Students are casting an aluminum cylinder of diameter D = 2.5 cm and length of L = 10 cm from molten aluminum. The heated aluminum comes out of the mold at Ti = 530°C where it is quenched to T = 30°C by a cold-water faucet at T∞= 20°C and ℎ=1000 W/m2⋅K. Assume the thermophysical properties of aluminum are k = 230 W/m⋅K, ρ= 2710 kg/m3, and cp = 0.9 kJ/kg⋅K. First, determine whether the Lumped Capacitance Method is valid. Then, use the appropriate equation to determine how much time the aluminum cylinder must remain under the faucet to reach the desired temperature.

Students are casting an aluminum cylinder of diameter D = 2.5 cm and length of L = 10 cm from molten aluminum. The heated aluminum comes out of the mold at Ti = 530°C where it is quenched to T = 30°C by a cold-water faucet at T∞= 20°C and ℎ=1000 W/m2⋅K. Assume the thermophysical properties of aluminum are k = 230 W/m⋅K, ρ= 2710 kg/m3, and cp = 0.9 kJ/kg⋅K. First, determine whether the Lumped Capacitance Method is valid. Then, use the appropriate equation to determine how much time the aluminum cylinder must remain under the faucet to reach the desired temperature.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.3P

See similar textbooks

Similar questions

A cylindrical vessel (D=98,4 cm) is filled with water (ρ=1000 kg/m3, c=4.187 kJ/kg.K) to a depth of 113,64 cm. The initial temperature of the water is 15°C. Determine the time [min] required to increase the water temperature to 50°C when it is immersed into tank, filled with oil at 105°C. (NOTE: The overall heat transfer coefficient between the oil and the water is 284 W/m2.K. The surface area is 4.2 m2.)
A 15 lb. block of brass with a specific heat of 0.089 is heated to 189°C and the immersed in 5 gal. of water at 66°C. What is the final temperature of the brass and water? Assume there is no heat loss.
Conduction 1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P= 5 MW of net power production. The compressor, at an average temperature of T. = 400°C, is driven by the turbine at an average temperature of T₁ = 1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal conductivity k = 40 W/m K. Compressor min T Combustion chamber Shaft L Turbine Th out (a) Compare the steady-state conduction rate through the shaft connecting the hot turbine to the warm compressor to the net power predicted by the thermodynamics- based analysis. (b) A research team proposes to scale down the gas turbine of part (a), keeping all dimensions in the same proportions. The team assumes that the same hot and cold temperatures exist as in part (a) and that the net power output of the gas turbine is proportional to the overall volume of the device. Plot the ratio of the conduction through the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a…
• An aluminum pot contains water that is kept steadily boiling (100 °C). The bottom surface of the pot, which is 12 mm thick and 1.5x10t mm2 in area, is maintained at a temperature of 102°C by an electric heating unit. Find the rate at which heat is transferred through the bottom surface. Compare this with a copper based pot. Tc 0 0 L=12mm Base of pot TH A= area of base
PLEASE SOLVE THE FOLLOWING THREE QUESTIONS Question G: Generally speaking, (no numbers required), at what point does Newton's Model of Cooling (T=A+Be^kx) (when regarding dead bodies' temperatures) no longer work? What in reality gives us an indication that we’ve taken it too far? Question H: Assuming that the temperature of the person at the time of death (TOD) was 98.6 °F, set up a TOD equation using the values of ,A, ,B, and k you’ve calculated. Then, solve the equation using the same logarithm method you used to solve for .k. A: 68 Farehneits, B: 17.9 Fareinheit K: -0.002564 TOD: 98.6 Fareinheit Plug the above info into Newton's law of cooling: (T=A+Be^kx) Write your answer as a time, not just as x minutes. Recall that when ,x=0, the time is 2:00 PM. Question I: When forensic expert determines the time of death, they often have additional information besides body temperature. Suppose a coroner finds that the person who was murdered had an infection that probably raised the…
Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. Such a radiator, made of copper, is filled to its 12-L capacity when at 10.0°C. -What volume of radiator fluid, in liters, will overflow when the radiator and fluid reach their 99.5°C operating temperature, given that the fluid’s thermal coefficient of volume expansion is 400.0 × 10-6 / °C? The coefficient of volume expansion for copper is 5.1 × 10-5 /°C.
Water in a hydraulic press is subjected to a pressure of 15000 psia at 68°F. If the initial pressure is 1500 psia, approximately what will be the percentage decrease in specific volume?
Isabelle pour 158cm^3 of glycerin, at a temperature of -12 °C, into a graduated cylinder initially at 19 °C, filling it to the very top. The cylinder is made of glass with a specific heat of 840 J/kg-K and a coefficient of volume expansion of 1.2 x10^−5 K^−1; its mass is 0.110kg. The mass of the glycerin is 0.0873 kg. What will be the final temperature of the glycerin, once thermal equilibrium is reached?
A 5.0 kg steel gear is heated to 210°C and then placed into a 0.5 gal container of water at 10° C. What is the final temperature of the metal and water? (Express your answer using three significant figures.) Tinal 1°C
K2a please help me with my reviewer. Provide me the full solution and answer thank you SN= 40
Q1) A steel cylinder 10 cm in diameter and 10 cm long is initially at 300 °C. It is suddenly immersed in an oil bath that is maintained at 40 °C, with h =280 W/m² °C. Find: (a) The temperature at the center of the solid after 2 min, and (b) The temperature at the center of one of the regular faces after 2 min.
Define the Under steady-flow conditions?