Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 2.3 W/m. °C, and surface area A = 20 m². The left side of the wall is maintained at a constant tem- perature of T₁ = 80°C while the right side loses heat by con- vection to the surrounding air at T = 15°C with a heat transfer coefficient of h = 24 W/m². °C. 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 trans- fer through the wall. Answer: (c) 6030 W

Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 2.3 W/m. °C, and surface area A = 20 m². The left side of the wall is maintained at a constant tem- perature of T₁ = 80°C while the right side loses heat by con- vection to the surrounding air at T = 15°C with a heat transfer coefficient of h = 24 W/m². °C. 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 trans- fer through the wall. Answer: (c) 6030 W

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.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.38P: 2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from...

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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.
/ Hot square plate (1 m ×1 m) is to be cooled by attaching aluminum circular pin fins (D=0.25 cm, L= 3 cm) distributed with distance 0.6 cm as illustrated in Figs.(1-a) & (1-b). If the fin base temperature is 100°C, cooling air temperature is 30°C and h= 35 W/m. °C. Determine the total rate of heat transfer from the finned plate and the effectiveness of the fins? Assume k= 237 W/m.°C and nr=tanh mL/ mL.
Consider a steam pipe of length L = 26 m, inner radius ? = 5 cm, outer radius ? = 7 cm, and thermal conductivity k = 25 W/m·K, as shown in Fig. The inner and outer surfaces of the pipearemaintainedataveragetemperaturesof? =120°Cand? =50°C,respectively.Obtain a general relation for the temperature distribution inside the pipe under steady conditions and determine the rate of heat loss from the steam through the pipe.
Liquid flows in a metal pipe with an inner diameter of D1 = 20 mm and an outer diameter of D2 = 30 mm. The thermal conductivity of the pipe wall is 10 W/m⋅K. The inner surface of the pipe is coated with a thin polyvinylidene chloride (PVDC) lining. Along a length of 95 cm, the pipe outer surface is exposed to convection heat transfer with hot gas, at T∞ = 95° C and h = 6 W/m2 ⋅K, and thermal radiation with a surrounding at Tsurr = 95° C. The emissivity at the pipe outer surface is 0.3. The liquid flowing inside the pipe has a convection heat transfer coefficient of 52 W/m2⋅K. If the outer surface of the pipe is at 86° C, determine the temperature at the PVDC lining and the temperature of the liquid.The ASME Code for Process Piping (ASME B31.3-2014, A323) recommends a maximum temperature for PVDC lining to be 81° C. Does the PVDC lining comply with the recommendation of the code?
A 6-m-long 2-kW electrical resistance wire is made of 0.2-cm-diameter stainless steel(? = 15.1 W/mK). The resistance wire operates in an environment at 30°C with a heattransfer coefficient of 140 W/m2K at the outer surface. Determine the maximumtemperature in the wire;(a) by using the applicable relations.(b) by setting up the proper differential equation and solving it.
A steel duct whose internal diameter is 5.0 cm, and external diameter is 7.6 cm and thermal conductivity is: k = 15.0 (W/(m ºC)) is covered with an insulating material whose thickness is 2.0 cm and of thermal conductivity k = 0.2 (W/(m ºC)). A hot gas flows through the interior of the duct at a temperature of 330.0 ºC that generates a heat transfer coefficient by forced convection h=400.0 (W/(m^2 · ºC)). The outer surface of the insulating layer is exposed to air whose temperature is 30.0 ºC with forced convection heat transfer surface h = 60.0 (W/(m^2 · °C)). As a process engineer and in charge of company operations, you have been asked to: i. Determine the heat loss experienced by the pipe along 10.0 m.ii. The temperature drops that are generated in the different thermal resistances of the system. That is, on the air side, the duct wall and on the hot gas side.
On a multi-layered square wall, the thermal resistance of the first layer is 0.005 ° C / W, the resistance of the second layer is 0.2 ° C / W, and the third layer is 0.1 ° C / W. The overall temperature gradient in the wall is multilayered from one side. to the other side is 70 ° C. a. Determine the heat flux through the walls. = Answerwatts / m2. b. If the thermal resistance of the second layer is changed to 0.4 ° C / W, what is the effect in% on heat flux, assuming the temperature gradient remains the same? = AnswerAnswer%.
7.A 5-m-internal-diameter spherical tank made of 1.5-cm-thick stainless steel (k =15 W/m · °C) is used tostore iced water at 0°C. The tank is located in a room whose temperature is 30°C. The walls of the room are also at 30°C. The heat transfer between the outer surface of the tank and the surroundings is by natural convection. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are 80 W/m 2 · °C and 10 W/m 2 · °C, respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 24-h period. The heat offusion of water at atmospheric pressure is hif = 333.7 kJ/kg.
A cylindrical body having 10 cm diameter and lenth of 30 cm passes through a heat treatment furnace which is 6 m in length. The body must reach a temperature of 800°C before it comes out of the furnace. The furnace gas is at 1250°C and body initial temperature is 90°C. How much time it will take to attain the required temperature ? Take h = 100 W/m² °C. Take K(steel) = 40 W/m°C and a (thermal diffusivity of steel) = 1.16 x 10-5 m²/s.
A 10-cm diameter pipe is covered by 2 layers of lagging. The insidelayer is 4 cm thick and has a coefficient of thermal conductivity of 0.08W/m-K. The outside layer is 3cm thick and has a coefficient of thermalconductivity of 0.15 W/m-K. The steam main conveys steam apressure of 1.7 MPa with 25 C superheat. The outside temperature ofthe lagging is 27 C. If the steam main is 30 m long, determine theinterface temperature of the lagging and overall coefficient of heattransfer based on outside area.
A freezer with dimensions of 4 m wide, 6 m long and 3 m high is under construction. The walls and ceiling are composed of 1.7 mm stainless steel (k = 15 W / [m ° C]), 15 cm thick foam insulation (k = 0.036 W / [m ° C]), specific thickness of corkboard (k = 0.043 W / [m ° C]), and 1.27 cm thick wood (k = 0.104 W / [m ° C]). The inside of the freezer is maintained at -40 ° C. The ambient air outside the freezer is 32 ° C. The convective heat transfer coefficient is 5 W / (m K) on wooden walls and 2 W / (m² K) on stainless steel surfaces. If the outside air has a dew point of 29 ° C, calculate the thickness of the corkboard insulation that will prevent moisture condensation on the outer walls of the freezer. Calculate the heat transfer rate through the walls and ceiling of this freezer. Ignore heat transfer from floors and corners of buildings. a. Thickness of corkboard insulation = Answer cm. b. Heat transfer rate through walls and ceiling = Answer watts.
EXAMPLE 1| Aspherical container of inner radius r1 =2 m, outer radius 2= 2.1 m, ‘and thermal conductivity k=30 Wim - °C is illed with iced water at 0°C e container is gaining heat by convection from the surrounding air at 7 = 25°C with a heat transfer coeflicient of h = 18 W/m2 - °C. Assuming the inner surface temperature of the container to be 0°C, ) express the differential equation and the houndary conditions for steady one-dimensional heat conduction through the container ) obtain a relation for the variation of temperature in the cantainer by solving the differential equation €) evaluate the rate of heat gain 10 the iced water.