change
b) Convection
c) Diffusion
d) Source term

Explanation: This term represents the rate of change of fluid property inside the model of flow. It does not involve any kind of flow of the property.

4. Which of these terms represent the flow of fluid into and out of the observation model?
a) $$\frac{\partial(\rho\Phi)}{\partial t}$$
b) $$div(\rho\Phi\vec{u})$$

Explanation: $$div(\rho\Phi\vec{u})$$ is the convective term of the transport equation. Convection is the flow of fluid into and out of the model of observation.

5. Which term represents the diffusion of the property Φ?
a) div(Φ)
c) curl(Φ)

Explanation: div(ΓgradΦ) represents diffusion. Diffusion is the movement of fluid from a high concentration to low concentration within the system.

6. What does this symbol Γ in the term div(ΓgradΦ) of the general transport equation mean?
a) Diffusion flux
b) Convection coefficient
c) Diffusion coefficient
d) Rate of diffusion

Explanation: Γ represents the diffusion coefficient. The diffusion coefficient is defined by Fick’s law of diffusion.

7. In terms of heat transfer, what does div(ΓgradΦ) mean?
b) Heat convection
c) Thermal flow
d) Heat conduction

Explanation: Diffusive heat transfer is called heat conduction. This refers to the process of heat transfer without any movement of the particles.

8. When the general transport equation is written in the energy equation form, what does Γ become?
a) k
b) μ
c) σ
d) κ

Explanation: k represents thermal conductivity. As diffusion in heat transfer is heat conduction, diffusion coefficient becomes, thermal conductivity.

9. Which of these statements hold true?
a) Diffusive flux is always positive
b) Diffusive flux is positive in the direction of the positive gradient of fluid property
c) Diffusive flux is positive in the direction of the negative gradient of fluid property
d) Diffusive flux is always negative

Explanation: Diffusive flux is positive in the direction of the negative gradient of fluid property. Example, heat is conducted in the direction of decreasing temperature.

10. To get the mass conservation equation from the general transport equation given below, Φ=?
$$\frac{\partial(\rho\Phi)}{\partial t}+div(\rho\Phi\vec{u})$$=div(ΓgradΦ)+SΦ
a) Mass of the fluid
b) 1
c) 0
d) Density of the fluid

Explanation: The mass conservation equation is obtained by replacing Φ with 1. As density is already present in the equation, 1 is enough to get mass conservation out of it.

11. The surface integral can be used to represent ____ and ____ terms of the transport equation.
a) Rate of change and diffusion
b) Rate of change and convection
c) Source and diffusion
d) Convection and diffusion