Consider a large plane wall of thickness L=0.4 m, thermal conductivity k =1.8 W/m.K, and surface area A=30 m2. The left side of the wall is maintained at a constant temperature of T1= 900C while the right side loses heat by convection to the surrounding air at T∞= 250C with a heat transfer coefficient of h = 24 W/m2.K. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall. (b) Obtain a relation for the variation of temperature in the wall by solving the differential equation and (c) evaluate the rate of heat transfer through the wall. Heat transfer course

Consider a large plane wall of thickness L=0.4 m, thermal conductivity k =1.8 W/m.K, and surface area A=30 m2. The left side of the wall is maintained at a constant temperature of T1= 900C while the right side loses heat by convection to the surrounding air at T∞= 250C with a heat transfer coefficient of h = 24 W/m2.K. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall. (b) Obtain a relation for the variation of temperature in the wall by solving the differential equation and (c) evaluate the rate of heat transfer through the wall. Heat transfer course

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.19P: 1.19 A cryogenic fluid is stored in a 0.3-m-diameter spherical container is still air. If the...

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2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.
1.19 A cryogenic fluid is stored in a 0.3-m-diameter spherical container is still air. If the convection heat transfer coefficient between the outer surface of the container and the air is 6.8 , the temperature of the air is 27°C, and the temperature of the surface of the sphere is –183°C, determine the rate of heat transfer by convection.
3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.
1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.
Heat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70C, determine the temperature of the cooler surface.
A cooling system is to be designed for a food storage warehouse for keeping perishable foods cool prior to transportation to grocery stores. The warehouse has an effective surface area of 1860 m2 exposed to an ambient air temperature of 32C. The warehouse wall insulation (k=0.17W/(mK)) is 7.5 cm thick. Determine the rate at which heat must be removed (W) from the warehouse to maintain the food at 4C.
Steam at 320°C flows in a stainless steel pipe (k = 15 W/m-°C) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation (k = 0.038 W/m-°C). Heat is lost to the surroundings at 5°C by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of 15Wm2-°C. Taking the heat transfer coefficient inside the pipe to be 80 W/m2-°C, determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation.
Consider a steam pipe of length 15 ft, inner radius 2 in., outer radius 2.4 in., and thermal conductivity 7.2 Btu/hr-ft-°F. Steam is flowing through the pipe at an average temperature of 250°F, and the average convection heat transfer coefficient on the inner surface is given to be 1.25 Btu/hr-ft2-°F. If the average temperature on the outer surfaces of the pipe is 160°F, determine the rate of heat loss from the steam through the pipe. ANSWER:______Btu/hr
Steam at T∞ 1 = 320°C flows in a cast iron pipe (k = 80 W/m · °C) whose inner and outer diameters are D1 = 5 cm and D2 = 5.5 cm, respectively (Figure Q2b). The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/m · °C. Heat is lost to the surroundings at T2 = 5°C by natural convection and radiation, with a combined heat transfer coefficient of h2 = 18 W/m2 · °C. Taking the heat transfer coefficient inside the pipe to be h1= 60 W/m2 · °C, determine; i) the rate of heat loss from the steam per unit length of the pipe; and ii) the temperature drops across the pipe shell and the insulation.
Steam at 280° C flows in a stainless steel pipe (k = 15 W/m⋅K) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation (k = 0.038 W/m⋅K). Heat is lost to the surroundings at 5° C by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of 22 W/ m2⋅K.Taking the heat transfer coefficient inside the pipe to be 80 W/ m2⋅K.Determine the rate of heat loss from the steam per unit length of the pipe and Determine the temperature decrease between the inner pipe surface and the outer insulation surface.
Steam at To1= 320°C flows through a cast iron pipe (k = 80 W/mK) with inner and outer diameters of D1= 5cm and D2 = 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/mk(Figure Q2). Heat is lost to the surroundings (To2 = 5°C) by natural convection and radiation, with a combinedheat transfer coefficient of h2 = 18 W/m2.K.(a) Taking the heat transfer coefficient inside the pipe to be h1 = 60 W/m2 K, Calculate the rate of heat lossfrom steam per unit length of pipe.(b) Calculate the temperature differences between the pipe shell and the insulation. Someone comments that a microwave oven can be viewed as a conventional oven with zero convectionresistance at the surface of the food. Is this a correct statement? Discuss the reason.
10 m long pipe is being used to deliver steam through a processing plant. The inner radius of the pipe is r1 = 6 cm and the thickness of the pipe is 2 cm. Thermal conductivity k = 8 W/m⋅K and the average temperature steam flowing through the pipe is 160°C, the average convection heat transfer coefficient on the inner surface is given to be h = 20 W/m2⋅K. If the average temperature on the outer surfaces of the pipe is T2 = 70°C, (a) express the differential equation and the boundary conditions for steady operating conditions, (b) determine a relation for the variation of temperature in the pipe, and (c) evaluate the rate of heat loss (heat of conduction) from the steam through the pipe.