What is the characteristic of the system matrix of a FEA analysis? Which information can you extract from the pivot ratio?

Question 2/ Method to assess the value of your analysis output

a) What is the characteristic of the system matrix of a FEA analysis? Which information can you extract from the pivot ratio?

b) Through three reasons discuss the possible errors occurred by un-correct loading.

c) Give three reasons for which non-linear FEA is required when not expected.

d) Which tools does Ansys propose to estimate errors? Give brief explanation and provide the command line for the three of them?

e) Discuss linear and parabolic elements within their application. Which one of linear or parabolic elements would you use for highly curved geometries? Explain why.

f) What is a discretisation error? What is a formulation error? What is a numerical error?

Question 3/ Thermal analysis

Problem description

The heat exchanger shown below is used to cool a motor. The coolant coming from the motor (hot fluid) runs through the block near a cold fluid coming from a separate reservoir. The base of the heat exchanger is mounted on an insulated surface (no heat transfer occurs across the base). The heat exchanger also utilizes fins along its top surface to increase heat transfer to the surrounding air through convection.

As shown in the figure below, the heat exchanger block is 54 mm wide by 80 mm high, and is sufficiently long that it can be analysed using a 2D thermal analysis; i.e., heat flow in the third direction (into the paper) can be neglected. The five fins on the top surface are 6 mm thick, with 6 mm spacing between fins, rounded on the inner and outer edges with a 3 mm radius. The fins are 20 mm long. Both fluid channels have a diameter of 24 mm and are centred horizontally in the block. 

The air temperature surrounding the heat exchanger is 300 K, and the convective heat transfer (film) coefficient can be assumed to be h = 400 W/m2-K. This convection acts on all external surfaces except for the base, which is insulated. The temperature of the hot fluid is T hot = 600 K, and the temperature of the cold fluid is Tcold = 285 K. The convective heat transfer coefficient of both fluids is h = 5000 W/m2-K.

The heat exchanger is made of an aluminium alloy with the following thermal properties (density, ? = 2702 kg/m3):

Temperature (K) 200 300 400 600

Thermal Conductivity, k (W/m-K) 237 237 240 231

Specific Heat, c (J/kg-K) 798 903 949 1033