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Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate
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Introduction to Heat Transfer
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- Find the steady-state temperature u(r,θ) in a quarter semi-circular plate of radius r=5 subject to the heat equation in polar coordinatesarrow_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_forwardAt a temperature of 21.4°C the hole in a steel plate has an area of 8.80 x 10- m2. You heat the plate until the area of the hole increases to 8.97 x 10- m2, which allows a steel rod to just slip through this hole. What is the final temperature of the plate? The coefficient of linear expansion of steel is 12 × 10-0/°C.arrow_forward
- The two-dimensional solid shown in Figure P3-64 generates heat internally at the rate of 90 MW/m3. Using the numerical method calculate the steady-state nodal temper- atures for k= 20 W/m.°C. %3D Figure P3-64 h = 100 W/m2. °C !3! T = 20°C 2 T 100°C 5 7 8 9. 10 11 12 Insulated Ax = Ay = 1 cm k= 20 W/m • °C 4 = 90 MW/m3 %3D Insulatedarrow_forwardA 0.025-mm-diameter stainless steel wire having k = 16W / m . °C is connected to two electrodes. The length of the wire is 80 cm and it is exposed to a convection environment at 20 degrees * C with h=500 W/m^ 2 . C C. A voltage is impressed on the wire that produces temperatures at each electrode of 200 degrees * C . Determine the total heat lost by the wire.arrow_forwardThe initial state of 1.00 mol of a dilute gas is P1 = 3.00 atm, V1 = 1.00 L, and Eint1 = 456 J and its final state is ?2 = 2.00 atm, V2 = 3.00 L, and Eint 2 = 912 J. The gas is heated and is allowed to expand such that it follows a single straight-line path on a PV diagram from its initial state to its final state. (a) Illustrate this process on a PV diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.arrow_forward
- A 30.14 g stainless steel ball bearing at 117.82°C is placed in a constant-pressure calorimeter containing 120 mL of water at 18.44°C. If the specific heat of the ball bearing is 0.474 J/g-°C, calculate the final temperature of the water. Assume the calorimeter to have negligible heat capacity. Specific heat of water is 4.184 J/g-°C .arrow_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= 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_forward
- A slab of iron with temperature, Tz=48 deg C is used to heat a flat glass plate that has an initial temperature of Tgi=18 deg C. Assuming no heat is lost to the environment, and the masses are m-0.49 kg for the slab and m;= 310 g for the plate, what is the amount of heat transferred when the two have reached equal temperature? Assume cF0.11 kcal/kg-deg C for iron and cg=0.20 kcal/kg- deg C for glass. Select the correct response: 32 kcal 53 kcal 860 cal 320 kcalarrow_forwardConsider two coffee cups A and B. Small coffee cup heaters are placed in cups A and B and heat is transferred to keep cup A at 45°C and cup B at 35°C. Room temperature is 25°C. The cups contain the same amount of water (100 grams). Which answer best describes the rates at which heat must be transferred to maintain the temperatures described above?: * A. Cup A will require heat at about five times the rate of B. B. Cup A will require heat at about twice the rate of B. C. Cup A will require heat at a slightly faster rate than B. D. Both cups will require heat at the same rate.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_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning