Clear["Global`*"]vars={Θ[t,x],t,{x}};Ω=Line[{{0},{1/5}}];=0.0;=1.0;tau=600;tend=4800;(*IBVP1*)pars=<|"MassDensity"->1.2,"SpecificHeatCapacity"->1006.14,"ThermalConductivity"->0.026|>;pars["HeatFlux"]=0;(*boundaryconditionatx=1/5*)pars["SurfaceTemperature"]=Sin[2πt/tau];(*boundaryconditionatx=0asasin-function*)pars["HeatSource"]=0;(*noheatsource*)ics=Θ[0,x]==;(*initialconditionatt=0*)eqn={HeatTransferPDEComponent[vars,pars]==HeatFluxValue[x==1/5,vars,pars],HeatTemperatureCondition[x==0,vars,pars]}Tfun=NDSolveValue[{eqn,ics},Θ,{t,0,tend},x∈Ω];(*alternativeformulationasIBVP2*)vars2={U[t,x],t,{x}};Ω2=Line[{{0},{1/5}}];pars2=<|"MassDensity"->1.2,"SpecificHeatCapacity"->1006.14,"ThermalConductivity"->0.026|>;pars2["HeatFlux"]=0;(*boundaryconditionatx=1/5*)pars2["SurfaceTemperature"]=0;(*boundaryconditionatx=0*)pars2["HeatSource"]=-2π/tauCos[2πt/tau];(*heatsourceasasin-function;afactorof1000willimprovetheresult,why??*)ics2=U[0,x]==;(*initialconditionatt=0*)eqn2={HeatTransferPDEComponent[vars2,pars2]==HeatFluxValue[x==1/5,vars2,pars2],HeatTemperatureCondition[x==0,vars2,pars2]}Tfun2=NDSolveValue[{eqn2,ics2},U,{t,0,tend},x∈Ω2];(*plottingbothsolutions*)Manipulate[Show[Plot[Tfun[t,x],{x,-0.01`,0.2`},PlotStyle->Green,Sequence[PlotRange->{Full,{-1,1}},AxesLabel->{"x","Θ"},Prolog->{LightGray,Rectangle[{0,-1},{0.2,1}]},AxesOrigin->{0,0}]],Plot[Tfun2[t,x]+Sin[2πt/tau]+0.005,{x,-0.01`,0.2`},PlotStyle->White,Sequence[PlotRange->{Full,{-1,1}},AxesLabel->{"x","Θ"},Prolog->{LightGray,Rectangle[{0,-1},{0.2,1}]},AxesOrigin->{0,0}]]],{{t,0},0,tend,20},SaveDefinitions->True]
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