# Chapter 7 : Forced Convection Systems¶

## Example 7.1 Page No : 275¶

In [2]:
import math

# Variables
Ta = 20;			#Temperature of air in degree C
Tp = 134;			#Temperature of heated plate in degree C
v = 3;			#Velocity of flow in m/s
L = 2;			#Length of plate in m
W = 1.5;			#Width of plate in m
x = 0.4;			#Distance of plane from the plate in m
k = (15.06*10**-6);			#Kinematic vismath.cosity in m**2/s

# Calculations
Re = (v*x)/k;			#Reynold number
q = ((5*x)/math.sqrt(Re))*1000;			#Thickness of boundary layer in mm
Cfx = (0.664/math.sqrt(Re))/10**-3;			#Local skin friction coefficient *10**-3

# Results
print 'Thickness of boundary layer is %3.1f mm Local skin friction coefficient is %3.2f*10**-3'%(q,Cfx)

Thickness of boundary layer is 7.1 mm Local skin friction coefficient is 2.35*10**-3


## Example 7.2 Page No : 275¶

In [1]:
# Variables
Ta = 20;			#Temperature of air in degree C
Tp = 134;			#Temperature of heated plate in degree C
v = 3;			#Velocity of flow in m/s
L = 2;			#Length of plate in m
W = 1.5;			#Width of plate in m
x = 0.4;			#Distance of plane from the plate in m
k = (15.06*10**-6);			#Kinematic vismath.cosity in m**2/s

# Calculations
Tf = (Ta+Tp)/2;			#Film temperature in degree C
pw = 0.998;			#Density of air at 77 degree C
Cp = 1009;			#Specific heat of air at 77 degree C
kw = (20.76*10**-6);			#Kinematic viscosity of air at 77 degree C
k = 0.03;			#Thermal conductivity of air at 77 degree C
Pr = 0.697;			#prantl number of air at 77 degree C
Re = (v*x)/kw;			#Reynolds number
Nu = (0.332*Re**0.5*Pr**(1./3));			#Nusselts number
h = (Nu*k)/x;			#Heat transfer coefficient in W/m**2.K
h1 = (h*2);			#Average value of heat transfer coefficient in W/m**2.K
Q = h1*x*W*(Tp-Ta);			#Heat flow in W
Q1 = (2*Q);			#Heat flow from both sides of the plate in W

# Results
print 'Heat flow from both sides of the plate is %3.0f W'%(round(Q1,-1))

Heat flow from both sides of the plate is 1450 W


## Example 7.3 Page No : 282¶

In [4]:
import math
# Variables
Ta = 20;			#Temperature of air in degree C
v = 3;			#Velocity of flow in m/s
L = 2;			#Length of plate in m
W = 1;			#Width of plate in m
x1 = 0.3;			#Initial point of the boundary layer in m
x2 = 0.8;			#Final point of the boundary layer in m
p = 1.17;			#Density of air at 20 degree C in kg/m**3
k = (15*10**-6);			#Kinematic vismath.cosity in m**2/s
Re = (5*10**5);			#Reynolds number at the transition frm laminar to turbulant

# Calculations
x = (k*Re)/v;		                    	#Critical length in m
Rel = (v*L)/k;                   			#Reynolds number
q = (4.64*L)/math.sqrt(Rel)*1000;			#Boundary layer thickness at the trailing edge of plate in mm
ts = 1.292*(0.5*p*v**2)*math.sqrt(1./Rel);	#Average shear stress in N/m**2
F = (2*L*ts);		                    	#Drag force on the two sides of the plate in N
q80 = (4.64*x2)/math.sqrt((v*x2)/k);			#Boundray layer thickness at x = 0.8 m
q30 = (4.64*x1)/math.sqrt((v*x1)/k);			#Boundray layer thickness at x = 0.3 m
m = ((5./8)*p*v*(q80-q30))/10**-3;			#Mass flow of air in kg/s

# Results
print 'Boundary layer thickness at the trailing edge of plate is % 3.2f mm \n \
Drag force on the two sides of the plate is %3.4f N \n \
Mass flow of air is %3.1f*10**-3 kg/s'%(q,F,m)

Boundary layer thickness at the trailing edge of plate is  14.67 mm
Drag force on the two sides of the plate is 0.0430 N
Mass flow of air is 7.9*10**-3 kg/s


## Example 7.4 Page No : 283¶

In [5]:
import math
# Variables
P = 8.;			#Pressure of air in kN/m**2
Ta = 250.;			#Temperature of air in degree C
L = 1.;			#Length of the palte in m
W = 0.3;			#Width of the plate in m
v = 8.;			#Velocity of air in m/s
Tp = 78.;			#Temperature of plate in degree C

# Calculations
Tf = (Ta+Tp)/2;			#Film temperature in degree C
Cp = 1018;			#Specific heat of air at 164 degree C and 1 atm pressure
kw = (30.8*10**-6);			#Kinematic viscosity of air at 164 degree C and 1 atm pressure
k = 0.0364;			#Thermal conductivity of air at 164 degree C and 1 atm pressure
Pr = 0.69;			#prant number of air at 164 degree C and 1 atm pressure
k1 = kw*(101330/(P*1000));			#Kinematic viscosity of air at 164 degree C and 8kN/m**2 pressure
Re = (v*L)/k1;			#Reynolds number
h = 0.662*(k/L)*math.sqrt(Re)*Pr**(1./3);			#Heat transfer coefficient in W/m.K
Q = 2*h*L*W*(Ta-Tp);			#Rate of heat removal in W

# Results
print 'Rate of heat removal is %3.1f W'%(Q)

#note : answer is slightly different because of rounding off error.

Rate of heat removal is 314.7 W


## Example 7.5 Page No : 286¶

In [8]:
import math
# Variables
P = 8.;			#Pressure of air in kN/m**2
Ta = 250.;			#Temperature of air in degree C
L = 1.;			#Length of the palte in m
W = 0.3;			#Width of the plate in m
v = 8.;			#Velocity of air in m/s
Tp = 78.;			#Temperature of plate in degree C
R = 287.;			#Universal gas constant in J/kg.K

# Calculations
Tf = (Ta+Tp)/2;			#Film temperature in degree C
Cp = 1018;			#Specific heat of air at 164 degree C and 1 atm pressure
kw = (30.8*10**-6);			#Kinematic viscosity of air at 164 degree C and 1 atm pressure
k = 0.0364;			#Thermal conductivity of air at 164 degree C and 1 atm pressure
Pr = 0.69;			#prant number of air at 164 degree C and 1 atm pressure
k1 = kw*(101330/(P*1000));			#Kinematic viscosity of air at 164 degree C and 8kN/m**2 pressure
Re = (v*L)/k1;			#Reynolds number
h = 0.662*(k/L)*math.sqrt(Re)*Pr**(1./3);			#Heat transfer coefficient in W/m.K
Q = 2*h*L*W*(Ta-Tp);			#Rate of heat removal in W
p = (P*1000)/(R*(Tf+273));			#Density in kg/m**3
St = (h/(p*Cp*v));			#Stanton number
Cfx2 = (St*Pr**(2/3));			#Colburn factor
ts = (Cfx2*p*v**2);			#Average shear stress in N/m**2
D = (0.0186*W*L);			#Drag force on one side of plate in N
D2 = (2*D)/10**-3;			#Total drag force on both sides of plate in N

# Results
print 'The drag force exerted on the plate is %3.2f*10**-3 N'%(D2)

The drag force exerted on the plate is 11.16*10**-3 N


## Example 7.6 Page No : 289¶

In [8]:
# Variables
L = 1;			#Length of the palte in m
W = 1;			#Width of the plate in m
Ts = 10;			#Temperature of free strem air in degree C
v = 80;			#Velocity of free stream air in m/s

# Calculations
k = 0.025;			                        #Thermal conductivity of air at 10 degree C
Pr = 0.72;			                        #prant number of air at 10 degree C
v1 = (14.15*10**-6);			            #Kinematic viscosity of air at 10 degree C
Re = (v*L)/v1;			                    #Reynolds number
q = 0.381*L*Re**(-1./5);		        	#Thickness of the boundary layer at the trailing edge of the plate in m
Nu = (0.037*Re**(4./5)*Pr**(1./3));			#Nusselts number
h = (Nu*k)/L;                   			#Mean value of the heat transfer coefficient in W/m**2.K

# Results
print 'Thickness of the boundary layer at the trailing edge of the plate is %3.4f m \n \
Mean value of the heat transfer coefficient is %3.0f W/m**2.K'%(q,h)

Thickness of the boundary layer at the trailing edge of the plate is 0.0170 m
Mean value of the heat transfer coefficient is 209 W/m**2.K


## Example 7.7 Page No : 290¶

In [9]:
# Variables
Ta = 0.;		    	#Temperature of air stream in degree C
Tp = 90.;    		#Temperature of heated plate in degree C
v = 75.;		    	#Speed of air in m/s
L = 0.45;			#Length of the palte in m
W = 0.6;			#Width of the plate in m
Re = (5.*10**5);		#Reynolds number at the transition from laminar to turbulant

# Calculations
Tf = (Ta+Tp)/2;			#Film temperature in degree C
k = 0.028;			#Thermal conductivity of air at 10 degree C
Pr = 0.698;			#prant number of air at 10 degree C
v1 = (17.45*10**-6);			#Kinematic viscosity of air at 10 degree C
x = (Re*v1)/v;			#Critical length in m
Rel = (v*L)/v1;			#Reynolds number
Cfl = ((0.074/Rel**(1./5))-(1740/Rel))/10**-3;			#Average value of friction coefficient *10**-3
Nu = ((0.037*Rel**(4./5))-870)*Pr**(1./3);			#Nussults number
h = (Nu*k)/L;			#Heat transfer coefficient in W/m**2.K
Q = (2*h*L*W*Tp);			#Rate of energy dissipation in W

# Results
print 'Average value of friction coefficient is %3.2f*10**-3 \n \
Heat transfer coefficient is %3.0f W/m**2.K \n \
Rate of energy dissipation is %i W'%(Cfl,h,Q)

# note : book answer is wrong

Average value of friction coefficient is 3.19*10**-3
Heat transfer coefficient is 170 W/m**2.K
Rate of energy dissipation is 8281 W


## Example 7.8 Page No : 296¶

In [11]:
# Variables
D = 0.3;			#Diameter of cylinder in m
L = 1.7;			#Height of cylinder in m
Ts = 30.;			#Surface temperature in degree C
v = 10.;			#Speed of wind in m/s
Ta = 10.;			#Temperature of air in degree C

# Calculations
Tf = (Ta+Ts)/2;			#Film temperature in degree C
k = 0.0259;			#Thermal conductivity of air at 20 degree C
Pr = 0.707;			#prant number of air at 20 degree C
v1 = (15*10**-6);			#Kinematic viscosity of air at 20 degree C
Re = (v*D)/v1;			#Reynolds number
Nu = 0.027*Re**0.805*Pr**(1./3)			#Nusselts number
h = (Nu*k)/D;			#Heat transfer coefficent in W/m**2.K
Q = (h*3.14*D*L*(Ts-Ta));			#Rate of heat loss in W

# Results
print 'Rate of heat loss is %3.1f W'%(Q)

Rate of heat loss is 1230.9 W


## Example 7.9 Page No : 297¶

In [12]:
# Variables
Ta = 27;			#Temperature of air stream in degree C
v = 0.3;			#Velodity of air in m/s
Q = 100;			#Poer of electric bulb in W
Te = 127;			#Temperature of electric bulb in degree C
D = 0.06;			#Diameter of sphere in m

# Calculations
Tf = (Ta+Te)/2;			#Film temperature in degree C
k = 0.03;			#Thermal conductivity of air at 77 degree C
Pr = 0.697;			#prant number of air at 77 degree C
v1 = (2.08*10**-5);			#Kinematic viscosity of air at 77 degree C
Re = (v*D)/v1;			#Reynolds number
h = (k*0.37*Re**0.6)/D;			#Heat transfer coefficient in W/m**2.K
Q = (h*3.14*D**2*(Te-Ta));			#Heat transfer rate in W
Qp = (Q*100)/100;			#Percentage of heat lost by forced convection

# Results
print "Heat transfer rate is %3.2f W \n \
Percentage of power lost due to convection is %3.2f percent"%(Q,Qp)

Heat transfer rate is 12.10 W
Percentage of power lost due to convection is 12.10 percent


## Example 7.10 Page No : 297¶

In [14]:
import math
# Variables
D = 0.015;			#Diamter of copper bus bar in m
Ta = 20;			#Temperature of air stream in degree C
v = 1;			#Velocity of air in m/s
Ts = 80;			#Surface temperature in degree C
p = 0.0175;			#Resistivity of copper in ohm mm**2/m

# Calculations
Tf = (Ta+Ts)/2;			#Film temperature in degree C
k = 0.02815;			#Thermal conductivity of air at 50 degree C
Pr = 0.703;			#prant number of air at 50 degree C
v1 = (18.9*10**-6);			#Kinematic viscosity of air at 50 degree C
Re = (v*D)/v1;			#Reynolds number
Nu = 0.3+(((0.62*math.sqrt(Re)*Pr**(1./3))/(1+(0.4/Pr)**(2./3))**(1./4))*(1+(Re/28200.)**(5./8))**(4./5));			#Nusselts number
h = (Nu*k)/D;			#Heat transfer coefficent in W/m**2.K
I = 1000*3.14*D*math.sqrt((h*(Ts-Ta)*D)/(4*p));			#Current in A

# Results
print 'Heat transfer coefficient between the bus bar and cooling air is %3.2f W/m**2.K \n \
Maximum admissible current intensity for the bus bar is %3.0f A'%(h,I)

Heat transfer coefficient between the bus bar and cooling air is 28.31 W/m**2.K
Maximum admissible current intensity for the bus bar is 899 A


## Example 7.11 Page No : 298¶

In [15]:
# Variables
Ta = 30;			#Temperature of air stream in degree C
v = 25;			#Velocity of stream in m/s
x = 0.05;			#Side of a square in m
D = 0.05;			#Diameter of circular cylinder in m
Ts = 124;			#Surface temperature in degree C

# Calculations
Tf = (Ta+Ts)/2;			#Film temperature in degree C
k = 0.03;			#Thermal conductivity of air at 77 degree C
Pr = 0.7;			#prantL number of air at 77 degree C
v1 = (20.92*10**-6);			#Kinematic viscosity of air at 77 degree C
Re = (v*D)/v1;			#Reynolds number
Nu1 = 0.027*Re**0.805*Pr**(1./3);			#Nussults number for circulat tube
h1 = (Nu1*k)/D;			#Heat tansfer coefficient for circular tube in W/m**2.K
Nu2 = 0.102*Re**0.675*Pr**(1./3);			#Nussults number for square tube
h2 = (Nu2*k)/D;			#Heat transfer coefficient for square tube in W/m**2.K

# Results
print 'Heat transfer coefficient for circular tube is %3.1f W/m**2.K \n \
Heat transfer coefficient for square tube is %3.2f W/m**2.K'%(h1,h2)

Heat transfer coefficient for circular tube is 100.7 W/m**2.K
Heat transfer coefficient for square tube is 91.02 W/m**2.K


## Example 7.12 Page No : 302¶

In [16]:
# Variables
n = 7;			#Number of rows of tube
Ta = 15;			#Temperature of air in degree C
v = 6;			#Velocity of air in m/s
ST = 0.0205;			#Transverse  pitch in m
SD = 0.0205;			#Longitudinal pitch in m
D = 0.0164;			#Outside diameter of the tube in m
Ts = 70;			#Surface temperature in degree C

# Calculations
Tf = (Ta+Ts)/2;			#Film temperature in degree C
k = 0.0274;			#Thermal conductivity of air at 42.5 degree C
Pr = 0.705;			#prant number of air at 42.5 degree C
v1 = (17.4*10**-6);			#Kinematic viscosity of air at 42.5 degree C
p = 1.217;			#Density in kg/m**3
vmax = (v*ST)/(ST-D);			#Maximum velocity in m/s
Re = (vmax*D)/v1;			#Reynolds number
Nu = (1.13*0.518*Re**0.556*Pr**(1./3))*0.97;			#Nusselts number
h = (Nu*k)/D;			#Heat transfer coefficent in W/m**2.K
f = 0.4;			#From Fig. 7.10 on page no 303
g = 1.04;			#From Fig. 7.10 on page no 303
dp = (n*f*p*vmax**2*g)/2;			#Pressure drop in N/m**2

# Results
print 'Heat transfer coefficent is %3.2f W/m**2.K \n \
Pressure drop is %3.0f N/m**2'%(h,dp)

Heat transfer coefficent is 252.04 W/m**2.K
Pressure drop is 1595 N/m**2


## Example 7.13 Page No : 304¶

In [1]:
# Variables
n = 7;			#Number of rows of tube
Ta = 15;			#Temperature of air in degree C
v = 6;			#Velocity of air in m/s
ST = 0.0205;			#Transverse  pitch in m
SD = 0.0205;			#Longitudinal pitch in m
D = 0.0164;			#Outside diameter of the tube in m
Ts = 70;			#Surface temperature in degree C

# Calculations
Tf = (Ta+Ts)/2;			#Film temperature in degree C
k = 0.0253;			#Thermal conductivity of air at 15 degree C
Pr = 0.710;			#prant number of air at 15 degree C
v1 = (14.82*10**-6);			#Kinematic viscosity of air at 15 degree C
p = 1.217;			#Density in kg/m**3
Pr1 = 0.701;			#prant number of air at 70 degree C
vmax = (v*ST)/(ST-D);			#Maximum velocity in m/s
Re = (vmax*D)/v1;			#Reynolds number
Nu = 0.35*Re**0.6*(Pr/Pr1)**0.25;			#
h = (Nu*k)/D;			#Heat transfer coefficient in W/m**2.K

# Results
print ' Heat transfer coefficient is %3.1f W/m**2 K'%(h)

 Heat transfer coefficient is 279.5 W/m**2 K


## Example 7.14 Page No : 305¶

In [18]:
# Variables
m = 0.314;			#Mass flow rate of air in m**3/s
n1 = 7;			#Number of tubes in the direction of flow
n2 = 8;			#Number of tubes perpendicular to the direction of flow
L = 1.25;			#Length of each tube in m
D = 0.019;			#Outer diameter in m
ST = 0.0286;			#Transverse  pitch in m
SD = 0.038;			#Longitudinal pitch in m
Ta = 200;			#Temperature of air in degree C
Ts = 96;			#Surface temperature in degree C

# Calculations
Tf = (Ta+Ts)/2;			#Film temperature in degree C
k = 0.039;			#Thermal conductivity of air at 15 degree C
Pr = 0.688;			#prantl number of air at 15 degree C
v1 = (3*10**-5);			#Kinematic vismath.cosity of air at 15 degree C
vmax = (m/((ST*n2*L)-(D*n2*L)));			#Maximum velocity in m/s
Re = (vmax*D)/v1;			#Reynolds number
Nu = (0.299*Re**0.602*Pr**(1./3));			#Nusselts number
X = 0.96;			#From Table 7.5 on page no.302
Nux = (X*Nu);			#Average nusselts number
h = (Nux*k)/D;			#Convective heat transfer coefficient in W/m**2.K

# Results
print 'Convective heat transfer coefficient is %3.2f W/m**2.K'%(h)

Convective heat transfer coefficient is 51.58 W/m**2.K


## Example 7.15 Page No : 310¶

In [19]:
# Variables
D = 0.2;			#Diameter of pipeline in m
#velocity profile is given by u = 96r-190r**2 m/s
#Temperature profile is given by T = 100(1-2r) degree C

# Calculations
vmax = (64*(D/2))-(95*(D/2)**2);			#Mean velocity in m/s
T = (2/(vmax*(D/2)**2))*(((9600*(D/2)**3)/3)-((38200*(D/2)**4)/4)+((38000*(D/2)**5)/5));			#Average temperature of the fluid in degree C

# Results
print 'Average temperature of the fluid is %3.2f degree C'%(T)

Average temperature of the fluid is 85.17 degree C


## Example 7.16 Page No : 311¶

In [1]:
# Variables
Di = 0.025;			#I.D of the tube in m
Do = 0.04;			#O.D of the tube in m
m = 5.;			#Mass flow rate of water in kg/m
T = [20.,70.];			#Temperature at entry and exit of water in degree C
Q = 10.**7;			#Heat in W/m**3
Ts = 80.;			#Surface temperature in degree C
Cp = 4179.;			#Specific heat of water in J/kg.K

# Calculations
Tb = (T[0]+T[1])/2;			#Film temperature in degree C
L = ((4*(m/60)*Cp*(T[1]-T[0]))/(3.14*(Do**2-Di**2)*Q));			#Length of tube in m
qs = ((Q*(Do**2-Di**2))/(4*Di));			#Heat flux at the surface in W/m**2
h = (qs/(Ts-T[1]));			#Heat transfer coefficient at the outlet in W/m**2.K

# Results
print 'Length of tube is %3.3f m \nHeat transfer coefficient at the outlet is %3.0f W/m**2.K'%(L,h)

Length of tube is 2.275 m
Heat transfer coefficient at the outlet is 9750 W/m**2.K


## Example 7.17 Page No : 312¶

In [21]:
# Variables
k = 0.175;			#Thermal conductivity in W/m.K
Di = 0.006;			#I.D of the tube in m
L = 8;			#Length of the tube in m
dT = 50;			#Mean temperature difference in degree C

# Calculations
h = (3.66*k)/Di;			#Heat transfer coefficient in W/m**2.K
Q = (h*3.14*Di*L*dT);			#Heat transfer rate in W

# Results
print 'Heat transfer coefficient is %3.2f W/m**2.K Heat transfer rate is %3.0f W'%(h,Q)

Heat transfer coefficient is 106.75 W/m**2.K Heat transfer rate is 804 W


## Example 7.18 Page No : 312¶

In [22]:
# Variables
Ti = 25;			#Initial temperature of water in degree C
D = 0.05;			#Diamter of the tube in m
Re = 1600;			#Reynolds number
q = 800;			#Heat flux in W/m
Tf = 50;			#Final temperature of water in degree C

# Calculations
k = 0.61;			#Thermal conductivity of water at 25 degree C in W/m.K
u = (915*10**-6);			#Dynamic viscosity in N.s/m**2
m = (Re*3.14*D*u)/4;			#Mass flow rate of water in kg/s
h = (4.364*k)/D;			#Heat transfer coefficient in W/m**2.K
qs = (q/(3.14*D));			#Constant heat flux in W/m**2
Cp = 4178;			#Specific heat of water in J/kg.K
L = ((m*Cp*(Tf-Ti))/q);			#Length of the tube in m

# Results
print 'Average heat transfer coefficient is %3.2f W/m**2.K \n \
Length of the tube is %3.3f m'%(h,L)

Average heat transfer coefficient is 53.24 W/m**2.K
Length of the tube is 7.502 m


## Example 7.19 Page No : 314¶

In [2]:
# Variables
Di = 0.015;			#I.D of the tube in m
Tb = 60;			#Temperature of the tube in degree C
m = 10;			#Flow rate of water in ml/s
Ti = 20;			#Temperature of water at entry in degree C
x = 1;			#Dismath.tance form the plane in m
Tx = 34;			#Temperature of water at 1 m dismath.tance in degree C

# Calculations
Tbm = (Ti+Tx)/2;			#Mean value of bulk temperature in degree C
pw = 997;			#Density of air at 27 degree C in kg/m**3
Cp = 4180;			#Specific heat of air at 27 degree C in J/kg.K
u = (855*10**-6);			#Dynamic vismath.cosity of air at 27 degree C in N.s/m**2
k = 0.613;			#Thermal conductivity of air at 27 degree C in W/m.K
Pr = 5.83;			#prantl number of air at 27 degree C
us = (464*10**-6);			#Dynamic vismath.cosity of air at 60 degree C in Ns/m**2
um = (m*10**-6)/((3.14/4)*Di**2);			#Mean speed in m/s
Re = (pw*um*Di)/u;			#Reynolds number
Nu = 3.66+((0.0668*(Di/x)*Re*Pr)/(1+(0.04*((Di/x)*Re*Pr)**(2./3))));			#Nusselts number in Haussen correlation
Nux = (1.86*((Re*Pr)/(x/Di))**(1./3)*(u/us)**0.14);			#Nusselsts number in Sieder - Tate correlation

# Results
print 'Nusselts number in Haussen correlation is %3.2f \n \
Nusselsts number in Sieder - Tate correlation is %3.3f'%(Nu,Nux)

Nusselts number in Haussen correlation is 6.90
Nusselsts number in Sieder - Tate correlation is 8.964


## Example 7.20 Page No : 318¶

In [2]:
# Variables
Tw = 50;			#Temperature of water in degree C
Di = 0.005;			#Inner diameter of the tube in m
L = 0.5;			#Length of the tube in m
v = 1;			#Mean velocity in m/s
Ts = 30;			#Surface temperature in degree C

# Calculations
Tf = (Tw+Ts)/2;			#Film temperature in degree C
k = 0.039;			#Thermal conductivity of air at 15 degree C
Pr = 0.688;			#prant number of air at 15 degree C
p = 990;			#Density of air at 50 degree C in kg/m**3
Cp = 4178;			#Specific heat of air at 50 degree C in J/kg.K
v1 = (5.67*10**-7);			#Kinematic viscosity of air at 50 degree C
v2 = (6.57*10**-7);			#Kinematic viscosity of air at 40 degree C
Re = (v*Di)/v1;			#Reynolds number
h = ((0.316/8)*((v*Di*10)/v2)**(-0.25)*p*Cp*v*(4.34)**(-2./3));			#Heat transfer coefficient umath.sing the Colburn anamath.logy in W/m**2.K

# Results
print 'Heat transfer coefficient using the Colburn analogy is %3.0f W/m**2.K'%(h)

Heat transfer coefficient using the Colburn analogy is 3697 W/m**2.K


## Example 7.21 Page No : 319¶

In [27]:
# Variables
Ti = 50;			#Temperature of water at inlet in degree C
D = 0.015;			#Diameter of tube in m
L = 3;			#Length of the tube in m
v = 1;			#Velocity of flow in m/s
Tb = 90;			#Temperature of tube wall in degree C
Tf = 64;			#Exit temperature of water in degree C

# Calculations
Tm = (Ti+Tf)/2;			#Bulk mean temperature in degree C
p = 990;			#Density of air at 57 degree C in kg/m**3
Cp = 4184;			#Specific heat of air at 57 degree C in J/kg.K
u = (0.517*10**-6);			#Kinematic viscosity of air at 57 degree C in m**2/s
k = 0.65;			#Thermal conductivity of air at 57 degree C in W/m.K
Pr = 3.15;			#prantl number of air at 57 degree C
Re = (v*D)/u;			#Reynolds number
Nu = (0.023*Re**(4./5)*Pr**0.4);			#Nusselts number
h = (Nu*k)/D;			#Heat transfer coefficient in W/m**2.K
Q = (h*3.14*D*L*(Tb-Tm))/1000;			#Rate of heat transfered in kW

# Results
print 'Heat transfer coefficient is %3.0f W/m**2.K \nRate of heat transfered is %3.2f kW'%(h,Q)

Heat transfer coefficient is 5861 W/m**2.K
Rate of heat transfered is 27.33 kW


## Example 7.22 Page No : 320¶

In [28]:
# Variables
D = 0.022;			#Diamter of the tube in m
v = 2;			#Average velocity in m/s
Tw = 95;			#Temperature of tube wall in degree C
T = [15,60];			#Initial and final temperature of water in degree C

# Calculations
Tm = (T[0]+T[1])/2;			#Bulk mean temperature in degree C
p = 990;			#Density of air at 37.5 degree C in kg/m**3
Cp = 4160;			#Specific heat of air at 37.5 degree C in J/kg.K
u = (0.69*10**-3);			#Dynamic viscosity of air at 37.5 degree C in Ns/m**2
k = 0.63;			#Thermal conductivity of air at 37.5 degree C in W/m.K
us = (0.3*10**-3);			#Dynamic viscosity of air at 37.5 degree C in Ns/m**2
Re = (p*v*D)/u;			#Reynolds number
Pr = (u*Cp)/k;			#Prantl number
Nu = (0.027*Re**(4./5)*Pr**(1./3)*(u/us)**0.14);			#Nusselts number
h = (Nu*k)/D;			#Heat transfer coefficient in W/m**2.K

# Results
print 'Heat transfer coefficient is %3.0f W/m**2.K'%(h)

Heat transfer coefficient is 9969 W/m**2.K


## Example 7.23 Page No : 320¶

In [29]:
# Variables
D = 0.05;			#Diamter of the tube in m
T = 147;			#Average temperature in degree C
v = 0.8;			#Flow vwlocity in m/s
Tw = 200;			#Wall temperature in degree C
L = 2;			#Length of the tube in m

# Calculations
p = 812.1;			#Density in kg/m**3 of oil at 147 degree C
Cp = 2427;			#Specific heat of oil at 147 degree C in J/kg.K
u = (6.94*10**-6);			#Kinematic viscosity of oil at 147 degree C in m**2/s
k = 0.133;			#Thermal conductivity of oil at 147 degree C in W/m.K
Pr = 103;			#prantl number of oil at 147 degree C
Re = (v*D)/u;			#Reynolds number
Nu = (0.036*Re**0.8*Pr**(1./3)*(D/L)**0.055);			#Nussults number
h = (Nu*k)/D;			#Average heat transfer coefficient in W/m**2.K

# Results
print 'Average heat transfer coefficient is %3.1f W/m**2.K'%(h)

Average heat transfer coefficient is 373.7 W/m**2.K


## Example 7.24 Page No : 321¶

In [31]:
# Variables
D = [0.4,0.8];			#Dimensions of the trunk duct in m
Ta = 20;			#Temperature of air in degree C
v = 7;			#Velocity of air in m/s
v1 = (15.06*10**-6);			#Kinematic viscosity in m**2/s
a = (7.71*10**-2);			#Thermal diffusivity in m**2/h
k = 0.0259;			#Thermal conductivity in W/m.K

# Calculations
Dh = (4*(D[0]*D[1]))/(2*(D[0]+D[1]));			#Value of Dh in m
Re = (v*Dh)/v1;			#Reynolds number
Pr = (v1/a)*3600;			#Prantl number
Nu = (0.023*Re**(4./5)*Pr**0.4);			#Nussults number
h = (Nu*k)/Dh;			#Heat transfer coefficient in W/m**2.K
Q = (h*(2*(D[0]+D[1])));			#Heat leakage per unit length per unit difference in W

# Results
print 'Heat leakage per unit length per unit difference is %3.2f W'%(Q)

Heat leakage per unit length per unit difference is 48.14 W


## Example 7.25 Page No : 322¶

In [33]:
# Variables
Di = 0.03125;			#I.D of the annulus in m
Do = 0.05;			#O.D of the annulus in m
Ts = 50;			#Outer surface temperature in degree C
Ti = 16;			#Temeperature at which air enters in degree C
Tf = 32;			#Temperature at which air exits in degree C
v = 30;			#Flow rate in m/s

# Calculations
Tb = (Ti+Tf)/2;			#Mean bulk temperature of air in degree C
p = 1.614;			#Density in kg/m**3 of air at 24 degree C
Cp = 1007;			#Specific heat of air at 24 degree C in J/kg.K
u = (15.9*10**-6);			#Kinematic viscosity of air at 24 degree C in m**2/s
k = 0.0263;			#Thermal conductivity of air at 24 degree C in W/m.K
Pr = 0.707;			#prantl number of air at 24 degree C
Dh = (4*(3.14/4)*(Do**2-Di**2))/(3.14*(Do+Di));			#Hydraulic diameter in m
Re = (v*Dh)/u;			#Reynolds number
Nu = (0.023*Re**0.8*Pr**0.4);			#Nussults number
h = (Nu*k)/Dh;			#Heat transfer coefficient in W/m**2.K

# Results
print 'Heat transfer coefficient is %3.1f W/m**2.K'%(h)

Heat transfer coefficient is 122.3 W/m**2.K


## Example 7.26 Page No : 324¶

In [34]:
# Variables
T = [120,149];			#Initail and final temperatures in degree C
m = 2.3;			#Mass flow rate in kg/s
D = 0.025;			#Diameter of the tube in m
Ts = 200;			#Surface temperature in degree C

# Calculations
Tb = (T[0]+T[1])/2;			#Bulk mean temperature in degree C
p = 916;			#Density in kg/m**3 of air at 134.5 degree C
Cp = 1356.6;			#Specific heat of air at 134.5 degree C in J/kg.K
u = (0.594*10**-6);			#Kinematic viscosity of air at 134.5 degree C in m**2/s
k = 84.9;			#Thermal conductivity of air at 134.5 degree C in W/m.K
Pr = 0.0087;			#prantl number of air at 134.5 degree C
Q = (m*Cp*(T[1]-T[0]))/1000;			#Total heat transfer in kW
v = (m/(p*(3.14/4)*D**2));			#Velocity of flow in m/s
Re = (v*D)/u;			#Reynolds number
Pe = (Pr*Re);			#Peclet number
Nu = (4.82+(0.0185*Pe**0.827));			#Nussults number
h = (Nu*k)/D;			#Heat transfer coefficient in W/m**2.K
L = ((Q*1000)/(h*3.14*D*(Ts-Tb)));			#Minimum length of the tube in m if the wall temperature is not to exceed 200 degree C

# Results
print 'Minimum length of the tube if the wall temperature is not to exceed 200 degree C is %3.3f m'%(L)

Minimum length of the tube if the wall temperature is not to exceed 200 degree C is 0.361 m