Posted: September 13th, 2017

Heat Transfer

Paper, Order, or Assignment Requirements

The object shown is square, with dimensions 20 cm by 20 cm. The entire object is made from a single material with uniform thermal conductivity of 200 W/mK. There is a cut out corner in the top lefthand side, with dimensions of 8 cm by 8 cm. In this corner convection heat transfer occurs with heat transfer coefficient, h, of 100 W/m2 K, and fluid temperature of 15 degrees C. In the upper right hand quadrant there is a
section with uniform heat generation at 107 W/m3 . The location and dimensions for this part are shown on the drawing and are 4 cm wide by 8 cm long. There is also a section on the bottom with uniform heat flux to the surface. This is located on the bottom face in the corner and is 8 cm along the bottom. The heat flux here is 105 W/m2 . The sides of the object are insulated everywhere EXCEPT for the cut out corner and the
section with heat flux on the bottom. This is shown in the drawing below.
Assuming 2dimensional steadystate conduction, calculate the temperature distribution in the object using the finite difference
technique. Use at least thirtysix nodes for your calculations. Plot the temperature isotherms along with lines showing the direction of heat flow.
a. A sketch of your nodal network with numbers.
b. Equations and boundary conditions, along with your finitedifference
equations. Write down the types that are not in the book you may refer to the types of boundary conditions that ARE shown in the book. One equation representative of each type (ie interior node with generation) is plenty. Handwritten
worksheets are OK. I even encourage these as there is no point wasting tons of time drawing sketches and typing equations.
c. A copy of your program and output a digital copy posted on—is preferable because I am only going to glance at this. You can post this even if the rest of your report is a hard copy. Just make a note that you posted this
part.
d. Plot of temperature isotherms (hand drawn, approximate is OK).
e. Draw in the adiabats (lines showing heat flux directions, perpendicular to the isotherms)
f. Brief discussion of the results and whether they seem valid or not. Mention whether or not this problem is 2D, whether your results seem hotter and cooler in the correct places, and anything interesting you may have noticed