# Variables
T1 = 65. #C, furnace temp.
T2 = 25. #C, ambient temp.
h = 1.5 #m, height of door
w = 1. #m, width of door
Tf = (T1+T2)/2 #c, average air film temp.
# Calculations
Pr = 0.695 #Prandtl no.
mu = 1.85*10**-5 #m**2/s, vismath.cosity
beeta = 1/(Tf+273) #K**-1. coefficient of volumetric expension
k = 0.028 #W/m C, thermal conductivity
g = 9.8 #m/s**2, gravitational consmath.tant
Grl = g*beeta*(T1-T2)*h**3/(mu**2) #Grashof no.
Ral = Grl*Pr #Rayleigh no.
#Nusslet no.
Nul = (0.825+(0.387*(Ral)**(1./6))/(1+(0.492/Pr)**(9./16))**(8./27))**2
hav = Nul*k/h #average heat transfer coefficient
Ad = h*w #m**2, door area
dt = T1-T2 #temp. driving force
q = hav*Ad*dt #W,rate of heat loss
# Results
print "The rate of heat loss is %.0f W"%(q)
# Variables
T1 = 60. #C, plate temp.
T2 = 25. #C, ambient temp.
h = 1.
w = 1. #m, width of door
q = 170. #W, rate of heat transfer
Tf = (T1+T2)/2 #c, average air film temp.
#Properties of air at Tf
Pr = 0.7 #Prandtl no.
mu = 1.85*10**-5 #m**2/s, vismath.cosity
beeta = 1./(Tf+273) #K**-1. coefficient of volumetric expension
k = 0.028 #W/m C, thermal conductivity
g = 9.8 #m/s**2, gravitational consmath.tant
#Calculation
A = h*w #m**2, plate area
P = 2*(h+w) #m,perimeter of plate
L = A/P #m characteristic length
Grl = g*beeta*(T1-T2)*L**3/(mu**2) #Grashof no.
Ral = Grl*Pr #Rayleigh no.
#Nusslet no.
Nul = 0.54*(Ral)**(1./4) #Nusslet no.
hav = Nul*k/L #average heat transfer coefficient
Ts = q/(hav*A)+T2
# Results
print "the steady state temp. of the plate is %.1f C"%(Ts)
import math
from scipy.integrate import quad
# Variables
d = 0.0254 #m, diameter of steel rod
l = 0.4 #m, length of rod
T1 = 80. #C, initial temp.
T2 = 30. #C, ambient temp.
T3 = 35. #c, temp. after cooling
rho = 7800. #kg/m**3 ,density of steel rod
cp = 0.473 #kj/kg C. specific heat
#Calculation
m = math.pi/4*d**2*l*rho #kg. mass of cylinder
A = math.pi*d*l #m**2, area of cylinder
dt = T1-T2 #c, insmath.tanmath.taneous temp. difference
h = 1.32*(dt/d)**0.25 #W/m**2 C, heat transfer coefficient
def f0(T):
return 1./(T**(5./4))
i = quad(f0,5,50)[0]
t = i/(3.306*A/(m*cp*10**3))
# Results
print "The required time for cooling is %.2f hr"%(t/3600.)
import math
# Variables
id_ = 78.*10**-3 #m, internal diameter
od = 89.*10**-3 #m, outer diameter
Pg = 15. #kg/cm**2, gauge pressure
t = 2.*10**-2 #m, thickness of preformed mineral fibre
k = 0.05 #W/m C. thermal conductivity
Ta = 25. #C, ambient air temp.
Pr = 0.705 #Prandtl no.
#assume
Ts = 50. #C, skin temp.
l = 1. #m, length
Ti = 200.5 #C, initial temp.
rs = od/2+t #m, outer radius of insulation
ri = od/2 #m, inner radius of insulation
# Calculations
Q = 2*math.pi*l*k*(Ti-Ts)/(math.log(rs/ri)) #W
#properties of air at taken at the mean film temp.
Tf = (Ta+Ts)/2 #C
mu = 1.76*10**-5 #m**2/s. vismath.cosity
beeta = (1/(Tf+273)) #K**-1, coefficient of volumetric expansion
k1 = 0.027 #W/m C, thermal conductivity
ds = 2*rs #m, outer dia. of insulated pipe
g = 9.8 #m/s**2, gravitational consmath.tant
Grd = g*beeta*(Ts-Ta)*ds**3/(mu**2) #Grashof no.
Rad = Grd*Pr #Rayleigh no.
#from eq. 5.9
#Nusslet no.
Nu = (0.60+(0.387*(Rad)**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27))**2
hav = Nu*k1/ds #W/ m**2 C, average heat transfer coefficient
Ts = (Q/(math.pi*ds*l*hav))+Ta #C, skin temp.
#revised calculation by assuming
Ts1 = 70. #C, skin temp.
#Rate of heat transfer through insulation
Q1 = 2*math.pi*l*k*(Ti-Ts1)/(math.log(rs/ri))
Tf1 = (Ta+Ts1)/2 #C, average aie mean film temp.
mu1 = 1.8*10**-5 #m**2/s. vismath.cosity
beeta1 = (1/(Tf1+273)) #K**-1, coefficient of volumetric expansion
k1 = 0.0275 #W/m C, thermal conductivity
Pr1 = 0.703 #Prandtl no.
Grd1 = g*beeta1*(Ts1-Ta)*ds**3/(mu1**2) #Grashof no.
Rad = Grd1*Pr1 #Rayleigh no.
#from eq. 5.9
# average heat transfer coefficient, in #W/ m**2 C,
hav1 = (0.60+(0.387*(Rad)**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27))**2*(k1/ds)
Ts2 = (Q1/(math.pi*ds*l*hav1))+Ta
#again assume skin temp. = 74
Ts2 = 74 #C, assumed skin temp.
Q3 = 2*math.pi*l*k*(Ti-Ts2)/(math.log(rs/ri))
# Results
print "the rate of heat loss by free convection per meter length of pipe. is %.0f W"%(Q3)
from scipy.optimize import fsolve
import math
# Variables
Ts = 65. #C, skin temp.
To = 30. #C, ambient temp.
Tw = 460. #C, wall temp.
Tf = (Ts+To)/2 #C,mean air film temp.
beeta = (1./(Tf+273)) #K**-1, coefficient of volumetric expansion
g = 9.8 #m/s**2, gravitational consmath.tant
mu = 1.84*10**-5 #m**2/s, vismath.cosity
L = 10.5 #m, height of converter
di = 4. #m,diameter of converter
Pr = 0.705 #Prandtl no.
k = 0.0241 #kcal/h m C, thermal conductivity
#Calculation
Grl = g*beeta*(Ts-To)*L**3/(mu**2) #Grashof no.
x = di/L #assume di/l = x
y = 35/(Grl)**(1./4) #assume 35/(Grl)**(3/4) = y
#for a verticla flat plate, from eq. 5.3
Ral = Grl*Pr #Rayleigh no.
#nusslet no.
Nu = (0.825+(0.387*(Ral)**(1./6))/(1+(0.496/Pr)**(9./16))**(8./27))**2
hav = Nu*k/L #kcal/h m**2 C, average heat transfer coefficient
#w = poly(0,"w")
#Dav = (4+(4+2*w))/2 #average diameter
#Aav = math.pi*Dav*L #average heat transfer area
#Qi = math.pi*Dav*L*0.0602*(Tw-Ts)/w #Rate of heat transfer through insulation
#rate of heat transfer from the outer surface of the insulation by free convection
#Qc = hav*math.pi*Dav*L*(Ts-To)
#Qi = Qc
def f(w):
return math.pi*(4+w)*L*0.0602*(Tw-Ts)/w-hav*math.pi*(4+2*w)*L*(Ts-To)
w = fsolve(f,0.1)
# Results
print "The required insulation thickness is %.3f m"%(w)
# Variables
L = 1.6 #m,height of enclosure
w = 0.04 #m, width of enclosure
b = 0.8 #m, breath
T1 = 22. #C,surface temp.
T2 = 30. #C, wall temp.
Tm = (T1+T2)/2 #C, Mean air temp.
Pr = 0.7 #Prandtl no.
# Calculations
#fpr air at 26 C
beeta = 1./(Tm+273) #K**-1. coefficient of volumetric expension
mu = 1.684*10**-5 #m**2/s, vismath.cosity
k = 0.026 #W/m C, thermal conductivity
alpha = 2.21*10**-5 #m**2/s, thermal diffusity
g = 9.8 #m/s**2, gravitational consmath.tant
Raw = g*beeta*(T2-T1)*w**3/(mu*alpha) #Rayleigh no.
Nuw = 0.42*(Raw)**0.25*Pr**0.012*(L/w)**-0.3 #Nusslet no.
h = Nuw*k/w #kcal/h m**2 C, heat transfer coefficient
q = h*(T2-T1)*(L*b) #W,the rate of heat transfer
# Results
print "the rate of heat transfer is %.1f W"%(q)
import math
# Variables
Ts = 60. #C, surface temp
To = 30. #C, bulk temp.
d = 0.06 #m, diameter of pipe
l = 1. #m, length
Tm = (Ts+To)/2
#for air at Tm
rho = 1.105 #kg/m**3, density
cp = 0.24 #kcal/kg C. specific heat
mu = 1.95*10**-5 #kg/m s. vismath.cosity
P = 0.7 #Prandtl no.
kv = 1.85*10**-5 #m**2/s, kinetic vismath.cosity
k = 0.0241 #kcal/f m C, thermal conductivity
beeta = (1./(Tm+273)) #K**-1. coefficient of volumetric expension
V = 0.3 #m/s, velocity
g = 9.8 #m/s**2, gravitational consmath.tant
#Calculation
Rad = g*beeta*(Ts-To)*d**3*P/(kv**2) #Rayleigh no.
#from eq. 5.9
Nufree = (0.60+(0.387*Rad**(1./6))/(1+(0.559/P)**(9./16))**(8./27))**2
#calculation of forced convection nusslet no.
#from eq. 4.19
Re = d*V/(kv)
Nuforced = 0.3+(0.62*Re**(1./2)*P**(1./3)/(1+(0.4/P)**(2./3))**(1./4))*(1.+(Re/(2.82*10**5))**(5./8))**(4./5)
Nu = (Nuforced**3+Nufree**3)**(1./3) #nusslet no. for mixed convection
#Nu = h*d/k
h = Nu*k/d #kcal/h m**2 C, heat transfer corfficient
q = h*math.pi*d*l*(Ts-To)
# Results
print "the rate of heat loss per meter length is %.1f kcal/h"%(q)