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13.72 An opaque, diffuse, gray (200 mm × 200 mm) plate with an emissivity of o.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25 W/m² . K and to large surroundings. The air and surroundings are each at 300 K.

13.72 An opaque, diffuse, gray (200 mm × 200 mm) plate with an emissivity of o.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25 W/m² . K and to large surroundings. The air and surroundings are each at 300 K.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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13.72 An opaque, diffuse, gray (200 mm x 200 mm) plate with an emissivity of o.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25 W/m² . K and to large surroundings. The air and surroundings are each at 300 K. Ty = 300 K - T = 300 K h = 25 W/m2 .K sur Air Plate, 400 K, ɛ = 0.8 -Insulated sidewalls 200 mm Furnace bottom, 1000 K (a) Evaluate the net rate of radiative heat transfer to the bottom surface of the plate. (b) If the plate has mass and specific heat of 2 kg and 900 J/kg · K, respectively, what will be the change in temperature of the plate with time, dT „/ dt? Assume convection to the bottom surface of the plate to be negligible.
Transcribed Image Text:13.72 An opaque, diffuse, gray (200 mm x 200 mm) plate with an emissivity of o.8 is placed over the opening of a furnace and is known to be at 400 K at a certain instant. The bottom of the furnace, having the same dimensions as the plate, is black and operates at 1000 K. The sidewalls of the furnace are well insulated. The top of the plate is exposed to ambient air with a convection coefficient of 25 W/m² . K and to large surroundings. The air and surroundings are each at 300 K. Ty = 300 K - T = 300 K h = 25 W/m2 .K sur Air Plate, 400 K, ɛ = 0.8 -Insulated sidewalls 200 mm Furnace bottom, 1000 K (a) Evaluate the net rate of radiative heat transfer to the bottom surface of the plate. (b) If the plate has mass and specific heat of 2 kg and 900 J/kg · K, respectively, what will be the change in temperature of the plate with time, dT „/ dt? Assume convection to the bottom surface of the plate to be negligible.
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