Show that the plate is lumped, and then find the time required for the plate to achieve a temperature of 40°C.
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- A long copper cylinder 0.6 m in diameter and initially at a uniform temperature of 38oC is placed in a water bath at 93oC. Assuming that the heat transfer coefficient between the copper and the water is 1248 W/(m2 * K), calculate the time required to heat the center of the cylinder to 66oC. As a first approximation, neglect the temperature gradient within the cylinder; then repeat your calculation without this simplifying assumption and compare your results.The 4cm thick large copper plate, initially at a uniform temperature of 25oC, is heated by passing it through an oven kept at 400oC. The copper plate remains in the oven for 5 minutes. Calculate the surface temperature of the copper plate when it is taken out of the furnace by taking the heat transfer coefficient h = 200W / m2oC.Properties of copper at room temperature: I want to solution with Biot numberA small stainless-steel rod 7 mm in diameter was heated so it is at 300 °C. It is quenched in a bath of room temperature water, where it has a heat transfer coefficient of 30 W/m2K. How long will it take to be cool to the touch? Justify your answer and all assumptions. (You will generate a time constant and the Bi for this problem.
- A thick concrete wall fairly large in size initially at 30 oC has its surface temperatureincreased to 600 oC by an intense fire which lasted for 25 minutes. The material maydisintegrate up to a depth where the temperature reaches 400 oC. Determine thethickness which may disintegrate and the heat flow at this depth and the total heatflow during that time. The thermal diffusivity is 4.92 x 19-7 m2/s and k = 1.28 W/m-K.Quenching is a rapid cooling process by which many metallic alloys are hardened. Brass (a copper alloy: 70 Cu, 30 Zn) plates that are 4 mm thick are quenched in a water bath at a heat treating plant. If a brass plate is initially at 4500C determine the quench time needed for the plate to attain 900C. The water bath temperature is 800C and has an average convective heat transfer coefficient of 45 W/(m2 K), determine how long the plate has to remain in the oven.An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose thermal conductivity of roughly k = 0.6- W mk overall density of p = 1000; and heat capacity of C₂ = 3000- kg m² The egg is initially at a uniform temperature of T₂ = 10°C and is dropped into boiling water at T.. = 90°C W - determine how long it will take for the egg to m²K Taking the convective heat transfer coefficient to be h reach T = 70°C. In solving the problem, please follow the steps below. For the Lump Model In solving this problem, please use the lump model method (ignoring the requirement of small Biot number and discuss the outcomes, 1. 2. Compute the characteristic length Lc Compute the volume and surface area of the sphere (as the egg model) Vol As 3. Compute the diffusivity α = = 10- k p Cp = J kgk Compute non-dimensional excessive temperature 0 = h Lc k 4. Compute the Biot number using the characteristic length found above Bi = T-Too 5. Ti-Too 6. Calculate the Fourier number from the equation =…
- Determine the amount of heat that must be removed from 1 kg of water at 40°C to convert it to ice at -5°C.(Obtain any relevant data that you need from the internet. Cite the source of that data in your answer)A long 3-mm diameter rod of steel (ρ = 7840 kg/m3, c = 460 J/kgK, k = 43 W/mK)has a uniform initial temperature of 650C. The rod is then suddenly immersed in alarge container of 25C water. The hot rod causes the water immediately surroundingthe rod to boil, giving rise to a heat transfer coefficient of 5600 W/m2K. The boilingstops when the rod reaches a temperature of 100C, at which time the heat transfercoefficient becomes 750 W/m2K. Find the time period during which boiling occursand the total time required for the rod to reach a temperature of 40C. Use acharacteristic length for this problem.A 30 mm diameter copper sphere and a 30 mm copper cube are both heated in a furnace to 923 K. They are then annealed in an air at 378K. If the external heat transfer coefficient h is 80 W/m2.K in both cases, what is the temperature of the sphere and of the cube at the end of 6 minutes
- In a quenching process, a copper plate of 3 mm thick is heated up to 350°C and then suddenly, it is dropped into a water bath at 25°C. (1) Calculate the time required for the plate to reach the temperature of 50°C. The heat transfer coefficient on the surface of the plate is 28 W/m2-K. The plate dimensions may be taken as length 40 cm and width 30 cm. (2) Also calculate the time required for infinite long plate to cool to 50°C. Other parameters remain same. (3) Calculate the heat transfer rate loss of the plate when it is at 50°C. Take the properties of copper as: CP = 380 J/kg-K, ρ = 8800 kg/m3, k = 385 W/m-KA 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.Water hardening process of 2 m long and 0.05 m diameter steel bars will be carried out. The steel bar, which is heated up to 900 °C in the oven, is cooled to an average temperature of 100 °C in a water bath. The water bath is kept at a uniform temperature of 30 °C and the heat transfer coefficient between the water and the rod surface is 325 W/m2K. Accordingly, calculate the time required for the steel bar to cool to 100°C in the water bath. (Steel bar p=7832 kg/m3, cp=434 J/kgK, k=63.9 W/mK)