determine the temperature distribution along the fin surface. The thermal conductivity of theheat from a small motorcycle engine. If the average engine surface temperature is 112°C,Exercise 4.6.4 A circular fin of inner diameter 20 cm and outer diameter of 26 cm transfers124STEADY STATE HEAT CONDUCTION IN ONE DIMENSIONn material is 21 W/m C and the convective heat transfer coefficient between the fin andthe atmosphere is 120 W/m2 C. Assume an atmospheric temperature of 32 C.Exercise 4.6.5 Consider a composite wall consisting of four different materials as shownin Figure 4.16. Assuming a one-dimensional heat flow, determine the heat flow through thecomposite slab and the interfacial temperatures. kA = 200 W/m °C, kB = 20 W/m°C andkc = 40 W/m °C and kp =60 W/m °C. Assume that the areas of the surfaces B anda C areequal to 0.1 m2.Exercise 4.6.6 Consider a composite wall, which has one linearly varying cross-sectionalarea as shown in Figure 4.17. Determine the heat flow and interfacial temperatures.Thickness = 10 cm, kA = 200 W/m C, kg = 20 W/m C and kc = 40 W/hm C.Exercise 4.6.7 A plane wall (k = 20 W/m C) of thickness 40 cm has its outer surfacesmaintained at 30 C. If there is uniform internal heat generation of 0.2 MW/m' in the planewall, determine the temperature distribution in the plane wall. Solve this problem using(a) four linear elements (b) one quadratic element and (c) one modified quadratic elementwith only two nodes. Compare the results with analytical solutions.Exercise 4.6.8 A plane wall (k = 10 W/m C) of thickness 50 cm has its exterior surfacesubiected to a convection environment of 30 C with a surface heat transfer coefficient of600 W/n? C. Determine the temperature distribution in the plane wall using (a) four lin-ear elements (b) one quadratic element and (c) one modified quadratic element with onlyO nodes. Compare the results with the analytical solution. If the heat transfer coefficientincreases to 10,000 W/m C, what happens to the temperature of the exterior surface2220 °CArea = 0.2 m22 cm20 °C5 cm3 cmFigure 4.16 A composite wall

Since we are allowed to answer one question at a time. We’ll answer the first question since the…

heat from a small motorcycle engine. If the average engine surface temperature is 112 C, Exercise 4.6.4 A circular fin of inner diameter 20 cm and outer diameter of 26 cm transfers determine the temperature distribution along the fin surface. The thermal conductivity of the ATE HEAT Cmine the temperature distribution along the fin surface. The thermal conductivity of the Jin material is 21 W/m C and the convective heat transfer coefficient between the fin and the atmosphere is 120 W/m2 C. Assume an atmospheric temperature of 32 C.

heat from a small motorcycle engine. If the average engine surface temperature is 112 C, Exercise 4.6.4 A circular fin of inner diameter 20 cm and outer diameter of 26 cm transfers determine the temperature distribution along the fin surface. The thermal conductivity of the ATE HEAT Cmine the temperature distribution along the fin surface. The thermal conductivity of the Jin material is 21 W/m C and the convective heat transfer coefficient between the fin and the atmosphere is 120 W/m2 C. Assume an atmospheric temperature of 32 C.

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 2.21P

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1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.
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
A high-speed computer is located in a temperature-controlled room at 26C. When the machine is operating, its internal heat generation rate is estimated to be 800 W. The external surface temperature of the computer is to be maintained below 85C. The heat transfer coefficient for the surface of the computer is estimated to be 10W/m2K. What surface area would be necessary to assure safe operation of this machine? Comment on ways to reduce this area.
2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .
An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70C. It is to be cooled in 25C air by attaching aluminum fins with a total surface area of 12cm2. The convection heat transfer coefficient between the fins and the air is 20W/m2K. Estimate the operating temperature when the fins are attached in such a way that (a) there is a contact resistance of approximately 50 K/W between the surface of the device and the fin array and (b) there is no contact resistance (in this case, the construction of the device is more expensive). Comment on the design options.
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.
One end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?
2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.
A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.
A steam pipe 200 mm in diameter passes through a large basement room. The temperature of the pipe wall is 500C, while that of the ambient air in the room is 20C. Determine the heat transfer rate by convection and radiation per unit length of steam pipe if the emissivity of the pipe surface is 0.8 and the natural convection heat transfer coefficient has been determined to be 10 W/m2K.
3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?