Analytic Solutions for Heat Conduction in Functionally Graded Circular Hollow Cylinders with Time-Dependent Boundary Conditions

Table 1

Temperature distribution of FG circular hollow cylinders with constant value of 𝛽₂ and various parameters of 𝛽₁ and 𝐶₀ at 𝜏=0.5, [𝑘_𝑚=1, 𝑐_𝑚=1, 𝜃(1,𝜏)=(𝐶₀sin𝜔𝜏)𝜃₂∶𝜃₂=4 and 𝜔=2.5].

𝐶0	𝛽1	𝛽2	𝜉
			0.5	0.6	0.7	0.8	0.9	1.0
0.1	0.75	1	0	4.595	2.259	1.845	1.632	0.380
	1		0	4.592	2.285	1.990	1.820	0.380
	1.25		0	4.486	2.279	2.133	1.975	0.380
1	0.75	1	0	45.952	22.589	18.453	16.320	3.796
	1		0	45.920	22.848	19.895	18.202	3.796
	1.25		0	44.865	22.788	21.329	19.752	3.796
10	0.75	1	0	459.520	225.888	184.526	163.201	37.959
	1		0	459.196	228.480	198.950	182.017	37.959
	1.25		0	448.647	227.881	213.290	197.520	37.959