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. EXAMPLE 1Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1 m,and thermal conductivity k = 30 W/m - °C is filled with iced water at 0°C.The container is gaining heat by convection from the surrounding air at 7= 25°C with a heat transfer coefficient of h= 18 W/m2 - °C. Assumingthe inner surface temperature of the container to be 0°C,a) express the differential equation and the boundary conditions forsteady one-dimensional heat conduction through the containerb) obtain a relation for the variation of temperature in the container bysolving the differential equationc) evaluate the rate of heat gain to the iced water.

Given: The inner radius of container, r1 = 2 m The outer radius oof container, r2 = 2.1 m The…

EXAMPLE 1 Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1m, and thermal conductivity k= 30 W/m - °C is filled with iced water at 0°C. The container is gaining heat by convection from the surrounding air at T - 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, a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container b) obtain a relation for the variation of temperature in the container by solving the differential equation c) evaluate the rate of heat gain to the iced water.

EXAMPLE 1 Aspherical container of inner radius rl = 2 m, outer radius r2 = 2.1m, and thermal conductivity k= 30 W/m - °C is filled with iced water at 0°C. The container is gaining heat by convection from the surrounding air at T - 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, a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container b) obtain a relation for the variation of temperature in the container by solving the differential equation c) evaluate the rate of heat gain to the iced water.

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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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.
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.
Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinder
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.
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.
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?
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 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.
/ 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.
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.
A:Find the amount of heat transferred through an iron fin of thickness 5 mm, length 10 cm and width 100 cm. Also determine the temperature difference e at the tip of the fin at: 1- adiabatic tip, 2-heat convection at the tip. Assuming the atmospheric temperature of 28°C K=50 w/mK, h=10 w/m’K, O,=80°C. B-Why is the dimensional heat flow assumption important in the analysis of fins problems? C- Why are the annular fins more efficiency than others?.
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.