This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Scalar Field Problems – Steady State Heat Transfer”.

1. What is the governing law of the conduction process?

a) Fourier’s Law

b) Euler’s Law

c) Rayleigh’s Law

d) Heaver’s Law

View Answer

Explanation: Conduction process is governed by the Fourier’s law of heat transfer. It is represented mathematically as –

q

_{x}= – kdT / dx

where q

_{x}= components of heat flux (W/m

^{2})

k = thermal conductivity (W/m

^{0}C)

dT / dx = Temperature gradient along x axis

2. In convection heat transfer, transfer of energy is between solid and solid only.

a) True

b) False

View Answer

Explanation: The given statement is false. In conduction heat transfer, there is transfer of energy between one solid to another. Whereas, in convection heat transfer, the transfer of energy takes place between solid surface and fluid only.

3. What is the governing equation of the convection process?

a) Rayleigh’s law

b) Euler’s law

c) Newton’s law of cooling

d) Law of conservation of mass transfer

View Answer

Explanation: The convection process is governed by Newton’s law of cooling. It is mathematically represented by –

q = h(T

_{s}– T

_{8})

where q = convective heat flux (W/m

^{2})

h = convective heat transfer coefficient (W/m

^{0}C)

T

_{s}and T

_{8}= Surface and fluid temperatures respectively (

^{0}C)

4. “In majority of the cases, Radiation mode of heat transfer is not considered for finite element analysis.” Why is this so?

a) It comes under linear dynamic analysis

b) It comes under linear static analysis

c) It comes under linear analysis

d) It comes under non linear analysis

View Answer

Explanation: In radiation mode of heat transfer, the heat flux is directly proportional to the fourth power of absolute temperature. This makes the problem nonlinear, and thus not considered for solving using the finite element method.

5. In one dimensional heat transfer, the temperature gradient exists along two co-ordinate axes only.

a) False

b) True

View Answer

Explanation: The given statement is false. In case of one dimensional heat transfer, the temperature gradient exists along one of the co-ordinate axes only. Temperature gradient is defined as the ratio of temperature difference to the length of material under discussion.

6. When is the boundary surface said to be perfectly insulated?

a) When q > 0

b) When q = 0

c) When q < 0

d) When q = 1

View Answer

Explanation: We know that ‘q’ represents heat flux at a particular point. When q = 0, it means that the heat flux of the body is equal to zero; implying that the body is perfectly insulated.

7. Which are the two physical methods generally used for solving one dimensional heat problems?

a) Euler Method & Heat flux boundary condition method

b) Rayleigh Method & Heat flux boundary condition method

c) Galerkin Method & Heat flux boundary condition method

d) Newton’s method & Heat flux boundary condition method

View Answer

Explanation: The two methods generally used for solving one dimensional heat problems are Galerkin method and heat flux boundary condition method respectively. In Galerkin method, we find out the solution making use of shape functions; whereas in the Heat flux boundary condition method, boundary conditions are made use of to arrive at the solution.

8. Which of the following condition corresponds to a forced boundary condition?

a) T > T_{o}

b) T < T_{o}

c) T * T_{o} = 0

d) T = T_{o}

View Answer

Explanation: In the Heat flux boundary condition method, there are two types of boundary conditions – natural and forced. A boundary condition is said to be of the forced type when the condition T = T

_{o}is satisfied. This is because the temperature lies on the field variable itself.

9. What is the purpose of using fins?

a) To increase rate of heat removal

b) To decrease rate of heat removal

c) To increase rate of heat addition

d) To decrease rate of heat addition

View Answer

Explanation: A fin is used for increasing the rate of heat removal on any surface. It is just an extended material that sticks on the periphery of the conducting material to aid removal of heat. Fins help enhance the efficiency of the entire system by removing heat at a quicker rate than normal.

10. What is the value of heat flux generated? Given k = thermal conductivity = 20 (W/m^{0} C), dT / dx = Temperature gradient along x axis = 5, mode of heat transfer = conduction.

a) – 100 W/m^{0} C

b) – 100 W/m^{2}

c) – 10 W/m^{2}

d) – 1 W/m^{2}

View Answer

Explanation: We know that for conduction, the mathematical representation of heat flux is given by –

q

_{x}= – kdT / dx

= – 20(5) W/m

^{2}

= – 100 W/m

^{2}

11. Which of the following is not an example of steady state heat transfer of one dimensional body?

a) Heat transfer through a piece of paper

b) Heat transfer along a line across x axis

c) Heat transfer across a curve across y axis

d) Heat transfer across a series of points along any one of the coordinate axes

View Answer

Explanation: Heat transfer through a piece of paper is not an example of steady state heat transfer of one dimensional body. It is clear that a piece of paper has two dominant coordinate axes coming into the picture, making it a two dimensional body.

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