In: Physics
Home is where the Heat is
The walls of a house are made of a 10 cm layer of brick, 10 cm of fiberglass insulation and
1cm of drywall.
Thermal conductivity values:
Brick: 1.31 W/m*K
Fiberglass : 0.04 W/m*K
dry wall : 0.17 W/m*K
a) Calculate the thermal conductivity of a 1 m 2 section of wall.
b) Find the relationship between the thermal conductivity, k, in W/m*K and the thermal
resistance = R in (m^2 *K)/W.
In order to be energy efficient, the air intake for the home is passed through a
countercurrent heat exchanger with the indoor air going the other direction. The system
is designed to absorb heat from the outgoing air and use it to warm the incoming air. In
order to accomplish this, the outgoing air is passed through a radiator which has ethylene
glycol flowing through it. As the ethylene glycol warms, its density decreases and it flows
upward into the radiator through which the incoming air passes.
density = 1.1153-.0007*T ; T in
t_brick = 10 cm = 0.1 m
t_fg = 10 cm = 0.1 m
t_drywall = 1 cm = 0.01 m
k_brick = 1.31 W/m-K
k_fg = 0.04 W/m-K
k_drywall = 0.17 W/m-K
a)
Area A = 1 m^2
Thermal resistances:
R = t / (k*A)
R_brick = 0.1 / (1.31*1) = 0.0763 K / W
R_fg = 0.1 / (0.04*1) = 2.5 K/W
R_drywall = 0.01 / (0.17*1) = 0.0588 K/W
Total thermal resistance R = R_brick + R_fg + R_drywall
R = 0.0763 + 2.5 + 0.0588
R = 2.635 K / W
So, t / (k_eq*A) = 2.635
(0.1 + 0.1 + 0.01) / (k_eq*1) = 2.635
k_eq = 0.0796 W/m-K
b)
R = t / (k*A)
c)
After plotting n(mPa) versus T(deg C) in Excel, and adding 5th order trendline eqn we get
n = -2*10^-7*T^5 + 6*10^-5*T^4 - 0.0061*T^3 + 0.2761*T^2 - 6.2325*T + 70.572
d)
Flowrate = rho*A*v
density rho = 1.1153 - 0.0007*T
At T = 10 deg C, density rho = 1.1153 - 0.0007*10 = 1.1083 g/cm^3
At T = 18 deg C, density rho = 1.1153 - 0.0007*18 = 1.1027 g/cm^3
(d2 / d1)^2 = rho1 / rho2
(d2 / 2)^2 = 1.1083 / 1.1027
d2 = 2.005 cm