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

We consider the heat conduction in a tube of diameter 2R, initially at a uniform temperature T0,
having heat generation (G) inside it and exchanging heat by convection at another side. A
constant heat transfer coefficient (h) is assumed on the other side and the ambient temperature
(T∞) is assumed to be constant. Assuming constant physical properties, k and α, the generalized
transient heat conduction valid for slab, cylinder and sphere can be expressed as:
Fig 3.4: Schematic of cylinder with heat generation
∂T 1 ∂ ⎛ m ∂T
⎞
= α r G
m ⎜ ⎟+
∂t r ∂r⎝ ∂r
⎠ (3.73)
Where, m = 0 for slab, 1 and 2 for cylinder and sphere, respectively. Here we have considered
tube geometry. Putting m=1, the above equation reduces to
Boundary conditions
2
∂T ∂ T
= α + G 2
∂t ∂ r
(3.74)
∂ T
k = 0
∂ r at r = 0
(3.75)
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