In [2]:

```
import math
# Variables
L = 0.3; #Length of the glass plate in m
Ta = 27; #Temperature of air in degree C
Ts = 77; #Surface temperature in degree C
v = 4; #Velocity of air in m/s
# Calculations
Tf = (Ta+Ts)/2; #Film temperature in degree C
k = 0.02815; #Thermal conductivity in W/m.K
v1 = (18.41*10**-6); #Kinematic viscosity in m**2/s
Pr = 0.7; #Prantl number
b = (3.07*10**-3); #Coefficient of thermal expansion in 1./K
Gr = (9.81*b*(Ts-Ta)*L**3)/v1**2; #Grashof number
q = L*((3.93*(1./math.sqrt(Pr))*(0.952+Pr)**0.25*Gr**(-0.25))); #Boundary layer thickness at the trailing edge of the plate in free convection in m
Re = (v*L)/v1; #Reynolds number
q1 = (5*L)/math.sqrt(Re); #Boundary layer thickness at the trailing edge of the plate in forced convection in m
# Results
print 'Boundary layer thickness at the trailing edge of the plate in free convection is % 3.4f m \
\nBoundary layer thickness at the trailing edge of the plate in forced convection is %3.4f m'%(q,q1)
```

In [3]:

```
import math
# Variables
L = 0.3; #Length of the glass plate in m
Ta = 27; #Temperature of air in degree C
Ts = 77; #Surface temperature in degree C
v = 4; #Velocity of air in m/s
# Calculations
Tf = (Ta+Ts)/2; #Film temperature in degree C
k = 0.02815; #Thermal conductivity in W/m.K
v1 = (18.41*10**-6); #Kinematic viscosity in m**2/s
Pr = 0.7; #Prantl number
b = (3.07*10**-3); #Coefficient of thermal expansion in 1./K
Gr = (9.81*b*(Ts-Ta)*L**3)/v1**2; #Grashof number
Re = (v*L)/v1; #Reynolds number
Nu = (0.677*math.sqrt(Pr)*(0.952+Pr)**(-0.25)*Gr**0.25); #Nusselts number
h = (Nu*k)/L; #Heat transfer coefficient for natural convection in W/m**2.K
Nux = (0.664*math.sqrt(Re)*Pr**(1./3)); #Nusselts number
hx = (Nux*k)/L; #Heat transfer coefficient for forced convection in W/m**2.K
# Results
print 'Heat transfer coefficient for natural convection is %3.1f W/m**2.K \n \
Heat transfer coefficient for forced convection is %3.2f W/m**2.K'%(h,hx)
```

In [4]:

```
# Variables
L = 0.609; #Height of the metal plate in m
Ts = 161.; #Temperature of the wall in degree C
Ta = 93.; #Temperature of air in degree C
# Calculations
Tf = (Ts+Ta)/2; #Film temperature in degree C
k = 0.0338; #Thermal conductivity in W/m.K
v1 = (26.4*10**-6); #Kinematic vismath.cosity in m**2/s
Pr = 0.69; #Prantl number
b = 0.0025; #Coefficient of thermal expansion in 1./K
a = (38.3*10**-6); #Thermal diffusivity in m**2/s
Ra = ((9.81*b*L**3*(Ts-Ta))/(v1*a)); #Rayleigh number
Nu = (0.68+((0.67*Ra**0.25)/(1+(0.492/Pr)**(9./16))**(4./9))); #Nussults number
h = (Nu*k)/L; #Heat transfer coefficient in W/m**2.K
Q = (h*L*(Ts-Ta)); #Rate of heat transfer in W
Nul = 0.59 * (3.72*10**8)**(1./4)
# Results
print 'Heat transfer coefficient is %3.3f W/m**2.K Rate of heat transfer is %3.2f W'%(h,Q)
print "NuL = %.2f W"%Nul
```

In [9]:

```
# Variables
W = 0.5; #Width of the radiator in m
L = 1.; #Height of the radiator in m
Ts = 84.; #Surface temperature in degree C
Ta = 20.; #Room temperature in degree C
# Calculations
Tf = (Ts+Ta)/2; #Film temperature in degree C
k = 0.02815; #Thermal conductivity in W/m.K
v1 = (18.41*10**-6); #Kinematic viscosity in m**2/s
Pr = 0.7; #Prantl number
b = 0.003077; #Coefficient of thermal expansion in 1./K
Ra = ((9.81*b*L**3*(Ts-Ta)*Pr)/(v1**2)); #Rayleigh number
Nu = (0.825+((0.387*Ra**(1./6))/(1+(0.492/Pr)**(9./16))**(8./27)))**2; #Nussults number
h = (1170.9*k)/L; #Heat transfer coefficient in W/m**2.K
Q = (h*W*L*(Ts-Ta)); #Convective heat loss in W
# Results
print 'Convective heat loss from the radiator is %3.2f W'%(Q)
```

In [6]:

```
# Variables
L = 0.8; #Height of the plate in m
W = 0.08; #Width of the plate in m
Ts = 170; #Surafce temperature in degree C
Tw = 70; #Temperature of water in degree C
Tf = 130; #Final temperature in degree C
# Calculations
Tb = (Ts+Tw)/2; #Film temperature in degree C
p = 960.63; #Density in kg/m**3
k = 0.68; #Thermal conductivity in W/m.K
v1 = (0.294*10**-6); #Kinematic viscosity in m**2/s
b = 0.00075; #Coefficient of thermal expansion in 1./K
Cp = 4216; #Specific heat in J/kg.K
a = (1.68*10**-7); #Thermal diffusivity in m**2/s
Lc = (W/2); #Characteristic length in m
Ra = ((9.81*b*Lc**3*(Tf-Tw))/(v1*a)); #Rayleigh number
Nu1 = (0.15*Ra**(1./3)); #Nussults number
h1 = (Nu1*k)/Lc; #Heat transfer coefficient at top surface in W/m**2.K
Nu2 = 0.27*(Ra)**(0.25); #Nusselts number
h2 = (Nu2*k)/Lc; #Heat transfer coefficient at bottom surface in W/m**2.K
Q = ((h1+h2)*W*L*(Tf-Tw))/1000; #Rate of heat input to the plate in kW
# Results
print 'Rate of heat input to the plate necessary to maintain the temperature at %3.0f degree C is %3.2f kW'%(Tf,Q)
```

In [7]:

```
# Variables
L = 0.3; #Height of the duct in m
W = 0.6; #Width of the duct in m
Ts = 15; #Surface temperature in degree C
Ta = 25; #Temeprature of air in degree C
# Calculations
Tb = (Ts+Ta)/2; #Film temperature in degree C
p = 1.205; #Density in kg/m**3
k = 0.02593; #Thermal conductivity in W/m.K
v1 = (15.06*10**-6); #Kinematic viscosity in m**2/s
b = 0.00341; #Coefficient of thermal expansion in 1./K
Cp = 1005; #Specific heat in J/kg.K
Pr = 0.705; #Prantl number
Ra = ((9.81*b*L**3*(Ta-Ts)*Pr)/(v1**2)); #Rayleigh number
Nux = (0.59*Ra**(0.25)); #Nusselts number
hx = (Nux*k)/L; #Heat transfer coefficient in W/m**2.K
Lc = (W/2); #Characteristic length in m
Nu1 = (0.15*Ra**(1./3)); #Nussults number
h1 = (Nu1*k)/Lc; #Heat transfer coefficient at top surface in W/m**2.K
Nu2 = 0.27*(Ra)**(0.25); #Nusselts number
h2 = (Nu2*k)/Lc; #Heat transfer coefficient at bottom surface in W/m**2.K
Q = ((2*hx*L)+(W*(h1+h2)))*(Ta-Ts); #Rate of heat gained per unit length in W/m
# Results
print 'Rate of heat gained per unit length is %3.2f W/m'%(Q)
```

In [8]:

```
# Variables
LH = 0.08; #Horizantal length in m
LV = 0.12; #Vertical length in m
Ts = 50; #Surface temperature in degree C
Ta = 0; #Temeprature of air in degree C
# Calculations
L = (LH*LV)/(LH+LV); #Characteristic length in m
Tb = (Ts+Ta)/2; #Film temperature in degree C
p = 0.707; #Density in kg/m**3
k = 0.0263; #Thermal conductivity in W/m.K
v1 = (15.89*10**-6); #Kinematic viscosity in m**2/s
b = (1./300); #Coefficient of thermal expansion in 1./K
Pr = 0.707; #Prantl number
Gr = ((9.81*b*L**3*(Ts-Ta))/(v1**2)); #Grashof number
Nu = 0.55*Gr**(0.25); #Nussults number
h = (Nu*k)/L; #Heat transfer coefficient in W/m**2.K
# Results
print 'Heat transfer coefficient is %3.2f W/m**2.K'%(h)
```

In [9]:

```
# Variables
D = 0.2; #Outer diameter of the pipe in m
Ts = 100; #Surface temperature in degree C
Ta = 20; #Temperature of air in degree C
L = 3; #Length of pipe in m
# Calculations
Tf = (Ts+Ta)/2; #Film temperature in degree C
k = 0.02896; #Thermal conductivity in W/m.K
v1 = (18.97*10**-6); #Kinematic viscosity in m**2/s
b = (1./333); #Coefficient of thermal expansion in 1./K
Pr = 0.696; #Prantl number
Gr = ((9.81*b*L**3*(Ts-Ta))/(v1**2)); #Grashof number
Ra = (Gr*Pr); #Rayleigh number
Nu = (0.1*Ra**(1./3)); #Nussults number
h = (Nu*k)/L; #Heat transfer coefficient in W/m**2.K
Q = (h*3.14*D*(Ts-Ta)); #Rate of heat loss per meter length of pipe in W/m
# Results
print 'Rate of heat loss per meter length of pipe is %3.2f W/m'%(Q)
```

In [16]:

```
# Variables
D = 0.1; #Outer diamter of the pipe in m
Ta = 30.; #Ambient temperature of air degree C
Ts = 170.; #Surface temperature in degree C
e = 0.9; #Emissivity
# Calculations
Tb = (Ts+Ta)/2; #Film temperature in degree C
k = 0.0321; #Thermal conductivity in W/m.K
v1 = (23.13*10**-6); #Kinematic viscosity in m**2/s
b = 0.00268; #Coefficient of thermal expansion in 1./K
Pr = 0.688; #Prantl number
Ra = ((9.81*b*D**3*(Ts-Ta)*Pr)/(v1**2)); #Rayleigh number
Nu = (0.6+((0.387*Ra**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27)))**2; #Nussults number
h = (Nu*k)/D; #Heat transfer coefficient in W/m**2.K
Q = (h*3.1415*D*(Ts-Ta))+(e*3.1415*D*5.67*10**-8*((Ts+273)**4-(Ta+273)**4)); #Total heat loss per meter length of pipe in m
NuD = 0.48*(4.72*10**6)*0.25
# Results
print 'Total heat loss per meter length of pipe is %3.2f W/m'%(Q)
print "NuD = %.2f"%NuD
# Note : rounding off error.
# Note : 2nd answer is wrong in book
```

In [11]:

```
import math
# Variables
Ta = 25; #Temperature of air in degree C
Ts = 95; #Surface temperature of wire in degree C
D = 0.0025; #Diameter of wire in m
R = 6; #Resistivity in ohm/m
# Calculations
Tf = (Ts+Ta)/2; #Film temperature in degree C
k = 0.02896; #Thermal conductivity in W/m.K
v1 = (18.97*10**-6); #Kinematic viscosity in m**2/s
b = (1./333); #Coefficient of thermal expansion in 1./K
Pr = 0.696; #Prantl number
Gr = ((9.81*b*D**3*(Ts-Ta))/(v1**2)); #Grashof number
Ra = (Gr*Pr); #Rayleigh number
Nu = (1.18*Ra**(1./8)); #Nussults number
h = (Nu*k)/D; #Heat transfer coefficient in W/m**2.K
Q = (h*3.14*D*(Ts-Ta)); #Rate of heat loss per unit length of wire in W/m
I = math.sqrt(Q/R); #Maximum current intensity in A
# Results
print 'Heat transfer coefficient is %3.2f W/m**2.K \n \
Maximum current intensity is %3.2f A'%(h,I)
```

In [12]:

```
# Variables
D = 0.01; #Diameter of spherical steel ball in m
Ts = 260; #Surface temperature in degree C
Ta = 20; #Temperature of air in degree C
# Calculations
Tf = (Ts+Ta)/2; #Film temperature in degree C
k = 0.0349; #Thermal conductivity in W/m.K
v1 = (27.8*10**-6); #Kinematic viscosity in m**2/s
b = (1./413); #Coefficient of thermal expansion in 1./K
Pr = 0.684; #Prantl number
Ra = ((9.81*b*D**3*(Ts-20)*Pr)/(v1**2)); #Rayleigh number
Nu = (2+(0.43*Ra**0.25)); #Nusuults number
h = (k*Nu)/D; #Heat transfer coefficient in W/m**2.K
Q = (h*3.14*D**2*(Ts-Ta)); #Rate of heat loss in W
# Results
print 'Rate of convective heat loss is %3.2f W'%(Q)
```

In [13]:

```
# Variables
D = 0.1; #Outer diamter of the pipe in m
Ta = 30; #Ambient temperature of air degree C
Ts = 170; #Surface temperature in degree C
e = 0.9; #Emissivity
# Calculations
h = (1.32*((Ts-Ta)/D)**0.25); #Heat transfer coefficient in W/m**2.K
q = (h*3.1415*D*(Ts-Ta)); #Heat transfer in W/m
# Results
print 'Heat loss due to free convection is %3.2f W/m'%(q)
```

In [15]:

```
# Variables
L = 0.015; #Thickness of the slot in m
D = 2; #Dimension of square plate in m
T1 = 120; #Temperature of plate 1
T2 = 20; #Temperature of plate 2
# Calculations
Tf = (T1+T2)/2; #Film temperature in degree C
k = 0.0295; #Thermal conductivity in W/m.K
v1 = (2*10**-5); #Kinematic viscosity in m**2/s
b = (1./343); #Coefficient of thermal expansion in 1./K
Gr = ((9.81*b*L**3*(T1-T2))/(v1**2)); #Grashof number
ke = (0.064*k*Gr**(1./3)*(D/L)**(-1./9)); #Effective thermal conductivity in W/m.K
Q = (ke*D**2*(T1-T2))/L; #Rate of heat transfer in W
# Results
print 'Effective thermal conductivity is %3.4f W/m.K Rate of heat transfer is %3.1f W'%(ke,Q)
```

In [16]:

```
# Variables
d = 0.0254; #Diamath.tance between the plates in m
Tl = 60; #Temperature of the lower panel n degree C
Tu = 15.6; #Temperature of the upper panel in degree C
# Calculations
Tf = (Tl+Tu)/2; #Film temperature in degree C
p = 1.121; #Density in kg/m**3
k = 0.0292; #Thermal conductivity in W/m.K
v1 = (0.171*10**-4); #Kinematic viscosity in m**2/s
b = (3.22*10**-3); #Coefficient of thermal expansion in 1./K
Pr = 0.7; #Prantl number
Gr = ((9.81*b*d**3*(Tl-Tu))/(v1**2)); #Grashof number
Nu = (0.195*Gr**0.25); #Nussults number
q = (Nu*k*(Tl-Tu))/d; #Heat flux across the gap in W/m**2
# Results
print 'Free convection heat transfer is %3.1f W/m**2'%(q)
```

In [17]:

```
# Variables
p = 3; #Pressure of air in atm
r1 = 0.075; #Radius of first sphere in m
r2 = 0.1; #Radius of second sphere in m
L = 0.025; #Distance in m
T1 = 325; #Temperature of first sphere in K
T2 = 275; #Temperature of second sphere in K
R = 287; #Universal gas consmath.tant in J/
# Calculations
Tf = (T1+T2)/2; #Film temperature in degree C
d = (p/(R*Tf)); #Desnsity in kg/m**3
k = 0.0263; #Thermal conductivity in W/m.K
v1 = (5.23*10**-6); #Kinematic viscosity in m**2/s
b = (1./300); #Coefficient of thermal expansion in 1./K
Pr = 0.707; #Prantl numbe
Gr = ((9.81*b*L**3*(T1-T2))/(v1**2)); #Grashof number
Ra = (Gr*Pr); #Rayleigh number
Ra1 = ((L/((4*r1*r2)**4))*(Ra/((2*r1)**(-7./5)+(2*r2)**(-7./5))**5))**0.25; #Equivalent Rayleigh's number
ke = (k*0.74*((Pr*Ra1)/(0.861+Pr))**0.25); #Effective thermal conductivity in W/m.K
Q = (ke*3.14*4*r1*r2*(T1-T2))/L; #Rate of heat loss in W
# Results
print 'Convection heat transfer rate is %3.2f W'%(Q)
```

In [18]:

```
# Variables
p = 1; #Pressure of air in atm
Ta = 27; #Temperature of air in degree C
D = 0.02; #Diamter of the tube in m
v = 0.3; #Velocity of air in m/s
Ts = 127; #Surface temperature in degree C
L = 1; #Length of the tube in m
# Calculations
k = 0.0262; #Thermal conductivity in W/m.K
v1 = (1.568*10**-5); #Kinematic viscosity in m**2/s
Pr = 0.708; #Prantl number
b = (1./300); #Coefficient of thermal expansion in 1./K
ub = (1.847*10**-5); #Dynamic viscosity in Ns/m**2
us = (2.286*10**-5); #Viscosity of wall in Ns/m**2
Re = (v*D)/v1; #Reynolds number
Gr = ((9.81*b*D**3*(Ts-Ta))/(v1**2)); #Grashof number
Gz = (Re*Pr*(D/L)); #Graetz number
Nu = (1.75*(ub/us)**0.14*(Gz+(0.012*(Gz*Gr**(1./3))**(4./3)))**(1./3)); #Nussults number
h = (k*Nu)/D; #Heat transfer coefficient in W/m**2.K
Q = (h*3.14*D*L*(Ts-Ta)); #Heat transfer in W
# Results
print 'Heat transfer in the tube is %3.2f W'%(Q)
```