Hello, I need this project done

The conductivity of the instrument box is k b = 0 :5 W m K while the conductivity of the wooden platform is k w = 0 :15 W m K . You may assume that steady state has been reached. 1.What are the governing equations for both the instrument box and the wooden platform?

Give the necessary boundary conditions for both governing equations. You may use a symmetry argument if you wish.

2.Use the energy balance method to develop a nite di erence approximation for an internal node on the instrument box. You may assume there is no generation. Write this equation in the general form (in terms of m & n). How would the equation for an internal node on the wooden platform di er?

3.Consider a rectangular space with length L= 420 mm and height H= 180 mm containing the instrument box, wooden platform, and 60mm of ice on either side. If you choose to use a symmetry argument, your dimensions will di er. Identify the 6 \anchor point" nodes and give their coordinates in terms of x and y. Note that the values for x and y will change, but the position of your \anchor point" node should not. Are there any stipulations on what x and y can be in order to hit all of these critical nodes?

4.Identify all node types present in the scenario and present the results graphically making sure to clearly identify the position of each type. You may graph this by hand or submit an imagesc plot of your ode type" matrix along with a list matching the numbers to each node type.

5.Using MATLAB, solve the Ax=btype problem and present the temperature distribution results graphically using pcolor,contourf , or a similar type of plot. Make sure to include a ME 603 1 of 2 Project Deliverable 01 title, axis labels, and include colorbar; if using pcolor, make sure to call shading(' at')to shade over the opaque grid lines. In your submission, please state the values you chose for x and y. Was there a reason you chose these values?

6.Create a second temperature plot using di erent values of x and y. This time, choose values such that x 6 = y. Is the model more accurate when x > yor when x < y?

Why is this?

SUBMISSION On Canvas, please submit your MATLAB codeand a pdf of your hand calcu- lations ,response to prompts , andgraphical results .

Your MATLAB code will be the basis on which you will build your nal project.

Here are two suggestions regarding your code:

1. Comment Often I prefer to comment at the beginning or end of a block of code rather than line by line (it can get messy), but either way is ne.

Try to make it so that if you were to look at this code 2 years from now it would take you less than 10 minutes to remember how it worked.

2. Use Functions Using functions will help you to organize your code into more manageable sections. Often, if everything is on the same page, it becomes a bit overwhelming.

ME 603 2 of 2 Project Deliverable 01