This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Heat Transfer – One Dimensional Conduction & Conduction with Convection”.

1. Identify the governing equation for a solid body undergoing heat direction along any one of its axes. Assume the axis to be x axis.

a) q_{x}Adt + QAdxdt = Δu + (q_{x} + ∂q_{x}/∂x dx)Adt

b) QAdxdt = Δu + (q_{x} + ∂q_{x}/∂x dx)Adt

c) q_{x}Adt = Δu + (q_{x} + ∂q_{x}/∂x dx)Adt

d) q_{x}Adt + QAdxdt = Δu + (q_{x})Adt

View Answer

Explanation: This equation is derived by making use of the principle of conservation of energy. The governing equation for a solid body undergoing heat direction along x axis is given by –

q

_{x}Adt + QAdxdt = Δu + (q

_{x}+ ∂q

_{x}/∂x dx)Adt.

where,

q

_{x}= heat flux across boundary

Q = internal heat generation rate

u = internal energy

2. Which of the following is the expression for increase in internal energy?

a) Δu = cρdxdt

b) Δu = cρAdxdt

c) Δu = ρAdxdt

d) Δu = cAdxdt

View Answer

Explanation: Internal energy is defined as the energy that arises from the internal interaction of atoms and molecules among one another. The expression for increase in internal energy is given by –

Δu = cρAdxdt

where,

c = material specific heat

ρ = material density

3. When can it be concluded that the finite element solution corresponds to the exact solution?

a) Global element matrices contain terms appearing in the exact solution

b) Global mass matrices contain terms appearing in the exact solution

c) Interpolation functions contain terms appearing in the exact solution

d) It is a hypothetical situation

View Answer

Explanation: In the case where a problem contains an exact solution; the finite element solution corresponds to the exact solution, if and only if the interpolation functions that are used in the finite element formulation consist of terms that are occurring in the exact solution as well.

4. Which of the following defines natural convection?

a) If fluid is in motion due to heat transfer only

b) If fluid is in motion due to external influence only

c) If fluid is in motion due to both heat transfer and external influence

d) If fluid is in motion naturally

View Answer

Explanation: When the fluid is in motion, only due to the process of heat transfer taking place; then the process is referred to as natural convection. Some examples of natural convection include sea and land currents, breeze and tornadoes etc.

5. Which of the following defines forced convection?

a) If fluid is in motion due to both heat transfer and external influence

b) If fluid is in motion due to external influence only

c) If fluid is in motion due to heat transfer only

d) If fluid is in motion due to collision of molecules

View Answer

Explanation: When the fluid is in motion due to the result of some external influence, then it is termed as forced convection. This external influence can be in the form of fan, pump etc. Some examples of forced convection include usage of water geysers, air conditioners etc.

6. What is the expression for the convective heat flux?

a) q = (T – T_{a})

b) q = h(T + T_{a})

c) q = h(T – T_{a})

d) q = h(T * T_{a})

View Answer

Explanation: The expression for heat flux generated due to convection is given by –

q = h(T – T

_{a})

where,

h = convective coefficient

T = temperature of the surface of the body

T

_{a}= temperature of the ambient fluid

7. Which of the following defines the imposed temperature type of boundary condition?

a) Temperature at each node is unknown

b) Temperature is constant

c) Temperature is fluctuating

d) Temperature at end node is of known value

View Answer

Explanation: The imposed temperature type of boundary condition corresponds to a known value of temperature at the end node of the element. This is possible if the end node is subjected to a constant process temperature and in turn heat is removed from the process by the body.

8. The imposed heat flux boundary condition corresponds to usage of conduction flux by coming in contact with fluid of known temperature.

a) False

b) True

View Answer

Explanation: The given statement is false. Imposed heat flux boundary condition corresponds to known values of heat flow rate into/out of an end of the body is specified. This is usually a theoretical formulation and cannot be experienced real time.

9. Which of the following corresponds to end node convection?

a) When end of the body is in contact with fluid of unknown temperature

b) When end of the body is in contact with fluid of known temperature

c) When end of the body is in contact with a solid

d) When the end of the body is in contact with vacuum

View Answer

Explanation: In end node convection, the end of the body is in contact with a fluid of known temperature. The conduction flux at the boundary can be removed through means of convection to the fluid media.

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