4. A 2-mm-diameter and 10-m-long electric wire is tightly wrapped with a 1-mm-thick plastic cover whose thermal conductivity is k = 0.15 W/m °C. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire is exposed to a medium at T = 30°C with a heat transfer coefficient of h = 24 W/m².°C, determine the temperature at the interface of the wire and the plastic cover in steady operation. Also determine if doubling the thickness of the plastic cover will increase or decrease this interface temperature. Tair = 30°C Electrical wire Insulation 10 m

4. A 2-mm-diameter and 10-m-long electric wire is tightly wrapped with a 1-mm-thick plastic cover whose thermal conductivity is k = 0.15 W/m °C. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire is exposed to a medium at T = 30°C with a heat transfer coefficient of h = 24 W/m².°C, determine the temperature at the interface of the wire and the plastic cover in steady operation. Also determine if doubling the thickness of the plastic cover will increase or decrease this interface temperature. Tair = 30°C Electrical wire Insulation 10 m

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.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.16P: 3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer...

See similar textbooks

Similar questions

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.
1.37 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.
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.
1.1 On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to temperature of –5°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the heat loss through the wall, which is 10-m long and 3-m high. Problem 1.1
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 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.
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.
2.29 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 .
Estimate the rate of heat loss per unit length from a 5-cm ID, 6-cm OD steel pipe covered with high-temperature insulation having a thermal conductivity of 0.11 W/(m K) and a thickness of 1.2 cm. Steam flows in the pipe. It has a quality of 99% and is at 150C. The unit thermal resistance at the inner wall is 0.0026(m2K)/W the heat transfer coefficient at the outer surface is 17W/(m2K) and the ambient temperature is 16C.
A 90-amp electric current is flowing through a 6-mm diameter lead wire. The thermal conductivity of the lead is k= 32 W/m K and the electrical resistance per unit length of the wire is R' = 0.0073 /m. The outer surface of the lead wire is exposed to 40°C air with a convection heat transfer coefficient of h=12 W/m².K. Find the temperature at the center of the lead wire.
Heat is produced in a long resistance wire q.u= 1.5 W/cm3. The radius of the wire is given as r1=0.3 cm and the thermal conductivity coefficient as ksteel=18 W/m.K. In addition, the wire is covered with a 0.4 cm thick plastic layer with a thermal conductivity coefficient of kplastic = 1.8 W/m.K. The outer surface of the plastic layer loses heat with an average heat transfer coefficient of h=14/W/m2K and by convection to the ambient air at T∞ =250 C. Considering the interface temperature as T1 and accepting the heat transfer as one-dimensional;
Problems within the wall is T(x) = a(L- ) +b where a = 10°C/m2 and b 30°C, what is the thermal con- ductivity of the wall? What is the value of the convec- tion heat transfer coefficient, h? 2.11 Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductiv- ity k 50 W/m K and a thickness L = 0.25 m, with no internal heat generation. 2. T2 T1 L Determine the heat flux and the unknown quantity for each case and sketch the temperature distribution, indi- cating the direction of the heat flux. 2 Case TC) dTldx (K/m) T2(°C) 1 50 -20 2 -30 - 10 3 70 160 4 40 -80 5 30 200