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A support rod
(a) Using an appropriate numerical technique, determine the thermal response of the rod to the convective heating. Plot the midspan temperature as a function of elapsed time. Using an appropriate analytical model of the rod, determine the steady-state temperature distribution, and compare the result with that obtained numerically for very long elapsed times.
(b) After the rod has reached steady-state conditions, the flow of hot gases is suddenly terminated, and the rod cools by free convection to ambient air at
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Chapter 3 Solutions
Introduction to Heat Transfer
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- 2. The initial temperature of the hot coffee cup is T(0) = 175°F. The cup is placed in a room temperature of T... = 70°F. The temperature T(t) of the coffee at time t can be approximated by Newton's law of cooling. ·+hT(t)=hT∞, where h is the convective heat transfer coefficient. dT dt (a) Find the transient solution, Ttran(t). (b) Find the steady-state solution. Tss(t). (c) Determine the total solution T(t). (d) Would increasing the value of h increase or decrease the time when the temperature of coffee reaches the room temp? (e) Would a lower or higher value of h be best for a cup of coffee?arrow_forwardAn array of 190 electrical components, each dissipating P = 35 W, are attached to the bottom surface of a square copper plate. The length of the edge of the square plate is L= 0.1 m. All of the energy dissipated in the electrical components is transferred to water flowing over the top surface of the copper plate. The water flow over the plate in a direction that is parallel to the edge of the plate. A proturbence at the leading edge of the plate acts to trip the bounary layer into turbulent flow. The plate may be assumed to be isothermal since the thermal conductivity of copper is so high. The water velocity and temperature far from the plate are u» = 2.3 m/s and To = 22 °C. The water's thermophysical properties (for application in correlations for the Nusselt number) may be approximated as v = 0.96×10-6 m2/s, kf = 0.62 W/m-K, and Pr = 5.2. What is the temperature of the copper plate in °C?arrow_forwardA steel ball with a diameter of 10 mm is taken suddenly from a medium at a temperature of 25ºc and annealed for 20 minutes in the furnace host at a temperature of 800ºc. How many ° C is the temperature of the steel ball when it comes out of the oven? (ρ(steel) = 7854 kg / m3, C(steel) = 434 J / kgK, h(air) = 10 W / m2K and h(oil) =100 W / m2K) a. 705.65 b. 662.90 c. 706.25 d. 750.81 e. 750.20arrow_forward
- Solve for the latent heat of water at Tw = 28C(and. λw = 2435 kJ/kg)arrow_forwardA certain gas was produced as a product of a decomposition reaction in a reactor vessel. The reaction generated a certain amount of force that allowed the gas to move at 35 m/s. The diatomic product gas (gamma = 1.36) will be transported adiabatically in a commercial steel pipe with a diameter of 1 inch. If the exit of the reactor and start of the pipe has a same pressure of 6 atm abs. and temperature of 120 degrees Celsius. The molecular weight of the gas is 70.91 kg/kgmol. 2. What is the Mach No. at the entry of the pipe? 0.36 0.41 0.14 none of the given 0.25 0.52 0.63arrow_forwardA steel tube with 5 cm ID, 7.6 cm OD and k = 15 W/m °C is covered with an insulative covering of thickness 2 cm and k = 0.2 W/m °C. A hot gas at 330 °C with h= 400 W/m² °C flows inside the tube. The outer surface of the insulation is exposed to cooler air at 30 °C with h = 60 W²/m °C. Calculate the heat loss from the tube to the air for 10 m of the tube and the temperature drops resulting from the thermal resistances of the hot gas flow, the steel tube, the insulation layer, and the outside air. (Ans: q/L=7451.72 W; AT₁=11.859 °C; AT₂=3.31 °C; AT₁=250.75 °C; AT₁= 34.07 °C)arrow_forward
- 2. A large sheet of glass 2” thick is initially at 300oF throughout. It is plunged into a stream of running water having a temperature of 60oF. How long will it take to cool the glass to an average temperature of 100oF. For glass k = 0.40BTU/ft-hroF, ρ = 155 lb/ft3 and Cp = 0.20 BTU/lboF.arrow_forwardA compressed air tank is designed to contain 50 standard cubic feet of air when Ölled to a gaugepressure of 200 atm at an ambient temperature of 70 F. Calculate the interior volume of thetank. One standard cubic foot of air occupies one cubic foot at standard temperature and pressure(T = 59 F and p = 2116 lb/ft2).arrow_forwardThree liquids given the following properties are poured into the cylindrical container with a diameter of 3 meters and a height of 6 meters. First fluid poured: sg = 1.0, V = 17.6715 m^3 Second fluid poured: sg = 0.81, V = 10.6029 m^3 Third fluid poured: sg = 2.94 , V = 7.0686 m^3 Assuming that the container is closed after pouring the fluids and the stable state in the container is reached, determine the pressure at the height of 4-m from the bottom of the tank Select the correct response 7.9461 kPa 12.8084 kPa 28.8414 kPa 9.8100 kPa Assuming seawater to have a constant specific weight of 10.05 kN/m^3, what is the absolute pressure at a depth of 10 km. Select the correct response(s): 939 atm 339 atm 993 atm 399 atmarrow_forward
- When a long section of a compressed air line passes through the outdoors, it is observed that the moisture in the compressed air freezes in cold weather, disrupting and even completely blocking the air flow in the pipe. To avoid this problem, the outer surface of the pipe is wrapped with electric strip heaters and then insulated. . Consider a compressed air pipe of length L = 6 m, inner ra- dius r₁ = 3.7 cm, outer radius r₂ = 4.0 cm, and thermal con- ductivity k = 14 W/m - °C equipped with a 300-W strip heater. Air is flowing through the pipe at an average temperature of -10°C, and the average convection heat transfer coefficient on the inner surface is h = 30 W/m². °C. Assuming 15 percent of the heat generated in the strip heater is lost through the insula- tion, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the pipe, (b) obtain a relation for the variation of temperature in the pipe material by solving the…arrow_forwardIn secondsarrow_forwardA 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_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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