@article{article_97829, title={TEMPORAL DIFFERENTIAL TRANSFORM AND SPATIAL FINITE DIFFERENCE METHODS FOR UNSTEADY HEAT CONDUCTION EQUATIONS WITH ANISOTROPIC DIFFUSIVITY}, journal={Gazi University Journal of Science}, volume={27}, pages={1063–1076}, year={2014}, author={Çilingir Süngü, İnci and Sungu, İ. Cilingir and Demir, Huseyin and Demır, H.}, keywords={Differential Transform Method; Finite-difference approximation; Heat conduction; anisotropic diffusivity time-dependent heating}, abstract={<!--[if gte mso 9]> <xml> <o:OfficeDocumentSettings> <o:RelyOnVML /> <o:AllowPNG /> </o:OfficeDocumentSettings> </xml> <![endif]--> <span style="font-size: 12.0pt; line-height: 115%; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman"; color: black; mso-ansi-language: EN-US; mso-fareast-language: TR; mso-bidi-language: AR-SA; mso-bidi-font-weight: bold;" lang="EN-US">Three unsteady heat conduction problems with anisotropic diffusivity and time-dependent heating or heat flux and/or heat source are considered in showing the utility of a hybrid method involving a combination of temporal differential transform and spatial finite difference methods. The segregation of time from the spatial component is the greatest advantage of the hybrid method that exhibits no instability of finite difference methods generally seen with parabolic equations. The easy-to-implement algorithm that is essentially a Poisson solver works with both linear and non-linear heat transport problems without any difficulty of sorts. To gain confidence in the results some simulation results are also presented of problems that have an Adomian solution. The method can be used in practical heat transfer problems concerning non-uniform materials like composites, alloys, heterogeneous porous media with thermal equilibrium or non-equilibrium, multi-layered media and such other problems. </span> <!--[if gte mso 9]> <xml> <w:WordDocument> <w:View>Normal </w:View> <w:Zoom>0 </w:Zoom> <w:TrackMoves /> <w:TrackFormatting /> <w:HyphenationZone>21 </w:HyphenationZone> <w:PunctuationKerning /> <w:ValidateAgainstSchemas /> <w:SaveIfXMLInvalid>false </w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false </w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false </w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF /> <w:LidThemeOther>TR </w:LidThemeOther> <w:LidThemeAsian>X-NONE </w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE </w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables /> <w:SnapToGridInCell /> <w:WrapTextWithPunct /> <w:UseAsianBreakRules /> <w:DontGrowAutofit /> <w:SplitPgBreakAndParaMark /> <w:DontVertAlignCellWithSp /> <w:DontBreakConstrainedForcedTables /> <w:DontVertAlignInTxbx /> <w:Word11KerningPairs /> <w:CachedColBalance /> </w:Compatibility> <m:mathPr> <m:mathFont m:val="Cambria Math" /> <m:brkBin m:val="before" /> <m:brkBinSub m:val="--" /> <m:smallFrac m:val="off" /> <m:dispDef /> <m:lMargin m:val="0" /> <m:rMargin m:val="0" /> <m:defJc m:val="centerGroup" /> <m:wrapIndent m:val="1440" /> <m:intLim m:val="subSup" /> <m:naryLim m:val="undOvr" /> </m:mathPr> </w:WordDocument> </xml> <![endif]--> <!--[if gte mso 9]> <xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true" DefSemiHidden="true" DefQFormat="false" DefPriority="99" LatentStyleCount="267"> <w:LsdException Locked="false" Priority="0" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Normal" /> <w:LsdException Locked="false" Priority="9" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="heading 1" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8" /> <w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9" /> <w:LsdException Locked="false" Priority="39" Name="toc 1" /> <w:LsdException Locked="false" Priority="39" Name="toc 2" /> <w:LsdException Locked="false" Priority="39" Name="toc 3" /> <w:LsdException Locked="false" Priority="39" Name="toc 4" /> <w:LsdException Locked="false" Priority="39" Name="toc 5" /> <w:LsdException Locked="false" Priority="39" Name="toc 6" /> <w:LsdException Locked="false" Priority="39" Name="toc 7" /> <w:LsdException Locked="false" Priority="39" Name="toc 8" /> <w:LsdException Locked="false" Priority="39" Name="toc 9" /> <w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption" /> <w:LsdException Locked="false" Priority="10" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Title" /> <w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font" /> <w:LsdException Locked="false" Priority="11" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Subtitle" /> <w:LsdException Locked="false" Priority="22" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Strong" /> <w:LsdException Locked="false" Priority="20" SemiHidden="false" UnhideWhenUsed="false" QFormat="true" Name="Emphasis" /> <w:LsdException Locked="false" Priority="59" SemiHidden="false" UnhideWhenUsed="false"}, number={4}, publisher={Gazi University}