analysis of transient heat conduction in different geometries - ethesis ...

∂T 1 ∂ ⎛ m ∂T
⎞
= α r G
m ⎜ ⎟+
∂t r ∂r⎝ ∂r
⎠ (3.47)
Fig 3.3: Schematic of slab with heat generation
Where, m = 0 for slab, 1 and 2 for cylinder and sphere, respectively. Here we have considered
slab geometry. Putting m=0, equation (3.47) reduces to
Boundary conditions
2
∂T ∂ T
= α + G 2
∂t ∂ r
(3.48)
∂ T
k = 0
∂ r at r = 0
(3.49)
∂ T
k =−h( T −T∞)
∂ r
at r = R
(3.50)
Initial condition T=T0 at t=0 (3.51)
Dimensionless parameters defined as
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