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

Substituting the value of θ at above equation we have
Integrating equation (3.123) we get
∂ θ 8Bθ
=−
∂ τ 4 + B
(3.147)
∂ θ 8B
= − ∂τ
θ B + 4
1 1
∫ ∫
0 0
Thus by simplifying the above equation we may write
θ = exp( −Pτ)
Or we may write
Where
42
(3.148)
⎛ 8B
⎞
θ = exp⎜−
τ ⎟
⎝ B + 4 ⎠ (3.149)
(3.150)
8B
P =
B + 4
(3.151)
Several profiles have been considered for the analysis. The corresponding modified Biot number,
P, has been deduced for the analysis and is shown in Table 4.3.
3.8 CLOSURE
At this section we have covered different heat conduction problems for the analysis. The
analytical method used here is polynomial approximation method. Two problems are taken for
heat flux, and two for heat generation. At the last a simple slab and cylinder is considered with
different profiles. The result and discussion from the above analysis has been presented in the
next chapter. Furthermore, the present prediction is compared with the analysis of P. Keshavarz
and M. Taheri[1] , Jian Su [2] and E.J. Correa, R.M. Cotta [4].