# Finite Element Method Questions and Answers – Time Dependent Heat Transfer

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Time Dependent Heat Transfer”.

1. Which of the following defines a consistent capacitance matrix?
a) Matrix formulated on basis of same functions as spatial distribution of temperature
b) Matrix formulated on basis of different functions other than the spatial distribution of temperature
c) Matrix formulated on basis of exponential temperature distribution
d) Matrix formulated on basis of constant temperature distribution

Explanation: A capacitance matrix is termed as consistent capacitance matrix; if and only if, it is formulated making use of same interpolation functions that are used to describe spatial distribution of temperature. Making use of Galerkin’s method, this matrix is a natural result of the so used mathematical procedure.

2. Which of the following is a difference between the lumped capacitance matrix and the consistent capacitance matrix?
a) Lumped capacitance matrix distributes capacitance throughout by virtue of interpolation functions
b) Consistent capacitance matrix distributes capacitance throughout by virtue of interpolation functions
c) No difference between the two matrices
d) Lumped capacitance matrix is more accurate in capacitance distribution

Explanation: A lumped capacitance matrix is one that makes use of an alternative approach for arriving at its formulation. It attributes the storage capacity strictly to the nodes only. Whereas, the consistent matrix distributes capacitance by virtue of the interpolation functions.

3. Which of the following is true with regards to the finite difference method?
a) It is based on approximating derivatives of a function
b) It is based on approximating integrals of a function
c) It is much more efficient than the finite element method
d) It is much less efficient than the finite element method

Explanation: The finite difference method is based on approximating derivatives of a function. The condition that, incremental changes in the value of this function should correspond to finite changes in the values of independent variables; must hold good for the method to be termed as the finite difference method.

4. Which of the following is not a type of the finite difference method?
a) Forward difference method
b) Backward difference method
c) Central difference method
d) Intermittent difference method

Explanation: There are three types of finite difference methods. They are Forward, Backward and Central difference method respectively. In backward difference method, the user looks back in time to approximate the derivative using the previous time step. Whereas, in forward difference method, the user looks ahead of time to approximate the derivative using the next time step.

5. Which of the following defines the central difference method?
a) Evaluated at the midpoint of the time step
b) Evaluated at the midpoint of the temperature distribution
c) Evaluated at the start of the time step
d) Evaluated at the end of the time step

Explanation: As the name suggests, in this method, the dependant variable and all corresponding functions are evaluated at the midpoint(center) of the time step. Average values of temperature and time are made use in this method. The corresponding functions that appear on the right hand side of the resulting equations are also referred to as reactions.
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6. How can we reduce the computational time involved in case of finite difference methods?
a) By increasing the time step
b) By decreasing the time step
c) We cannot reduce computational time in case of finite difference method
d) By making use of powerful processors

Explanation: The user can reduce the computational time involved in finite difference methods by decreasing the time step involved. As such, the selected time step is the key parameter that governs speed and accuracy in case of finite difference methods.

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