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Lecture 48

MECH 4406 Lecture Notes - Lecture 48: Error Function, Thermal Diffusivity, Grashof Number


Department
Mechanical Engineering
Course Code
MECH 4406
Professor
Sarah Johnson
Lecture
48

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0.0 General
0.1 
 
 

  
0.2 Fourier’s Law

 
 


0.3 Newton’s Law

   
0.4 Stefan-Boltzman Law




  
1.0 Conduction
1.1.0 Fourier’s Law
1.1.1 Cartesian
 





 

 

 

1.1.2 Cylindrical
 






 




 

1.1.3 Spherical
 






 




 


1.2.0 HDE
1.2.1 Cartesian













where
 (thermal diffusivity)
1.2.2 Cylindrical







1.2.3 Spherical









1.3.0 1D Steady Conduction/Electrical Analog

 




 



 
1.3.1 Plane Wall








1.3.2 Cylindrical Wall



 
 

 



 


 
 
 


1.3.3 Spherical Wall






 
  
 

 
  
 
  
  
 

 
1.4 Conduction with



1.5.0 Extended Surfaces and Fins
Infinitely Long Fin (Table 3.4)

1.5.1 Annular Fins
General Fin Equation





Annular Fin:










1.5.2 Fin Arrays
Single Fin

 



Fin Array


 
 

  
 
 
 

1.6.0 Transient Conduction
1.6.1 Lumped Capacitance


 

 




, the error for lumped capacitance method is small




No ,  << , no heat flux:








No ; just , , and flux:



 

1.6.2.0 Transient Conduction w/ Spatial Temp. Variation:






if  only need 1st term of the infinite series
Semi-Infinite Solid
1.6.2.1 Plane Wall 







1.6.2.2 Cylindrical Geometries 






1.6.2.3 Spherical Geometries 







1.6.3.0 Semi-Infinite Solid
1.6.3.1 Case 1 Constant Surface Temperature






1.6.3.2 Case 2 Constant Surface Heat Flux




 
 




1.6.3.3 Case 3 Surface Convection










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