Design an HVAC system for an office building. All of the offices should be maintained at 72°F.

Model a corner office, 6m by 6m and 2m high. Make the exterior walls glass and the interior walls are drywall at the ambient temperature. Model a cold winter day as -5°C with a 10 m/s wind and a hot summer day at 40°C with a 4 m/s wind. Model a person as a 37°C vertical cylinder with 1 m² surface area 170 cm high. Ignore heat transfer to the top of the cylinder.

Include convection and radiation. The person is losing heat by natural convection to the environment at its ambient temperature (27°C) and gains or loses heat by radiation to the windows. The window temperature will be at whatever the steady-state conduction temperature is assuming natural convection on the inside and forced convection on the outside. The window is 1 cm thick glass with thermal properties of ordinary window glass. The area affected is only half the person’s surface area.

Compute the radiation loss or gain for the person and the total heat loss from the person in each season

An ideal gas is contained in a piston-cylinder device and undergoes a power cycle as follows: 1-2 isentropic compression from an initial temperature T1 5 208C with a compression ratio r 5 5 2-3 constant pressure heat addition 3-1 constant volume heat rejection The gas has constant specific heats with cv 5 0.7 kJ/kg·K and R 5 0.3 kJ/kg·K. (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the heat and work interactions for each pro- cess, in kJ/kg. (c) Determine the cycle thermal efficiency. (d) Obtain the expression for the cycle thermal efficiency as a function of the compression ratio r and ratio of specific heats k.

Design a Turing Machine to construct the function f(n) = 4 [1/4 n] + 2, (that is, 2 more than 4 times the integer part of 1/4 n) for n Element N. Do not just produce a TM, but also describe briefly how it works. There is a TM in the Cooper notes that does something similar. You may modify it to produce the required TM, or produce a machine totally independently.

Evaluate a room 12'x12' height 10' write a heat transfer equation consistent with the room dimension,

Anisotropy frequently occurs in materials. Suggest how this anisotropy might occur
(hint: consider manufacturing processes) and how a knowledge of the level of anisotropy
might be important when designing components. Use polymer shopping bags as an example. Can anisotropy be “useful”?

You are one of five astronauts in a spacecraft that is traveling in deep space. Your spacecraft can be thermally modeled as a cylindrical shell made of polished aluminum with uniform thickness that is capped at the ends, being 20m long and having an inner and outer radius of 2.9 m and 3 m with the cap at each end being 10 cm thick. Aluminum has a constant thermal conductivity of 237 W/m K over a wide temperature range, from -70oC to 120oC. The convective heat transfer coefficient in space is always 0 W/m2 K. That means that all losses from the spacecraft will be from radiative losses into space which will be purely a function of the outer wall temperature.
1. 10pt – Radiation
a. 2.5pt – If the outer wall of the spacecraft were at 5oC and had an emissivity of 1, what would the rate of heat loss be for the spacecraft into space? Assume the incoming solar radiation is negligible since the spacecraft is so far away from the sun.
b. 7.5pt – The emissivity of polished aluminum is actually 0.05. Using this fact and the fact that the measured heat loss is 7151 W, calculate the temperature of the outside of the spacecraft.
2. 10pt – Steady Conduction
Create a thermal circuit model of the spacecraft. Using the losses and temperature from part 1.b, calculate the temperature of the inner wall of the spacecraft. Assume the temperatures are all at steady state since the electronics in the spacecraft produce exactly the correct amount of heat to prevent the craft from cooling off. Also assume the inner wall is a uniform temperature and that the cap and cylindrical shell of the spacecraft conduct heat in parallel to one another.
3. 10pt – Convection
A burst of high energy cosmic rays knocks out all electronics in the spacecraft. The spacecraft cools down to an uninhabitable level. As you succumb to the freezing temperatures, you realize that there is an emergency heat fan in the spacecraft. You turn it on before losing consciousness. If the fan heats the air inside to 30oC, what must be the convective heat transfer coefficient inside the spacecraft in order to deliver enough heat to the walls to bring the inside of the walls up to 10oC and keep them there so that the electronics can restart? Since most of the astronauts are already dead, assume all of the heat must come from the heat fan and the losses are still only from radiation into space. How much power must the heat fan output in order to do this?

How does automation harm and benefit humanity?

-----Demonstrate both sides of the ethical dilemma-----

a.What is the difference between endurance limit materials and others?

b.What is an S-N curve? And explain this based on the wing of an aircraft in flight.

c.Why do fatigue cracks only grow during tension and not compression?

d.Tensile stress levels affect the life expectancy of a part - why?

Explain the significance of, and the mechanisms behind, slip in metals. What is a slip system? In a pure material, what governs the ease of slip? Why are some crystal structures easier to slip than others? Why are ceramic materials normally very resistant to slip?

Use Matlab and write entier script

Problem 2.

Generate the estimate (linear estimate) for y_est, and plot(x , y_est).

Use “hold on” and plot(x,y) and plot(x,y_est), so that you can see the result of the line and how it fits the data.   Does it look like it did a pretty good job?

An estimate of the “residual error” is the sum of the squares of the difference between y and y_est.

This is often denoted as r2.

r2 = sum( (y – y_est) .^2)

or equivalently

r2 = sum( (y – y_est)’ * (y – y_est)’)

What is the residual error for the above problem?

Use Matlab and write entier script

Problem 1.

Using the information above, find y(n) for all n between 1:N.

y(tn)=mx(tn)+b+r(tn)

y=mx+b

Plot the points on a graph, without connecting them with a line.   Use a command like:

plot( x, y, ‘.r’ )

Now we want to find the “best fit” solution.   As was mentioned before, this was defined in the prior exercise. (You may wish to read this to understand how the algorithm works.)   Use the MATLAB code below.

You have the vectors x and y already. You need a vector I, which is a column which each element equal to 1.

Programming Steps:

I = ones(length(x),1);

u = [ x , I ];

w = (u’ * u) \ ( u’ * y) ;

The result is an estimate of the values of m and b.   The estimate for m is w(1) and the estimate for b is w(2). The resulting estimate for y is:

                y_est = u * w;

use newton raphson method to solve the following system of nonlinear equations

x1^2+x2^2=50 ; x1*x2=25

stop after three iterations. initial guess : (x1,x2) = (2,1)