Computational Fluid Dynamics online test on “Energy Equation – Temperature Terms”.
1. The physical principle behind the energy equation is _____________
a) Newton’s second law of motion
b) Zeroth law of thermodynamics
c) First law of thermodynamics
d) Newton’s first law of motion
Answer: c
Clarification: First law of thermodynamics is the physical principle behind the energy equation. This law states that “Energy can neither be produced nor be destroyed but can be converted from one form into another”.
2. Consider an infinitesimally small fluid element moving along with the flow. Apply the first law of thermodynamics to this model. Which of these statements is correct?
a) The rate of change of the total energy is equal to the rate of heat addition and work extraction
b) The rate of work extraction is equal to the rate of heat addition and the rate of change of the total energy
c) The rate of heat addition is equal to the rate of work extraction and the rate of change of the total energy
d) The rate of change of the total energy is equal to the rate of work extraction
Answer: a
Clarification: The first law of thermodynamics applied to a system states that “The rate of change of the total energy is equal to the rate of heat addition and work extraction”.
3. The rate of heat increase in a system depends on __________
a) the rate of heat transferred to the system
b) the rate of heat generated by the system
c) neither the rate of heat generated by the system nor the rate of heat transferred to the system
d) both the rate of heat transferred to the system and the rate of heat generated by the system
Answer: d
Clarification: Heat can be added to a system in two ways:
Transfer of heat across the surface of the element by surface forces.
The heat generated by the system itself.
4. To get the energy equation in terms of temperature, this law is used.
a) Newton’s third law of motion
b) Zeroth law of thermodynamics
c) Fick’s law
d) Fourier’s law of heat conduction
Answer: d
Clarification: Fourier’s law of heat conduction gives the relationship between heat energy and temperature. This is used in the energy equation to convert heat terms to temperature terms.
5. The rate of change of energy in a moving model is (rhofrac{De}{Dt}). In the final equation, this term is reduced to (frac{partial(rho e)}{partial t}+nabla.(rho evec{V})). Which of these equations is used for this reduction?
a) Equations of state
b) Stress-strain equation
c) Momentum equation
d) Continuity equation
Answer: d
Clarification: Continuity equation is used as given below.
(rhofrac{De}{Dt}=rhofrac{partial e}{partial t}+rhovec{V}.nabla e )
But,
(rhofrac{partial e}{partial t}=frac{partial(rho e)}{partial t}-efrac{partial rho}{partial t})
And
(rhovec{V}.nabla e=nabla.(rho evec{V})-enabla.(rho vec{V}))
Therefore,
(rhofrac{De}{Dt}=frac{partial(rho e)}{partial t}-efrac{partial rho}{partial t}+nabla.(rho evec{V})-enabla.(rho vec{V}))
(rhofrac{De}{Dt}=frac{partial(rho e)}{partial t}-e(frac{partial rho}{partial t}+nabla.(rho vec{V}))+nabla.(rho evec{V}))
Applying the continuity equation, (frac{partial rho}{partial t}+nabla.(rho vec{V})=0), and hence
(rhofrac{De}{Dt}=frac{partial(rho e)}{partial t}+nabla.(rho evec{V})).
6. The relationship between the rate of heat transfer per unit area (dot{q}_s)=-(k∇T). Where, k is a scalar value of thermal conductivity and ∇T is the gradient of temperature. Which of these following is wrong according to the above equation?
a) Heat transfer is different in different directions
b) The rate of heat transfer depends upon the temperature gradient
c) Heat transfer is in the opposite direction of increasing temperature
d) k is the proportionality constant