5 added 1 character in body edited Sep 19 '18 at 13:40 xzczd 29.8k66 gold badges8484 silver badges276276 bronze badges Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefortherefore using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefore using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. 4 added 51 characters in body edited Mar 7 '18 at 11:40 J. M. will be back soon♦ 101k1010 gold badges319319 silver badges478478 bronze badges Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc sourceTemperature rise in a semi-infinite medium heated by a disc source) and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. 3 added 85 characters in body edited Mar 7 '18 at 11:20 ferodeto 1844 bronze badges Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a what,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a what I understand is a correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0])  while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. Good day community, I try to solve the 2D heat equation in cylindrical coordinates. I wanna follow a paper (Selim et al.: Temperature rise in a semi-infinite medium heated by a disc source) and therefor using a Laplace transform and a Hankel transform, subsequently, and there I encountered a problem. I'll jump right in, my equation is: eqn = D[T[r, z, t], {r, 2}] + 1/r D[T[r, z, t], r] + D[T[r, z, t], {z, 2}] == 1/[Alpha] D[T[r, z, t], t]  lapl = LaplaceTransform[eqn,t,p] gives me a ,what I understand is a, correct result: LaplaceTransform[(T^(0,2,0))[r,z,t],t,p]+LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r+ LaplaceTransform[(T^(2,0,0))[r,z,t],t,p]== (p LaplaceTransform[T[r,z,t],t,p]-T[r,z,0])/[Alpha]  However, when applying HankelTransform[lapl,r,s,0] the result I'm getting is: HankelTransform[LaplaceTransform[(T^(0,2,0))[r,z,t],t,p],r,s,0]+ HankelTransform[LaplaceTransform[(T^(1,0,0))[r,z,t],t,p]/r,r,s,0]+ HankelTransform[LaplaceTransform[(T^(2,0,0))[r,z,t],t,p],r,s,0]== (1/[Alpha])(p HankelTransform[LaplaceTransform[T[r,z,t],t,p],r,s,0]- HankelTransform[T[r,z,0],r,s,0]) ` while, based on the paper, I'm supposed to get: $$\frac{\mathrm d^2 \overline{T_0}}{\mathrm dz^2}-\left(s^2+\frac{p}{\alpha}\right)\overline{T_0}=0$$ (In case the output is to tiring to read, as summary: there is no occurrence of s whatsoever, which makes doubt the correctness.) Do I use the functions in wrong way (which I suppose is more likely) or is Mathematica (11.2) not able to transform this kind of input. Thanks in advance and forgive me my poor formatting skills. 2 added 111 characters in body; edited tags; edited title edited Mar 7 '18 at 9:47 J. M. will be back soon♦ 101k1010 gold badges319319 silver badges478478 bronze badges 1 asked Mar 7 '18 at 9:41 ferodeto 1844 bronze badges