Reference no: EM131007469
1. Derive finite difference equations for all the interior nodes.
2. Develop a MATLAB code, and determine temperatures at all interior nodes.
The generalized heat equation for laser melting is given by
ρc(T)dT/dt = ddx[kx(T)dT/dx] + d/dy[ky(T)dT/dy] + d/dZ[kz(T)dT/dz] + ρc(T)(VxdT/dx + VydT/dY + VzdT/dz) + Q
where
T = temperature of the weldment (K)
k(T) = thermal conductivity of the material (J mm ) as a function of temperature
ρ(T)= density of the matenal (J/mms-1k-1) as a fun cton of temp.
C(T) = specific heat of the material (J/g-1 K-1), as a function of temperature
Vx, Vy and Vz = components of velocity
Q = rate of any internal heat generation. (W/mm3)
Reduce the above equation for steady-state thermal analysis of a system having a stationary heat flux and no-heat generation. Then solve the following problem:
Consider a case where the surface of an aluminum plate is irradiated by a stationary laser so that the steady-state temperature at the laser-irradiated region is defined by Gaussian distribution. The remaining boundaries are maintained room temperature (23°C).
Consider kx = ky = 50 W/m2-K, and grid sizes Δx = Δy = 5, mm.
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Derive finite difference equations for all interior nodes
: Derive finite difference equations for all the interior nodes - develop a MATLAB code, and determine temperatures at all interior nodes.
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