1. Consider the base plate of a 800-W household iron with a thickness of L = 0.6 cm, base area of A =160 cm2, and thermal conductivity of k = 20 W/m - °C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (c) evaluate the inner surface temperature. Base plate 85°C

1. Consider the base plate of a 800-W household iron with a thickness of L = 0.6 cm, base area of A =160 cm2, and thermal conductivity of k = 20 W/m - °C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (c) evaluate the inner surface temperature. Base plate 85°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 2.32P

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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.)
2.55 A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square concrete block. If the outside temperature of the concrete is 25oC and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine temperatures at the outer surface and at the center of the cable.
1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.
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.
2.34 Show that the temperature distribution in a sphere of radius . made of a homogeneous material in which energy is released at a uniform rate per unit volume , is
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.
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?
2. A steel plate of k=50w/mk and thickness 10cm passes a heat flux by conduction of 25kW/m² . If the temperature of hot surface of plate is 100C, then what is the temperature of the cooler side of plate?
Q1) Consider the base plate of a 800-W household iron having a thickness of L=0.6 cm, base area of A=160 cm2, and thermal conductivity of k3120 W/m-°C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron and taking the nodal spacing to be 0.2 cm, (a) obtain the finite difference formulation for the nodes and (b) determine the inner surface temperature of the plate by solving those equations. Insulation Resistance heater, 800 W 85°C Base plate Ar= 0.2 cm 160 cm? 11111111111I D00000000000000000000000
Example 10: Consider a long resistance wire of radius r1 = 0.2 cm and thermal conductivity kwire = 15 W/m·°C in which heat is generated uniformly as a result of resistance heating at a constant rate of g = 50 W/cm3. The wire is embedded in a 0.5-cm-thick layer of ceramic whose thermal conductivity is kceramic = 1.2 W/m·°C. If the outer surface temperature of the ceramic layer is measured to be Ts = 45°C, determine the temperatures at the center of the resistance wire and the interface of the wire and the ceramic layer under steady conditions.
Q2. Steam pumped through a long- insulated pipe at a temperature of T= 500 K and provides a convection coefficient of h, = 100 W/m?K at the inner surface of the pipe. The inner and outer radius of the pipe and insulation material are r1 = 10, r2 = 12 and r3 = 17 cm, respectively. The thermal conductivity of the pipe is 100 W/mK. The insulation material is glass fiber and its outer surface is exposed to ambient air at 300 K. If the ambient air provides a convection coefficient of ho = 20 Internal flow Ambient air W/m?K, determine the followings: a. What are the thermal resistance coefficients for convections and conductions b. What is the heat transfer rate per unit length of the pipe c. If the pipe is 30 m long, what will be total heat transfer rate from the pipe. t00 noints)