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.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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QUESTION THREE
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.
d) The heat generated in the plate is transferred by natural convection to the air in
the room which has a temperature of 30°C. Calculate the expected convective
heat transfer coefficient 'h' from this plate using the convection correlations
available in the formula sheet.
Transcribed Image Text:QUESTION THREE 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. d) The heat generated in the plate is transferred by natural convection to the air in the room which has a temperature of 30°C. Calculate the expected convective heat transfer coefficient 'h' from this plate using the convection correlations available in the formula sheet.
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