A heat pack can be modeled as a plane wall of thickness L=2cm. Assume that the pack has a constant thermal conductivity (4.0 W/(m*K)) and constant heat generation (800 W/m3 ) with one side (x=0) maintained at a constant temperature T1 = 80°C and the other side (x=L) cooled by moving air at T∞ = 25°C with a heat transfer coefficient of h = 20 W/(m2K). a. Reduce the heat equation with clearly stated assumptions b. Find the steady-state temperature distribution T(x) in the pack.

A heat pack can be modeled as a plane wall of thickness L=2cm. Assume that the pack has a constant thermal conductivity (4.0 W/(m*K)) and constant heat generation (800 W/m3 ) with one side (x=0) maintained at a constant temperature T1 = 80°C and the other side (x=L) cooled by moving air at T∞ = 25°C with a heat transfer coefficient of h = 20 W/(m2K). a. Reduce the heat equation with clearly stated assumptions b. Find the steady-state temperature distribution T(x) in the pack.

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 1.20P: A high-speed computer is located in a temperature-controlled room at 26C. When the machine is...

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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.
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.
1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.
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.
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.
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.
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.
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.
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.
2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)
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.
Steam at T1 = 320°C and h1 = 60 W/m2·°C flows in a cast iron pipe (k = 80 W/m·°C). The inner and outer diameters are D1 = 5 cm and D2 = 5.5 cm, respectively. The insulation thickness is 3-cm-glass wool insulation with k= 0.05 W/m · °C. The temp. of the surroundings at T2 = 5°C and heat transfer coefficient of h2=18 W/m2·°C. Determine 1. Heat loss from the steam per unit length of the pipe. 2. Determine the temperature at the surfaces of the pipe and the insulation.