A long cylinder of 30-mm diameter, initially at a uniform temperature of 1100 K, is suddenly quenched in a large, constant- temperature oil bath at 350 K. The cylinder properties are k = 1.7 W/m-K, c = 1600 J/kg-K, and p = 400 kg/m³, while the convection coefficient is 54 W/m².K.
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Assume the Fourier number, Fo, is greater than or equal to 0.2 (note that you still need to calculate the Biot number, and possibly a second Biot number).
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- Indirect Cooling With Liquid Nitrogen. You are designing a system to cool an insulated silver plate of dimensions 2.00 cm × 2.00 cm x 0.40 cm. One end of a thermally insulated copper wire (diameter D = 2.70 mm and length L = 12.0 cm) is dipped into a vat of liquid nitrogen (T = 77.2 K), and the other end is attached to the bottom of the silver plate. (a) If the silver plate starts at room temperature (73.0°F), what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir? (b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.Indirect Cooling With Liquid Nitrogen. You are designing a system to cool an insulated silver plate of dimensions 2.00 cm × 2.00 cm × 0.60 cm. One end of a thermally insulated copper wire (diameter D = 2.70 mm and length L = 18.0 cm) is dipped into a vat of liquid nitrogen (T = 77.2 K), and the other end is attached to the bottom of the silver plate.(a) If the silver plate starts at room temperature (65.0 °F), what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir?(b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.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 =…
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