Steel balls 12 mm in diameter are annealed by heating to 1150K and then slowly cooling to 400 K in an air environment for which
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Fundamentals of Heat and Mass Transfer
- 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…arrow_forwardSolve (c) please.arrow_forward19 mm diameter steel balls are quenched by heating to 989 K followed by slow cooling to 400 K in an environment with air at T∞ = 325 K and h = 39 W/m2.K. Assuming that the steel properties are k = 40 W/m.K, ρ = 7800 kg/m3 and C = 600 J/kg.K, estimate the time (in "minutes") required for the cooling process. Bolas de aço com 19 mm de diâmetro são temperadas pelo aquecimento a 989 K seguido pelo resfriamento lento até 400 K em um ambiente com ar a T∞ = 325 K e h = 39 W/m2.K. Admitindo que as propriedades do aço sejam k = 40 W/m.K, ρ = 7800 kg/m3 e C = 600 J/kg.K, estime o tempo (em "minutos") necessário para o processo de resfriamento.arrow_forward
- Determine the time needed to decrease the temperature of a solid cylinder from 40 C to 35 C if the ambient temperature is equal to 31 C. The cylinder has a length equals to 0.9 m and diameter equals to 100 mm. The heat convective coefficient is equal to 1.3 W/m^2.K. The cylinder has a conductivity equals to 2 W/m.K, a density equals to 1200 kg/m^3 and its Cp is equal to 4.700 kJ/kgK. Select one: a. 83325 s O b. 10500s O c. 45360 s O d. 30050 sarrow_forwardExample 10: Consider a long resistance wire of radius r1 = 0.2 cm and thermal conductivity kwire = 15 W/m·°C in which heat is generated uniformly as a result of resistance heating at a constant rate of g = 50 W/cm3. The wire is embedded in a 0.5-cm-thick layer of ceramic whose thermal conductivity is kceramic = 1.2 W/m·°C. If the outer surface temperature of the ceramic layer is measured to be Ts = 45°C, determine the temperatures at the center of the resistance wire and the interface of the wire and the ceramic layer under steady conditions.arrow_forwardA solid hemisphere of radius 5 cm to be cooled in air (at 20 o C, h=10 W/m 2 .K) from 200 oC to center of 150 oC, assume following sphere properties ρ=8500kg/m3, k=20W/m.K , C=400 J/kg.Ka. List assumptions and justify selected method of solution b. How long does it take to cool the hemisphere? c. What is the temperature of the surface at end of cooling?arrow_forward
- Determine the time needed to decrease the temperature of a solid cylinder from 40 C to 35 C if the ambient temperature is equal to 31 C. The cylinder has a length equals to 0.9 m and diameter equals to 100 mm. The heat convective coefficient is equal to 9 W/m^2.K. The cylinder has a conductivity equals to 2 W/m.K, a density equals to 1200 kg/m^3 and its Cp is equal to 4.700 kJ/kgK.arrow_forwardA mass of 300kg of oil is cooled in 1 hour from 70 celcius to 35 celcius in a cooler consisting of a bank of tubes through which hot oil passes. Cooling water circulates around the outside of the tubes. Calculate the mass of cooling water required per hour if the water temp increases by 21 degrees celcius . Specific Heat of Oil - 2.0 kJ/kg deg C Specific Heat of Water - 4.186 kJ/kg deg Carrow_forwardSteel cubes 10 mm in width are annealed by heating to 1,377 K and then slowly cooling to 469 K in an air environment for which T∞ = 301 K and h = 24 W/m2-K. Assuming the properties of the steel to be k = 24 W/m · K, ρ = 7,047 kg/m3, and c = 916 J/kg · K, estimate the time required for the cooling process.arrow_forward
- 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.)arrow_forwardSuppose that as a body cools, the temperature of the surrounding medium increases because it completely absorbs the heat being lost by the body. Let T(t) and Tm (t) be the temperatures of the body and the medium at time t, respectively. If the initial temperature of the body is T1 and the initial temperature of the medium is T2, then it can be shown in this case that Newton's law of cooling is dT/dt = k(T - Tm ), k 0 is a constant. (a) The foregoing DE is autonomous. Determine the limiting value of the temperature T(t) as t→ o What is the limiting value of Tm (t) as t→o? (b) Verify your answers in part (a) by actually solving the differential equation. (c) Discuss a physical interpretation of your answers in part (a).arrow_forward5. A 0.350 kg metal ball at an unknown initial temperature is dropped into a Styrofoam cup containing 0.400 kg of water. The initial temperature of the water is 17.0°C. The ball and the water then come to a final temperature of 28.0°C. If the metal has a specific heat capacity of 386 J/(kg-°C) and water has a specific heat capacity of 4186 J/(kg-ºC), find the initial temperature of the metal.arrow_forward
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