A 1 m x 1 m plate made of brass (k = 70 W/mK) with a thickness of 5 cm is used a heating element (see Fig. Q3). Heat is generated uniformly within the plate though a mesh of thin electrical wires. The total power of the heating elements is 1900 W. To test this plate, it is hung vertically in a room and the surface at x = 0 m is kept insulated. Measurements from a thermal camera show that the temperature on the surface at x = 5 cm is 250°C. Brass plate T = 250°C L =5 cm Fig. Q3: A hot vertical brass plate. a) Starting from the general conduction equation, express the simplified differential equation and state the boundary conditions for heat conduction through the plate. b) Obtain a relation for the variation in temperature through the thickness of the plate by solving the differential equation. c) Calculate the temperature on the insulated surface side of the plate.

A 1 m x 1 m plate made of brass (k = 70 W/mK) with a thickness of 5 cm is used a heating element (see Fig. Q3). Heat is generated uniformly within the plate though a mesh of thin electrical wires. The total power of the heating elements is 1900 W. To test this plate, it is hung vertically in a room and the surface at x = 0 m is kept insulated. Measurements from a thermal camera show that the temperature on the surface at x = 5 cm is 250°C. Brass plate T = 250°C L =5 cm Fig. Q3: A hot vertical brass plate. a) Starting from the general conduction equation, express the simplified differential equation and state the boundary conditions for heat conduction through the plate. b) Obtain a relation for the variation in temperature through the thickness of the plate by solving the differential equation. c) Calculate the temperature on the insulated surface side of the plate.

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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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?
2.55 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.
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.
1.37 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.
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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.
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