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

U =
θ =
Where ( + B)
54
− τU
e + V
U
B
4 8
V =
G
, ( 1 3 ) B +
4. A long cylinder subjected to heat generation at one side and convective heat transfer on
the other side is considered for the analysis. Based on the analysis a closed form solution
has been obtained.
θ =
− τU
e + V
⎛
2B
⎞
G
U = ⎜ ⎟ V =
⎜1+ B ⎟
Where ⎝ 4 ⎠ ( 1+
B )
, 4
5. Based on the analysis a unique parameter known as modified Boit number obtained from
the analysis and is shown in Table 2 and 3. With higher value of heat source parameter,
the temperature inside the tube does not vary with time. However at lower values of heat
source parameters, the temperature decreases with increase of time. With lower value of
Biot numbers, the temperature inside the tube does not vary with time. For higher value
of Biot numbers, the temperature decreases with the increase of time.
5.2 SCOPE FOR FURTHER WORK
1. Polynomial approximation method can be used to obtain solution of more complex
problem involving variable properties and variable heat transfer coefficients, radiation at
the surface of the slab.
2. Other approximation method, such as Heat Balance Integral method, Biots variation
method can be used to obtain the solution for various complex heat transfer problems.
3. Efforts can be made to analyze two dimensional unsteady problems by employing various
approximate methods.
U