Finite Element Method Questions and Answers – Two Dimensional Heat transfer Formulation with Heat Generation

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Two Dimensional Heat transfer Formulation with Heat Generation”.

1. What might be the causes of heat generation in two dimensional bodies?
a) From chemical reactions, electrical resistance etc
b) From chemical reactions only
c) From electrical resistance only
d) Due to an external source of power

Explanation: To increase the ease of such computations, most finite element models involving thermal analysis are based on the assumption that the internal heat generated is zero. However, this is far from true in the practical scenarios. Internal heat generated might be due to chemical reactions(exothermic), electrical resistance, or collision of intra-molecular particles etc.

2. Which of the following defines the semi infinite boundary condition?
a) Represents a continuous, non uniform material extending towards infinity in one direction
b) Represents a continuous, uniform material extending towards infinity in one direction
c) Represents a non continuous, uniform material extending towards infinity in one direction
d) Represents a continuous, uniform material extending towards infinity in all directions

Explanation: The semi infinite boundary condition represents a continuous, uniform material extending at infinitum in one direction, with a known value of temperature at infinity. For computing the same in the system, boundary is approximated by mentioning a large distance gap between the boundary node and its adjacent node.

3. Which of the following is the function of the subroutine ISOTHM?
a) It helps examine the initial temperature distribution in the grid
b) It helps compute the expected temperature distribution in the grid
c) It helps examine the final temperature distribution in the grid
d) It helps in extrapolation of temperatures of any two consecutive nodes

Explanation: This subroutine helps examine the final temperature distribution in the grid. This is done by performing linear interpolations between grid temperatures to help determine the spatial coordinates of user-specified isotherms. These coordinates are then used to plot temperature distribution curves.

4. What is the significance of the unit impulse function?
a) It is a function that is infinite everywhere, but at the origin
b) Function that simplifies extrapolation between grid temperatures
c) Function that simplifies interpolation between grid temperatures
d) It is a function that is zero everywhere, but at the origin

Explanation: This subroutine helps examine the final temperature distribution in the grid. This is done by performing linear interpolations between grid temperatures to help determine the spatial coordinates of user-specified isotherms. These coordinates are then used to plot temperature distribution curves.

5. For development of finite element formulation of two dimensional problems involving heat transfer, initially a specific element geometry is used.
a) False
b) True

Explanation: The given statement is false. For finite element formulation of two dimensional problems involving conduction with convection; a general approach is initialized first. Specific element geometry is not in use; instead the geometry is assumed to have a certain number of nodes which cater to a specific temperature distribution.

6. Geometric symmetry is more than sufficient to ensure that a problem is symmetric.
a) True
b) False

Explanation: The given statement is false. Geometric symmetry alone is not sufficient to ensure that a problem is symmetric. In addition to this, the material properties, boundary conditions and the applied loads must be symmetric along the axis/plane of geometric symmetry.

7. How are global heat transfer values calculated in finite element analysis of heat transfer problems?
a) Calculating determinant of global mass matrix
b) Calculating determinant of global coefficient matrix
c) Nodal temperatures are back substituted into reaction equations
d) Fourier’s law is used

Explanation: In finite element analysis of heat transfer problems, the values of nodal temperatures need to be back substituted into reaction equations in order to calculate the global heat transfer values. This procedure is analogous to the structural problems; in the sense that more importance is given to the stresses than the nodal displacements.

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