Plaster Insulation Brick Inside Air Outside Air le ra A particular house wall consists of three layers and has a surface area A. The inside layer is made of plaster board, the middle layer is made of fiberglass insulation, and the outside layer is made of brick. The thermal conductivity of all three layers is known, and the thickness of the plaster board and siding are also known. The convection coefficient for the inside and outside wall surfaces are known: System Parameters - (h; = 40.0 h,= 60.0 kị = 0.2 k,= 0.04 kz = 0.3 A = 30.0) System_Parameters - (L = 10.0 L½= unknown Lz= 100.0 c„ = 950.0 cp2 = 10.0 cp3=800.0 pi = 700.0 p2= 0.5 P3 = 2000.0) L ~ mm; A ~ m²; k~ _W m °C , kg ; T ~ °C m² °C kg °C a) If the thermal capacitances of the walls is ignored, How thíck must the insulation layer be so that the heat loss is no greater than 400W if the outside temperature is -15-C? b) Now consider the situation where the thermal capacitance is also considered. Develop the state variable model of the temperatures at the midpoints of each of the materials. Assume perfect conduction at the interfaces. Write the state equations in terms of the variables provided (not numbers). c) Consider the following situation: This wall represents the external wall of a small room. Throughout the night, there is no heat source turned on in the room, so the air temperature in the room is nearly the same as the temperature outside, which is 17 •C. Just before 7:00 am an air handling system is turned on which quickly stabilizes the room temperature at a constant 21 •C. At 7:00 am, the sun begins to rise and warms the outside air at a fairly constant rate, so that by 3:00 pm, the outside air temperatures is 30 ·C. Plot the thermal response of each of the layers of the wall throughout this time period. What can you identify about the thermal behavior of each of the layers in the wall?
Plaster Insulation Brick Inside Air Outside Air le ra A particular house wall consists of three layers and has a surface area A. The inside layer is made of plaster board, the middle layer is made of fiberglass insulation, and the outside layer is made of brick. The thermal conductivity of all three layers is known, and the thickness of the plaster board and siding are also known. The convection coefficient for the inside and outside wall surfaces are known: System Parameters - (h; = 40.0 h,= 60.0 kị = 0.2 k,= 0.04 kz = 0.3 A = 30.0) System_Parameters - (L = 10.0 L½= unknown Lz= 100.0 c„ = 950.0 cp2 = 10.0 cp3=800.0 pi = 700.0 p2= 0.5 P3 = 2000.0) L ~ mm; A ~ m²; k~ _W m °C , kg ; T ~ °C m² °C kg °C a) If the thermal capacitances of the walls is ignored, How thíck must the insulation layer be so that the heat loss is no greater than 400W if the outside temperature is -15-C? b) Now consider the situation where the thermal capacitance is also considered. Develop the state variable model of the temperatures at the midpoints of each of the materials. Assume perfect conduction at the interfaces. Write the state equations in terms of the variables provided (not numbers). c) Consider the following situation: This wall represents the external wall of a small room. Throughout the night, there is no heat source turned on in the room, so the air temperature in the room is nearly the same as the temperature outside, which is 17 •C. Just before 7:00 am an air handling system is turned on which quickly stabilizes the room temperature at a constant 21 •C. At 7:00 am, the sun begins to rise and warms the outside air at a fairly constant rate, so that by 3:00 pm, the outside air temperatures is 30 ·C. Plot the thermal response of each of the layers of the wall throughout this time period. What can you identify about the thermal behavior of each of the layers in the wall?
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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Transcribed Image Text:Plaster
Insulation
Brick
Inside
Outside
Air
Air
R/2
R3/2
G R/2
A particular house wall consists of three layers and has a surface area A. The inside layer is made of plaster board, the middle layer is made
of fiberglass insulation, and the outside layer is made of brick. The thermal conductivity of all three layers is known, and the thickness of the
plaster board and siding are also known. The convection coefficient for the inside and outside wall surfaces are known:
System_Parameters - (h; = 40.0 h, = 60.0 k = 0.2 k = 0.04 k3 = 0.3 A= 30.0)
System_Parameters =
(L = 10.0 L2= unknown L3 = 100.0 cp1 = 950.0 c p2 = 10.0 cp3= 800.0 P1 = 700.0 Pz = 0.5 P3= 2000.0)
W
- mm; A ~ m²; k ~.
m °C
;p~ 8: T ~ °C
kg °C
L
m² °C
m-
a) If the thermal capacitances of the walls is ignored, How thick must the insulation layer be so that the heat loss is no greater than 400W if the
outside temperature is -15-C?
b) Now consider the situation where the thermal capacitance is also considered. Develop the state variable model of the temperatures at the
midpoints of each of the materials. Assume perfect conduction at the interfaces. Write the state equations in terms of the variables provided
(not numbers).
c) Consider the following situation:
This wall represents the external wall of a small room. Throughout the night, there is no heat source turned on in the room, so the air
temperature in the room is nearly the same as the temperature outside, which is 17 -C. Just before 7:00 am an air handling system is turned
on which quickly stabilizes the room temperature at a constant 21 -C. At 7:00 am, the sun begins to rise and warms the outside air at a fairly
constant rate, so that by 3:00 pm, the outside air temperatures is 30 -C.
Plot the thermal response of each of the layers of the wall throughout this time period. What can you identify about the thermal behavior of
each of the layers in the wall?
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