# Chapter 12: Convection Heat Transfer1¶

## Exa 12.1¶

In [1]:
#An electrically heated vertical plate, 5 in square has a temperature of
#150 F and is being cooled by natural convection in 50 F air. What is the
#heat transfer rate from both sides of the plate?
import math
#initialisation of variables
d= 5. 								#ft
Tw= 150. 							#F
T= 50 								#F
Pr= 0.72
k= 0.015 							#Btu/hr ft F
r= 1.76*1000000. 					#(F ft^3)^-1
#CALCULATIONS
D= d*(0.42/5.) 						#Diameter
dt= Tw-T 							#change in temp
Gr= r*D*D*D*dt 						#Grashof number
z= Gr*Pr
h= 0.59*(math.pow(z,(0.25))) *(k/D) #Heat transfer coefficient
q= (2*h*dt*d*d)/144. 				#Heat transfer rate
#RESULTS
print '%s %.2f' % ('Heat transfer rate from both sides of the plate (Btu/hr) = ',q)
raw_input('press enter key to exit')

Heat transfer rate from both sides of the plate (Btu/hr) =  40.50
press enter key to exit

Out[1]:
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## Exa 12.2¶

In [2]:
#Cooling water at an average temperature of 70 F flows through a tube of
#0.9 in ID, with an average velocity of 7 ft/s. What is the heat transfer
#coefficient when the flow is fully developed?
#initialisation of variables
import math
T= 70. 										#F
l= 0.9 										#in
v= 7. 										#ft/s
d= 62.3 									#lbm/ft^3
m= 6.58*math.pow(10,-4) 					#lbm/ft s
Pr= 6.82
k= 0.347 									#Bt/hr ft F
#CALCULATIONS
l1= l*0.075/l
Re= (d*v*l1)/m 								#Reynold's number
Nu= 0.023*math.pow(Re,0.8)*math.pow(Pr,0.4) #Nusselt number
h= Nu*k/l1 									#Transfer coefficient
#RESULTS
print '%s %.2f' % ('Heat transfer coefficient when the flow is fully devoloped (Btu/hr ft^2 F) = ',h)
raw_input('press enter key to exit')

Heat transfer coefficient when the flow is fully devoloped (Btu/hr ft^2 F) =  1311.13
press enter key to exit

Out[2]:
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## Exa 12.3¶

In [3]:
#Air at 1 atm pressure and a mixing cup temperature of 450k flows through
#a 3 cm diameter tube with a velocity of 6 m/s. determine the heat transfer
#rate per unit length if tube if a constant heat flux condition is maintained
#at the tube wall and the wall temperature is 10 C above the air temperature
import math
#initialisation of variables
P= 1 										#atm
d= 0.783 									#Kg/m^3
K= 0.0371 									#W/m C
m= 2.48*math.pow(10,-5) 					#Ns/m^2
Pr= 0.683
D= 0.03 									#m
v= 6 										#m/s
T= 10 										#C
#CALCULATIONS
Re= d*v*D/m 								#Reynolds number
Nu= 0.023*math.pow(Re,0.8)*math.pow(Pr,0.4) #Nusselt number
h= Nu*K/D 									#Heat transfer coefficient
ql= h*math.pi*D*T 							#Heat transfer rate
#RESULTS
print '%s %.2f' % ('Heat transfer rate per unit lenght (W/m) = ',ql)
raw_input('press enter key to exit')

Heat transfer rate per unit lenght (W/m) =  23.21
press enter key to exit

Out[3]:
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## Exa 12.4¶

In [4]:
#Air at 1 atm pressure and 25 C flows past a horizontal 5 cm diameter with
#a velocity of 46 m/s. If the surface of the cylinder is kept at 135 C, determine
#the rate of heat flow from the cylinder
import math
#initialisation of variables
T= 25 						#C
P= 1 						#atm
v= 46 						#m/s
d= 5 						#cm
T1= 135 					#C
d1= 0.998 					#kg/m^3
k= 0.03 					#W/m C
m= 2.08*math.pow(10,-5) 	#Kg/s m
c= 0.024
n= 0.81
#CALCULATIONS
Tf= (T+T1)/2. 				#Final temp.
D= d/100.
Re= d1*v*D/m 				#Reynolds number
h= c*math.pow(Re,0.81)*k/D 	#Heat transfer coefficient
dt= T1-T 					#temp diff.
ql= h*math.pi*D*dt 			#Heat transfer rate
#RESULTS
print '%s %.2f' % ('Heat transfer rate per unit lenght of cylinder (W/m) = ',ql)
raw_input('press enter key to exit')

Heat transfer rate per unit lenght of cylinder (W/m) =  3023.70
press enter key to exit

Out[4]:
''