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A long rod of 60-mm diameter and thermophysical properties
(a) What is the centerline temperature of the rod when the surface temperature is 550 K?
(b) In a heat-treating process, the centerline temperature of the rod must be increased from
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Chapter 3 Solutions
Introduction to Heat Transfer
- A cylindrical shape body of length is 1.9 m and diameter is 400 mm is inside a room where the ambient temperature is equal to 300 K. The initial temperature of the body is equal to 350 K. If the heat convective coefficient is equal to 1.3 W/m^2.K. What is the thermal conductivity K.arrow_forwardA 10.0-cm cube of stainless steel is initially at 500oC. It is suddenly immersed in a tank of oil maintained at 100oC. The convection coefficient is 1000 W/m2×oC. Calculate the temperature at the center of one face after 1 min.Data: stainless steel properties, k = 22 W/m×oC, r = 7,689 kg/m3, c = 460 J/kg×oC.arrow_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
- What is the temparature at depth 1 cm from the surface at t=2 minutes after the start of the coolıng ?arrow_forwardNumber 4 A food product wants to be produced in a small round shape (pellet) by freezing it in a water blast freezer freezer. Air freezer operates at -25°C. The initial product temperature is 25°C. The pellet has a diameter of 1.2 cm, and a density of 980 kg/m³. The initial freezing temperature is -2.5°C. The latent heat of freezing of the product is 280 kJ/kg. The thermal conductivity of the frozen product is 1.9 W/(m °C). The convective heat transfer coefficient is 40 W/(m² K). Calculate the freeze time. tf = answer in hourarrow_forwardQ1/ The center to surface temperature difference in a heat generating cylindrical rod of 4 m diameter was 30°C. What is the difference temperature between the center and surface in the case of a sphere of 2 m diameter under similar conditions? * Your answer Q2/ A metal plate of 4mm thickness (k = 95.5 W/m°C) is exposed to vapor at 100°C on one side and cooling water at 25°C on the opposite side. The heat transfer coefficients on vapor side and waterside are 14500 W/m^2°C and 2250 W/m^2 °C respectively. Determine the overall heat transfer coefficient * Your answerarrow_forward
- A composite plane wall consisting of materials, 1.5-in steel (k = 312 BTU-in/HR.ft2.0F) and 2-in aluminum (k = 1400 BTU-in/HR.ft2.0F), separates a hot gas at Ti = 2000F, hi = 2 BTU/HR.ft2.0F, from cold gas at To = 80 deg F, ho = 5. If the hot fluid is on the aluminum side, find: a) Transmittance, U; b) The heat through 100 sq. ft of the surface under steady state condition and c) The interface temperature at the junction of the metals.arrow_forwardA glass door is used on a fireplace to reduce exfiltration of room air through the chimney. The door, 0.70m high and 1.00m wide, reaches a uniform temperature of 232oC. If the room air temperature is 23oC, estimate the rate of heat transfer to the room air due to convection. Air properties: k=0.0338W/m-K ν=26.4x10-6 m2/s Pr=0.690arrow_forwardb. Consider a large plane wall of thickness L = 0.25 m, thermal conductivity k= 0.77 W/m-K, and surface area A = 15 m. The outside wall is subjected to convection with T1 = 100 °C and h, = 5 W/m? · K and the inside wall is maintained at constant temperatures of T2 = 50 °C, respectively, as shown in Fig. 2. Determine: i. express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, and obtain a relation for the variation of temperature in the wall by solving the differentiai equation 11. -T2arrow_forward
- It is required to perform a heat treatment for gas turbine applications, for them it is required to analyze a sample of the material to be used. The analysis will be performed using the method of a semi-infinite cylinder of stainless steel 12Awith the following thermal properties; (ρ=8700 kg/m3, Cp = 897 J/kg. °C and k = 242 W/m. °C. Of diameter D=12 cm is initially at a uniform temperature of 120 °C. Then the cylinder is placed in a furnace at a constant heat flux of 3800 W/m2, a temperature of 60 °C andh= 170 W/m2. Determine the temperature at the center of the cylinder 3.5 cm from the end surface 6 minutes after placing it in the furnace.arrow_forwardA 3 cm diameter Aluminum sphere (k = 204 W / mK, p = 2700 kg / m² and C = 896 J / Kg.K initially at 175 ° C. It is suddenly immersed in a well stirred fluid at 25 ° C. The temperature of the sphere is lowered to 100 ° C in 42 second, calculate the heat transfer coefficient and the rate of heat transfer.arrow_forwardThe temperature of a gas stream is measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere. Take the junction’s properties as: k of 32 W/m K, density of 8.2 kg/m^3, c of 300 J/Kg K. On its surface, the overall heat transfer coefficient is 200 W/m^2 K. Neglect any conduction loss from the sphere to other parts of the thermocouple. Create a plot of measurement error as a function of time for the thermocouple.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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