A flat wall is formed by connecting layers A, [B and E parallel] and C in series. The thicknesses of A, B and E layers are equal and are 40 mm. There is a uniformly distributed heat generation of 9.0x105 W/m3 in layer A; There is no heat generation in layers B, E and C. The surface of the A surface open to the atmosphere is completely insulated. In order to keep the temperature of the C layer below 75 oC, water at 20 oC is continuously supplied from its outer surface (h=900 W/m2. K) to cool it. a) Calculate the outer surface temperatures of layers A and C and the interface temperatures between the layers. b) Calculate the thickness of layer C. The TB and TE interface temperatures and heat transfer surface areas (AB=AE= A/2) are equal. Thermal conductivities: KA (W/m K) 62 a) b) A A B KB (W/m K) 96 B E kc (W/m K) 160 Yükseklik 2 m Genişlik 80 cm KE (W/m K) 130 Prove whether or not the C-layer temperature changes when the same flat wall (choice a) heat generation is replaced by the B and E parallel layers of the thickness you calculated in a by the same amount. Calculate the interface temperatures of each layer.

A flat wall is formed by connecting layers A, [B and E parallel] and C in series. The thicknesses of A, B and E layers are equal and are 40 mm. There is a uniformly distributed heat generation of 9.0x105 W/m3 in layer A; There is no heat generation in layers B, E and C. The surface of the A surface open to the atmosphere is completely insulated. In order to keep the temperature of the C layer below 75 oC, water at 20 oC is continuously supplied from its outer surface (h=900 W/m2. K) to cool it. a) Calculate the outer surface temperatures of layers A and C and the interface temperatures between the layers. b) Calculate the thickness of layer C. The TB and TE interface temperatures and heat transfer surface areas (AB=AE= A/2) are equal. Thermal conductivities: KA (W/m K) 62 a) b) A A B KB (W/m K) 96 B E kc (W/m K) 160 Yükseklik 2 m Genişlik 80 cm KE (W/m K) 130 Prove whether or not the C-layer temperature changes when the same flat wall (choice a) heat generation is replaced by the B and E parallel layers of the thickness you calculated in a by the same amount. Calculate the interface temperatures of each layer.

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 2.30P: 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is...

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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.
2.30 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 plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.
2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
1.76 Explain a fundamental characteristic that differentiates conduction from convection and radiation.
1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4
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 .
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.
1.77 Explain each in your own words. (a) What is the mode of heat transfer through a large steel plate that has its surfaces at specified temperatures? (b) What are the modes when the temperature on one surface of the steel plate is not specified, but the surface is exposed to a fluid at a specified temperature?
A. Calculate the heat transfer per unit area of a concrete which has a thickness of 300 mm, the temperature on the outer surface is 20 C and the temperature on the inner surface is 5 C. It is known that the heat conductivity of concrete is 0.935 W/mC B. The storage wall has a height of 3 m and a width of 10 m with a thickness of 25 cm. The wall heat conductivity is 0.85 W/mC. The temperature outside is 20 C and inside 4 C. The area of the storage space is: C. A storage room 3 m high and 10 m wide, has a heat conductivity of 0.85 W/mC. The temperature outside is 20 C and inside is 5 C. nThe thickness of the storage chamber is 25 cm. The heat transfer that occurs is:
4. A wall of thickness 10cm conducts heat at rate of 30W/m² when the temperature difference across wall is 10K. What is thermal conductivity (W/mK)
A rectangular electrical heater is attached to a metal sheet. Measurements show the surface temperatures of T1, T2, T3 are 55, 60 and 42 °C, respectively. Both sides of the heater and metal sheet are exposed to an environment where h is equal, and T∞ = 23 °C. Assume K values & you can neglect the contact resistance. a. Find the value of h.b. Find the value of the volumetric heat generation.c. Draw the sketch of the temperature as a function of the direction of heat dissipation.d. What is the exact location of the maximum temperature in the plate-heater assembly?e. If h = 230 W/m2K, q_dot = 1 x 103 W/m3, what is the maximum temperature in the heater?