Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates

Table 1

A comparison between three-point central difference, five-point central difference, and exact solutions for , , and at .

	Three-point	Five-point	Exact
0.00	0.000000000000000	0.000000000000000	0.000000000000000
0.04	0.141167318169372	0.141166758064519	0.141166884260490
0.08	0.279851722594559	0.279851442827940	0.279851504083418
0.12	0.413620240060011	0.413620053894126	0.413620092689910
0.16	0.540134995908254	0.540134856713342	0.540134883710731
0.20	0.657199736440746	0.657199625616869	0.657199645115001
0.24	0.762802389453587	0.762802297753132	0.762802311937449
0.28	0.855153914264679	0.855153836454283	0.855153846609828
0.32	0.932722595399281	0.932722528256234	0.932722535221977
0.36	0.994263078395229	0.994263019815159	0.994263024185258
0.40	1.038839561708914	1.038839510257916	1.038839512481672
0.44	1.065842682476337	1.065842637145032	1.065842637580800
0.48	1.074999766554258	1.074999726612890	1.074999725558872
0.52	1.066378252502174	1.066378217410049	1.066378215122743
0.56	1.040382242096527	1.040382211442770	1.040382208148242
0.60	0.997742273569401	0.997742247032389	0.997742242933349
0.64	0.939498554978806	0.939498532297632	0.939498527577856
0.68	0.866978030944270	0.866978011898022	0.866978006725110
0.72	0.781765783532420	0.781765767924871	0.781765762451923
0.76	0.685671384652756	0.685671372300945	0.685671366667532
0.80	0.580690920462760	0.580690911188447	0.580690905521146
0.84	0.468965495818468	0.468965489441841	0.468965483854484
0.88	0.352737096917630	0.352737093252795	0.352737087846569
0.92	0.234302741522606	0.234302740374549	0.234302735238026
0.96	0.115967877485432	0.115967878648705	0.115967873857390
1.00	0.000000000000000	0.000000000000000	0.000000000000002