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In a material processing experiment conducted aboard the space shuttle, a coated niobium sphere of 10-min diameter is removed from a furnace at 900°C and cooled to a temperature of 300°C. Although properties of the niobium vary over this temperature range, constant values may be assumed to a reasonable approximation, with
(a) If cooling is implemented in a large evacuated chamber whose walls are at 25°C, determine the time required to reach the final temperature if the coating is polished and has an emissivity of £ = 0.1. How long would it take if the coating is oxidized and
(b) To reduce the time required for cooling, consideration is given to immersion of the sphere in an inert gas stream for which
(c) Considering the effect of both radiation and convection, what is the time required for cooling if
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Chapter 3 Solutions
Introduction to Heat Transfer
- The initial temperature of a 50 cm long silver wire is 50 °C. The circumference of the wire in question is completely insulated, but both ends are kept at a temperature of 0 °C (zero degrees Celsius). Obtain the heat conduction along the wire as a function of time and position and, taking a single term in the solution, determine how many degrees Celsius the temperature in the middle of the rod will be after 7 minutes. (For silver wire, α=1.70 cm2/s.)arrow_forward= Consider a large plane wall of thickness L=0.3 m, thermal conductivity k = 2.5 W/m.K, and surface area A = 12 m². The left side of the wall at x=0 is subjected to a net heat flux of ɖo = 700 W/m² while the temperature at that surface is measured to be T₁ = 80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary equations for steady one- dimensional heat conduction through the wall, (b) obtain a relation for the variation of the temperature in the wall by solving the differential equation, and (c) evaluate the temperature of the right surface of the wall at x=L. Ti до L Xarrow_forwardHow long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of = 1000 kg/m3 and thermal conductivity of k = 0.606 Watts/(mC) and specific heat of c = 4182 J/(kg C). Suppose that an egg is fully cooked when the temperature at the center reaches 70 C. Initially the egg is taken out of the fridge at 4 C and placed in the boiling water at 100 C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100 C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes.arrow_forward
- 3. 100-gram oil at 20°C and 50-gram iron at 75 °C are placed in 200-gram iron container. The increase in temperature of the container is 5°C and the specific heat of oil is 0.43 cal/g °C. What is the specific heat of the iron?arrow_forwardFind the steady-state temperature distribution in a (very long) solid cylinder if the boundary temperatures are T(s=0, θ, z)=0 and T(s, θ, z=0)=s*sinθarrow_forwardEx1. A piece of chromium steel of length 7.4cm (density=8780kg/m³ ; k = 50w/mK and specific heat cp = 440j/kgK) with mass 1.27kg is rolled into a solid cylinder and heated to a temperature of 600°C and quenched in oil at 36°c. Show that the lumped capacitance system analysis is applicable and find the temperature of the cylinder after 4min. What is the total heat transfer during this period? You may take the convective heat transfer coefficient between the oil and cylinder at 280w/m2k.arrow_forward
- A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the block? (specific heat of aluminium : 0.91 J/(g°C))arrow_forwardThermal conductivity for pure aluminum: kal = 238 W/m⋅K ; Thermal conductivity for glass: kgl = 1.4 W/m⋅K.arrow_forwardThe bottom of a 50mm diameter, 2mm thick metallic induction heater is 120C while its thermal conductivity is 60 W/m-C. The voltage and current flowing into the heater are 220V and 5A, respectively. Find the temperature at the top portion of the pan. Sketch diagram and show pertinent solutions. Box your final answer and express numerical values in 2 decimal placesarrow_forward
- Determine the heat absorbed, when 1 mol of carbon monoxide gas is heated from 212.4 K to 437.2 K. The relationship for the heat capacity at constant pressure in J mol-1 K-1 is Cp = a + bT + cT2, with a = 25, b = 7.0 x 10^-3, and c = -8 x 10^-7arrow_forward1arrow_forwardR_1=67. The value of R_1in the given question is 67.so please add this value for R_1. Solution of the question should be detailed enough to understand.arrow_forward
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