∂/∂x (λ ∂T/∂x)+ ∂/∂y (λ ∂T/∂y)+ ∂/∂z (λ ∂T/∂z)+ q_v= ρC_p ∂T/∂t------1
T - Temperature (Temperature of the material) ρ - Density of the material C_p - Specific heat capacity of the material t - time q_v - rate of internal heat generation (W/m3)
The above equation is a 3D Transient heat condcution equation with q_v is the internal heat generation term. I am pretty much confused with term q_v.
I work with laser applications with laser processing of materials. My question is that when I use laser as my source for heating the material. How should I substitute the laser source term into the above heat conduction equation ?. Since q_v is a heat generation term I cannot use laser source into q_v. Is my thing right ?
Another possible way is to incorporate the laser source term as heat flux with a boundary conditon as shown below.
λ ∂T/∂x=q ------- 2
q- laser heat flux (w/m2) λ - thermal conductivity
Which is the right way to include the laser source term ? Either with equation 2 or 1?
Any help will be appreciated?