A pure aluminum bar has a diameter of 15 cm and a length of 1.25 m. The rod is initially uniform in temperature at 300?C. The bar is now suddenly exposed to a convection environment at 50?C with h = 1250 W/m K. How long does it take the center to cool to a temperature of 80?C? (a) Determine if a lumped capacitance analysis is or is not appropriate. (b) Determine the cooling time assuming the lumped capacitance model is valid. (c) Finally, determine the time required for a point 0.5 cm from the surface to drop to 275?C

(Fluid Mechanics; Euler's equation and Bernoulli equation)

As I know, in order to derive Euler's equation from Naveri-Stokes equation, the additional conditions are 1)Incompressible and 2)Inviscid

Then, in order to derive Bernoulli's equation from Euler's equation, what additional conditions are needed?

As I thought, Euler's equation already meets the incompressible and invsicid condtion, so only "steady state" is the additional condition to derive Bernoulli equation from Euler's equation.

Am I right? In addition, are both Navier-stokes equation and Euler's equation need not to be steady state?

In addition, would you derive Bernoulli equation from Euler's equation?

What extra steps must you add for a rendezvous between non-coplanar spacecrafts?

List at least three advantages and disadvantages of a powder-bed laser sintering process.

Nitrogen (N2) contained in a piston–cylinder arrangement, initially at 9.9 bar and 421 K, undergoes an expansion to a final temperature of 300 K, during which the pressure–volume relationship is pV1.1 = constant. Assuming the ideal gas model for the N2, determine the heat transfer in kJ/kg.

An as-wound helical-coil compression spring with infinite fatigue life is needed to resist a dynamic load that varies from 8.0 to 24.0 lbf at 45.0 Hz over a dynamic deflection of 0.3 in. Because of assembly considerations, the solid length of the spring cannot be more than 1.2 in. The spring should have squared and ground ends and is to be made from peened music wire. Upon closure, use a design factor of 1.2 guarding against yielding and a fractional overrun to closure x = 0.15. The fundamental critical frequency should be greater than 10 times the frequency of the dynamic load. The springmaker has the following wire sizes in stock: 0.059, 0.063, 0.072, 0.075, 0.085, and 0.090 in. Select a suitable spring with a fatigue design factor of 1.9 using the Goodman-Zimmerli fatigue failure criterion. Calculate the cost of the wire from which the spring is wound and use it as the figure of merit for your selection

A piston-cylinder has a volume of 1 ft3 and contains a substance initially at 50 °F and 1 atm. The system is then heated until the temperature becomes 300 °F. Determine the total heat added (Btu) and final volume (ft3) assuming the substance is: a) water, b) copper, c) neon, d) air.

Refrigerant-134a enters the condenser of a residential heat pump at 900 kPa and 65^oC at a rate of 0.018 kg/s and leaves at 750 kPa subcooled by 2^oC. The refrigerant enters the compressor at 200 kPa superheated by 3^oC. Determine (a) the isentropic efficiency of the compressor in decimal (up to two decimals), (b) the rate of heat supplied to the heated room, and (c) the COP of the heat pump. Also determine (d) the COP if this heat pump operated on the ideal vapour compression cycle between the pressure limits of 200 and 900 kPa

show the correlation between weight percent carbon, volume percent pearlite, and tensile strength for hot rolled carbon

steels by

1- Looking up the tensile strengths in psi for the following hot rolled AISI carbon steels in matweb.com: 1006, 1010,

1020, 1025, 1030, 1035, 1040, 1045, 1050, 1055, 1060, 1065, and 1070.

2- Calculating the volume percent pearlite for each steel (assume that vol.% pearlite = wt.% pearlite) using the lever

rule and the nominal carbon content indicated by the AISI number.

3- Recording the values in an EXCEL Worksheet that has columns for wt. %C, vol.% pearlite, and tensile strength.

4- Plotting EXCEL graphs of vol.% pearlite versus wt. %C, tensile strength versus wt. %C, and tensile strength

versus vol.% pearlite

1. A black thermocouple measures the temperature in a chamber with black walls. If the air around the thermocouple is at 20°C, the walls are at 100°C, and the heat transfer coefficient between the thermocouple and the air is 15 W /m2·°C, what temperature will the thermocouple read

3. A stainless steel sphere of thermal conductivity 16 W/m · K with a diameter of 4 cm is exposed to a convective environment of 15 W/m2 · K, 20?C. Heat is generated uniformly in the sphere at a rate of 1.0 MW/m3 . Determine the steady-state temperature of the sphere at its center and its surface. Also determine the heat flux at a radius of 1.5 cm.