# Introduction to conduction¶

## Example 2.1 Page 68¶

In [1]:
def alpha(p, Cp, k):
a=k/(p*Cp); #[m^2/s]
return a;

p = 2702.;  		#[Kg/m^3] - Density Of Material
Cp = 903.; 			#[J/kg.K] - Specific heat of Material
k = 237.;    		#[W/m.k] - Thermal Conductivity of Material

print '%s %.2e %s' %("\n (a) Thermal Diffuisivity of Pure Aluminium at 300K = ",alpha(p, Cp, k)," m^2/s\n");

#(b) Pure Aluminium at 700K
# From Appendix A, Table A.1

p = 2702.;  		#[Kg/m^3] - Density Of Material
Cp = 1090.; 		#[J/kg.K] - Specific heat of Material
k = 225.;    		#[W/m.k] - Thermal Conductivity of Material

print '%s %.2e %s' %("\n (b) Thermal Diffuisivity of Pure Aluminium at 700K =",alpha(p, Cp, k)," m^2/s\n");

#(c) Silicon Carbide at 1000K
# From Appendix A, Table A.2

p = 3160.;  		#[Kg/m^3] - Density Of Material
Cp = 1195.; 		#[J/kg.K] - Specific heat of Material
k = 87.;    		#[W/m.k] - Thermal Conductivity of Material

print '%s %.2e %s' %("\n (c) Thermal Diffuisivity of Silicon Carbide at 1000K =",alpha(p, Cp, k)," m^2/s\n");

#(d) Paraffin at 300K
# From Appendix A, Table A.3

p = 900.;  			#[Kg/m^3] - Density Of Material
Cp = 2890.; 		#[J/kg.K] - Specific heat of Material
k = .24;    		#[W/m.k] - Thermal Conductivity of Material

print '%s %.2e %s' %("\n (d) Thermal Diffuisivity of Paraffin at 300K = ",alpha(p, Cp, k),"m^2/s");
#END

 (a) Thermal Diffuisivity of Pure Aluminium at 300K =  9.71e-05  m^2/s

(b) Thermal Diffuisivity of Pure Aluminium at 700K = 7.64e-05  m^2/s

(c) Thermal Diffuisivity of Silicon Carbide at 1000K = 2.30e-05  m^2/s

(d) Thermal Diffuisivity of Paraffin at 300K =  9.23e-08 m^2/s


## Example 2.2 Page 75¶

In [2]:
a = 900.;    			#[degC]
b = -300.;   			#[degC/m]
c = -50.;    			#[degC/m^2]

q = 1000.;    			#[W/m^2.K] - Uniform heat Generation
A = 10. ;      			#[m^2]    - Wall Area
#Properties of Wall
p = 1600.;    			#[kg/m^3]  - Density
k = 40.;      			#[W/m]    - Thermal Conductivity
Cp = 4000.;   			#[J/kg.K]  - Specific Heat
L = 1;      			  #[m]    - Length of wall
#calculations and results

#(i) Rate of Heat Transfer entering the wall and leaving the wall
# From Eqn 2.1
# qin = -kA(dT/dx)|x=0 = -kA(b)

qin= - b*k*A;

# Similarly
# qout = -kA(dT/dx)|x=L = -kA(b+2cx)|x=L

qout= - k*A*(b+2*c*L);

print '%s %d %s' %("\n (i) Rate of Heat Transfer entering the wall =",qin," W ");
print '%s %d %s' %("\n And leaving the wall =",qout,"W ");

#(ii) Rate of change Of Energy Storage in Wall Est
# Applying Overall Energy Balance across the Wall
#Est = Ein + Eg + Eout = qin + qAL - qout
Est = qin + q*A*L - qout;

print '%s %d %s' %("\n (ii) Rate of change Of Energy Storage in Wall =",Est," W\n");

#(iii) Time rate of Temperature change at x= 0, 0.25 and .5m
#Using Eqn 2.19
# T= dT/dt = (k/p*Cp)*d(dT/dx)/dx + q/p*Cp
#As d(dT/dx)/dx = d(b + 2cx)/dx = 2c - Independent of x
T = (k/(p*Cp))*(2*c)+ q/(p*Cp);
print '%s %.6f %s' %("\n (iii) Time rate of Temperature change independent of x =",T," degC/s\n");

#END

 (i) Rate of Heat Transfer entering the wall = 120000  W

And leaving the wall = 160000 W

(ii) Rate of change Of Energy Storage in Wall = -30000  W

(iii) Time rate of Temperature change independent of x = -0.000469  degC/s