A 2-mm diameter electric wire has a 1 mm-thick electrical insulation with a k of 0.1 W/m K. The overall heat transfer coefficient on the outside of the wire is 10 W/m^2 K. a. Determine the critical radius and discuss what will happen to the heat transfer rate if the thickness of the insulation increases to 2 mm b. Sometimes the insulation layer is not put on the wire properly so there is a small gap between them. That creates a “contact resistance” with a value of 5e^-4 (W/m2 K)^-1 Would this change the critical radius?

A 2-mm diameter electric wire has a 1 mm-thick electrical insulation with a k of 0.1 W/m K. The overall heat transfer coefficient on the outside of the wire is 10 W/m^2 K. a. Determine the critical radius and discuss what will happen to the heat transfer rate if the thickness of the insulation increases to 2 mm b. Sometimes the insulation layer is not put on the wire properly so there is a small gap between them. That creates a “contact resistance” with a value of 5e^-4 (W/m2 K)^-1 Would this change the critical radius?

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...

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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.
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.
Determine the rate of heat transfer per meter length to a light oil flowing through a 2.5-cm-ID, 60-cm-long copper tube at a velocity of 0.03 m/s. The oil enters the tube at 16C, and the tube is heated by steam condensing on its outer surface at atmospheric pressure with a heat transfer coefficient of 11.3 kW/m K. The properties of the oil at various temperatures are listed in the following table: Temperature, T(C) 15 30 40 65 100 (kg/m3) 912 912 896 880 864 c(kJ/kgK) 1.80 1.84 1.925 2.0 2.135 k(W/mK) 0.133 0.133 0.131 0.129 0.128 (kg/ms) 0.089 0.0414 0.023 0.00786 0.0033 Pr 1204 573 338 122 55
Heat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70C, determine the temperature of the cooler surface.
2.46 The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of with a heat transfer coefficient of . On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular steel fins 0.5 cm thick and 1.25 cm high as shown in the accompanying sketch. The fins are 3 m long and the heat transfer coefficient on the gas side is . Assuming that the thermal resistance of the wall is negligible, determine the rate of heat transfer if the overall temperature difference is .
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.
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?
A cooling system is to be designed for a food storage warehouse for keeping perishable foods cool prior to transportation to grocery stores. The warehouse has an effective surface area of 1860 m2 exposed to an ambient air temperature of 32C. The warehouse wall insulation (k=0.17W/(mK)) is 7.5 cm thick. Determine the rate at which heat must be removed (W) from the warehouse to maintain the food at 4C.
A conductor with a diameter D= 0.8 cm, covered by an electric current, passes through an environment at T∞= 30 °C with convective heat transfer coefficient h= 120 W/(m² °C). The conductor temperature must be maintained at Ti= 130 °C. Calculate the rate of heat loss per meter of conductor length with:a) the uncoated conductor;b) the conductor covered with bakelite [k = 1.2 W/(m°C)] with a radius corresponding to the critical insulation radius.
Consider a stainless steel spoon (k = 15 W/m·K) partially immersed in boiling water at 95°C in a kitchen at 25°C. The handle of the spoon has a cross section of 0.2cm x 1.2 cm, and extends 18 cm in the air from the free surface of the water. If the heat transfer coefficient at the exposed surfaces of the spoon handle is 15 W/m2·°C, determine the temperature difference across the exposed surface of the spoon handle. State your assumptions.
A refrigerator door of area 0.6 sq.m consists of 25 mm of insulation on top of a thin metal sheet. The film heat transfer coefficients inside and outside the refrigerator are 10.0 and 15.0 W m-2K -1 , respectively, and the thermal conductivity of the insulation is 0.25 W m-1K -1 . If the working temperature of the refrigerator is 0oC and ambient temperature is 20oC, determine the heat flow through the refrigerator door and the temperature of the inside surface of the door.
The walls of the refrigerated storage room are 10 m long and 3 m high and constructed with 90 mm concrete blocks (k = 0.935 W / [m ° C]) and 8 cm fiber insulation board (k = 0.048 W). / [m ° C]). The cold room temperature is -10 ° C and the convective heat transfer coefficient is 40 W / (m² K); the outside air temperature is 30 ° C with the outer wall surface convection heat transfer coefficient of 10 W / (m² K). Calculate the overall heat transfer coefficient. Overall heat transfer coefficient = Answer W / (m² K).