Conduction  Heat Equation  Units Don't Add Up!!by chrissimpson Tags: conduction, equation, heat, units 

#1
Apr212, 10:07 AM

P: 11

Hi there
I have what I think/hope is a simple question: I've been working on heat inputs and outputs in inertia friction welds and have managed to produce a net power term (W) as a function of time. I now want to use that in the heat equation to come up with heating rates, temperature profiles and final cooling rates (these can then be related back to the final weld microstructure). So, the equation I wish to use is: utαuxx=(α/κ)*f(x,t)  a nonhomogeneous pde The problem I'm having with this is that my heat input term is in watts or watts/m^2, not watts/m^3. This is because my heat input is coming from one surface into a long/infinite length bar. When heat generation is in watts/m^3 you get consistent units of K/s throughout the equation. I don't! Any ideas? Cheers Chris 



#2
Apr312, 04:18 AM

P: 11

I think that I may have made a mistake with my formulation of the problem; I actually have a nonhomogeneous boundary condition, so:
ut=αuxx with Neumann boundary conditions of: ux(0,t)=Q/kA  with both sides having units of K/m ux(L,t)=0 Does this seem like the correct way of looking at the problem? Cheers Chris 


Register to reply 
Related Discussions  
Heat conduction through a slab with internal heat generation  Advanced Physics Homework  5  
SI units for Heat transfer equation  Introductory Physics Homework  5  
1D steady state heat conduction equation (Cartisian, Cylindrical and Sperical)  Calculus & Beyond Homework  34  
Equation of heat conduction, vague text book  Differential Equations  7  
Question about heat conduction equation.  Differential Equations  6 