Chapter1:Fundamental Concepts¶
Example 1.1 Page No.7¶
In [3]:
k=9.4 # thermal conductivity in [BTU/hr.ft. ˚Rankine]
q=6.3 # heat flux in [BTU/s. sq.ft]
T1=350 # the outside surface temperature of one aide of the wall [˚F]
Q=6.3*3600 # [BTU/hr.sq.ft]
dx=0.5 # thickness in [inch]
Dx=0.5/12.0 # thickness in [ft]
T2=T1-(Q*Dx/k) # [˚F]
print"The required temperature on the other side of the firewall is ",round(T2,1),"F"
Example 1.2 Page No.9¶
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k_ss=14.4 # thermal conductivity of stainless steel in [W/m.K]
dt_ss=40 # [K]
dt_al=8.65 # [K]
dz_ss=1 # [cm]
dz_al=3 # [cm]
k_al=k_ss*dt_ss*dz_al/(dt_al*dz_ss);# thermal conductivity of Al in [W/m.K]
print"The thermal conductivity of aluminium is",round(k_al,0),"W/m.K"
Example 1.3 Page No.13¶
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h_c=3 # convective coefficient in [BTU/hr.ft**2
A=30*18 # Cross sectional area in ft**2
T_w=140 # Roof surface temperature in degree Fahrenheit
T_inf=85 # Ambient temperature in degree Fahrenheit
dT= (T_w-T_inf)
Q_c=h_c*A*dT # Convective heat transfer in BTU/hr
print"The heat transferred by convection is",round(Q_c,2),"BTU/hr"
Example 1.4 Page No.14¶
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D=0.0243 # diameter in meter
L=0.2 # length in meter
A=3.14*D*L # cross-sectional area in sq.m
cp=4200.0 # specific heat of water in J/kg.K
T_b2=21.4 # temperature of bulk fluid in degree celsius
T_in=20.0 # temperature of inlet water in degree celsius
T_w=75.0 # temperature of wall in degree celsius
Q=500.0 # volumetric flow rate in cc/s
density=1000 # density of water in kg/cu.m
m=Q*density/10**6 # mass flowa rate in kg/s
hc=m*cp*(T_b2-T_in)/(A*(T_w-T_in))
print"The average film conductance is ",round(hc,0),"W/sq.m. K"
Example 1.5 Page No.18¶
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W=14 # width in ft
L=30.0 # length in ft
A=W*L # area in ft**2
F_12=1 # view factor assumed to be 1
T1=120+460 # driveway surface temperature in degree Rankine
T2=0 # space temperature assumed to be 0 degree Rankine
sigma=0.1714*10**(-8) # value of Stefan-Boltzmann's constant in BTU/(hr.ft**2.(degree Rankine)**4)
e=0.9 # surface emissivity
q=sigma*A*e*F_12*((T1)**4-(T2)**4);
print"The heat loss rate by radiation is ",round(q,0),"BTU/hr"
Example 1.6 Page No.19¶
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A=420.0 # area in sq.ft
T1=580.0 # driveway surface temperature in degree Rankine
T2=0 # surface temperature assumed to be 0 degree Rankine
Qr=73320 # heat loss rate in BTU/hr
hr=Qr/(A*(T1-T2)) # radiation thermal conductance in BTU/(hr.ft**2.(degree Rankine)
print"the radiation thermal conductance is ",round(hr,2),"BTU/(hr. sq.ft R)"
Example 1.7 Page No. 21¶
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%matplotlib inline
In [24]:
A=1.0 # assuming A=1 m**2 for convenience
hc1_avg=15.0 # taking average of extreme values for hc [W/m**2.K]
k=(0.38+0.52)/2.0 # thermal conductivity of common brick in W/M.k
L=0.1 #10 cm converted into m
Rk=(L/(k*A)) # resistance of construction material, assume common brick
T_inf1=1000.0 # temperature of exhaust gases in K
T_inf2=283.0 # temperature of ambient air in K
Rcl=1/(hc1_avg*A) # resistance on left side of wall [K/W]
Rc2=Rcl
q=(T_inf1-T_inf2)/(Rcl+Rk+Rc2) # heat transferred per unit area
T_in=T_inf1-Rcl*q #inlet temprature
T_out=T_inf2+Rc2*q
print"(b)"
print"The resistance on left side of wall is ",round(Rcl,2),"K/W"
print"The resistance of construction material of wall is",round(Rk,2),"K/W"
print"The resistance on right side of wall is ",round(Rc2,2),"K/W"
print"(c)The Heat transferred per unit area is ",round(q/1000,2),"kw"
print "(d)"
print"The inside wall temperature is ",round(T_in,0),"K"
print"The outside wall temperature is",round(T_out,1),"K"
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
x1=[5,5]
T1=[0,1000]
x2=[8,8]
T2=[0,1000]
x3=[1,4]
T3=[1000,1000]
x4=[4,5]
T4=[1000,866]
x5=[5,8]
T5=[866,417]
x6=[8,9]
T6=[417,290]
x7=[9,10]
T7=[290,283]
xlabel("x")
ylabel("T (K)")
plt.xlim((0,11))
plt.ylim((0,1200))
ax.plot([1], [1000], 'o')
ax.annotate('(1000K)', xy=(1,1020))
ax.plot([5], [866], 'o')
ax.annotate('(T1)', xy=(5.5,866))
ax.plot([8], [417], 'o')
ax.annotate('(T2)', xy=(7.5,417))
ax.plot([10], [283], 'o')
ax.annotate('(283K)', xy=(10.5,283))
a1=plot(x1,T1)
a2=plot(x2,T2)
a3=plot(x3,T3)
a4=plot(x4,T4)
a5=plot(x5,T5)
a6=plot(x6,T6)
a7=plot(x7,T7)
show(a1)
Example 1.8 Page No.24¶
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k=0.604 # [BTU/(hr.ft.degree Rankine)]
hc=3.0 # average value for natural convection in BTU/(hr.ft**2.degree Rankine)
ew=0.93
f_wr=1.0 # shape factor
sigma= 0.1714*10**(-8) # BTU/(hr.ft**2.degree Rankine).
L=4/12.0 # length in ft
T1=80+460 # temperature of side-walk in degree Rankine
T_inf=20+460 # temperature of ambient air in degree Rankine
T_r=0 # assuming space temperature to be 0 degree Rankine
a=((k/L)+hc) #Coefficient of Tw in the equation
b=(sigma*ew*f_wr) #Coefficient of Tw**4 in the equation
c=(k*T1/L)+(hc*T_inf)+(sigma*f_wr*ew*T_r**4) #right hans side of the equation
Tw1=470 #assumed first value of temprature
LHS1=a*Tw1+b*Tw1**4
Tw2=480 #assumed 2nd value of temprature
LHS2=a*Tw2+b*Tw2**4
Tw3=490 #assumed 3rd value of temprature
LHS3=a*Tw3+b*Tw3**4
Tw4=485 #assumed 4th value of temprature
LHS4=a*Tw4+b*Tw4**4
Tw5=484.5 #assumed fifth value of temprature
LHS5=a*Tw5+b*Tw5**4
print"RHS",round(c,1)
print"LHS at surface Temprature 1=",round(LHS1,1)
print"LHS at surface Temprature 2=",round(LHS2,1)
print"LHS at surface Temprature 3=",round(LHS3,0)
print"LHS at surface Temprature 4=",round(LHS4,1)
print"LHS at surface Temprature 5=",round(LHS5,1)
print"\nLHS is close enough to RHS at Temprature 484.5. So Surface Temprature is",Tw5,"R"
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