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A large steel plate having a thickness of L = 4 in, thermal conductivity of k= 7.2 Btu/h·ft. °F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is known to exchange heat by convection with the ambient air at T∞ = 90°F with an average heat transfer coefficient of h = 12 Btu/h·ft².°F as well as by radiation with the open sky with an equivalent sky temperature of Tsky =480 R. Also, the temperature of the upper surface of the plate is measured to be 80°F. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the variation of temperature in the plate by solving the differential equation, and (c) determine the value of the lower surface temperature of the plate at x = 0. Tsky h, To Convection Radiation XA 80°F L E Plate 0 Ground

A large steel plate having a thickness of L = 4 in, thermal conductivity of k= 7.2 Btu/h·ft. °F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is known to exchange heat by convection with the ambient air at T∞ = 90°F with an average heat transfer coefficient of h = 12 Btu/h·ft².°F as well as by radiation with the open sky with an equivalent sky temperature of Tsky =480 R. Also, the temperature of the upper surface of the plate is measured to be 80°F. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the variation of temperature in the plate by solving the differential equation, and (c) determine the value of the lower surface temperature of the plate at x = 0. Tsky h, To Convection Radiation XA 80°F L E Plate 0 Ground

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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A large steel plate having a thickness of L = 4 in, thermal conductivity of k= 7.2 Btu/h·ft. °F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is known to exchange heat by convection with the ambient air at T∞ = 90°F with an average heat transfer coefficient of h = 12 Btu/h·ft².°F as well as by radiation with the open sky with an equivalent sky temperature of Tsky =480 R. Also, the temperature of the upper surface of the plate is measured to be 80°F. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the variation of temperature in the plate by solving the differential equation, and (c) determine the value of the lower surface temperature of the plate at x = 0. Tsky h, To Convection Radiation XA 80°F L E Plate 0 Ground
Transcribed Image Text:A large steel plate having a thickness of L = 4 in, thermal conductivity of k= 7.2 Btu/h·ft. °F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is known to exchange heat by convection with the ambient air at T∞ = 90°F with an average heat transfer coefficient of h = 12 Btu/h·ft².°F as well as by radiation with the open sky with an equivalent sky temperature of Tsky =480 R. Also, the temperature of the upper surface of the plate is measured to be 80°F. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the variation of temperature in the plate by solving the differential equation, and (c) determine the value of the lower surface temperature of the plate at x = 0. Tsky h, To Convection Radiation XA 80°F L E Plate 0 Ground
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