To find a positive root for , write a MATLAB script file that uses Bisection method. Choose any initial value that is needed. Use absolute relative approximate error to be less than 0.01. Your code should report the number of iteration and the value of x.

Write a MATLAB script file to integrate  using trapezoid method (do not use trapz command for this part, write your own script). Consider x=-0.5 to 3 with Δt=0.01, and compare your result with using “integral” and "trapz" commands (all in one file).

A power plant operates on a regenerative vapor power cycle with one open feedwater heater. Steam enters the first
turbine stage at 12 MPa, 520◦C and expands to 1 MPa, where some of the steam is extracted and diverted to the open
feedwater heater at 1 MPa. The remaining steam expands through the second turbine stage to the condenser pressure of
6 kPa. Saturated liquid exits the open feedwater heater at 1 MPa. For isentropic processes in the turbines and pumps,
determine for the cycle.
a) The thermal efficiency.
b) The net power developed, in MW, for a mass flow rate of 106 kg/h into the first-stage turbine.

Steam at 32 MPa, 520◦C leaves the steam generator of an ideal Rankine cycle modified to include three turbine

stages with reheat between the stages. The reheat pressures are 4 and 0.5 MPa, respectively, and steam enters the second-
stage turbine at 440◦C and the third-stage turbine at 360◦C. The condenser pressure is 0.08 bar. Determine for the cycle

a) The net work per unit mass of steam flowing, in kJ/kg.
b) The thermal efficiency.

Analyze the different types of defects that can be developed in plastic injection moulding processes. Your analysis must include the defects explanation, causes of the defects and the remedy of reducing the defects

A SMC is being used to mold the outer panel of an automobile hood. The inner panel of the hood will be made from a thin-gage steel. Write three concerns you may have for using SMC in this application. Suggest a method of improving the stiffness of the outer panel without increasing its weight and discuss a molding defect that may be associated with this method.

An object is initially traveling at a velocity of 12 m/s. It then begins to change it’s velocity according to the function ?=2.5?+3? v = 2 . 5 s + 3 a , where v is the velocity of the object, s is the objects position, and a is the acceleration. Determine the velocity of the object 30 meters after the velocity begins to change. (17.5 m/s)

The propane is contained in a piston-cylinder assembly, which maintains constant pressure at 0.2 MPa. If a mixture with a quality of 0.65 and a total volume of 0.07 m3 is slowly heated to a temperature of 54°C, a) what was the total work into the system b) what was the total amount of heat added to the system.

Please explain what tables you use to find the answer.

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2. Water at a temperature of 80 °C and velocity of 1.2 m/s is flowing parallel to one side of a smooth flat plate. The plate is maintained at a constant temperature of 24 °C and is 0.8 m long and 0.5 m wide. Determine the following:

1. The heat flux at a distance x = 0.6m from the front edge of the plate, q” = ____________
2. The location of the maximum heat flux on the plate, x = _________
3. The total convective heat transfer from the water to the top surface of the plate,

                                                                                                                   q = __________

4. The convective heat transfer between the water and the plate from x = 0.6 m to x = 0.8m

                                                                                                                   q₂ = __________

for water: ρ = 987 kg/m³, µ = 528 x 10^-6 N·s/m², k = 645 x 10^-3 W/m·K, Pr = 3.42

An uninsulated steam pipe with a wall temperature of 140 °C passes through a room of quiescent air of 14 °C. The pipe is horizontal and has an outer diameter of 20 cm. Find the following (include units if needed):

a) The temperature to evaluate properties = __________

b) The Rayleigh number, _____________

c) The heat transfer coefficient, h = ____________

d) q’ along the pipe = ________________

e) The pipe diameter is decreased by 50%. If all other parameters remain the same, will the heat transfer coefficient increase, decrease or stay the same? ___________. Justify your answer mathematically. For air: ν = 20.92 x 10-6 m2/s, α = 29.9 x 10-6 m2/s, 30 x 10-3 W/m·K, Pr = 0.7

1. Rank in order of total heat input (Note: don’t confuse with heat input RATE) and overall size of heat affected zone: GTAW, SMAW, Oxyfuel, laser beam welding

2. What are the advantages of reducing total heat input in a weld?