Heat PDE

1.1 Homogeneous Heat PDE in 1D. bounded domain. (No source term)

1.1.1 Pure diﬀusion. Both ends at zero temperature

1.1.2 Pure diﬀusion. Left end at non zero temperature, right end zero temperature

1.1.3 Pure diﬀusion. Both ends insulated

1.1.4 Pure diﬀusion. Left end insulated, right end at non-zero temperature

1.1.5 Diﬀusion-Reaction. Case when both ends insulated

1.1.6 Pure diﬀusion. Left end nonhomogeneous time dependent Neumann, right end at zero temperature

1.1.7 Pure diﬀusion. Left end nonhomogeneous and time dependent Dirichlet, right end at zero temperature

1.1.8 Pure diﬀusion. Both ends at ﬁxed non-zero temperature (not time dependent)

1.1.9 Pure diﬀusion. Both ends at temperature that is time dependent

1.1.10 Diﬀusion-Reaction. Both ends at zero temperature, no source. reaction term is \(xu(x,t)\)

1.1.11 Diﬀusion-Convection. Both ends at zero temperature, no source. (also called advection)

1.2 Nonhomogeneous heat PDE in 1D bounded domain. (Source term present)

1.2.1 Both ends at temperature that depends on time. Source term depends on x only

1.2.2 Both ends at temperature that depends on time. Source term depends on x and t

1.2.3 Both ends at zero temperature. Source term depends on \(x\) only

1.2.4 Both ends at zero temperature. Source term depends on \(x\) and \(t\)

1.2.5 Left end at ﬁxed temperature, right end zero temperature. Source term depends on \(x\) and \(t\).

1.2.6 Both ends at ﬁxed temperature (not time dependent). Source term depends on x only

1.2.7 Both ends at ﬁxed temperature. Source term depends on x and t

1.3 Homogeneous Heat PDE in 1D, Semi-inﬁnite domain, No source. Laplace Transform method

1.3.1 Left end at zero temperature, No source term, zero initial conditions

1.3.2 Left end at temperature that depends on time. No source term, zero initial conditions

1.4 Heat PDE in 2D

1.4.1 Heat PDE in 2D inside a Disk, zero temperature at boundary (circumference) of disk.

1.4.2 Heat PDE in 2D inside a Disk, insulated boundary conditions

1.1.1 Pure diﬀusion. Both ends at zero temperature

1.1.2 Pure diﬀusion. Left end at non zero temperature, right end zero temperature

1.1.3 Pure diﬀusion. Both ends insulated

1.1.4 Pure diﬀusion. Left end insulated, right end at non-zero temperature

1.1.5 Diﬀusion-Reaction. Case when both ends insulated

1.1.6 Pure diﬀusion. Left end nonhomogeneous time dependent Neumann, right end at zero temperature

1.1.7 Pure diﬀusion. Left end nonhomogeneous and time dependent Dirichlet, right end at zero temperature

1.1.8 Pure diﬀusion. Both ends at ﬁxed non-zero temperature (not time dependent)

1.1.9 Pure diﬀusion. Both ends at temperature that is time dependent

1.1.10 Diﬀusion-Reaction. Both ends at zero temperature, no source. reaction term is \(xu(x,t)\)

1.1.11 Diﬀusion-Convection. Both ends at zero temperature, no source. (also called advection)

1.2 Nonhomogeneous heat PDE in 1D bounded domain. (Source term present)

1.2.1 Both ends at temperature that depends on time. Source term depends on x only

1.2.2 Both ends at temperature that depends on time. Source term depends on x and t

1.2.3 Both ends at zero temperature. Source term depends on \(x\) only

1.2.4 Both ends at zero temperature. Source term depends on \(x\) and \(t\)

1.2.5 Left end at ﬁxed temperature, right end zero temperature. Source term depends on \(x\) and \(t\).

1.2.6 Both ends at ﬁxed temperature (not time dependent). Source term depends on x only

1.2.7 Both ends at ﬁxed temperature. Source term depends on x and t

1.3 Homogeneous Heat PDE in 1D, Semi-inﬁnite domain, No source. Laplace Transform method

1.3.1 Left end at zero temperature, No source term, zero initial conditions

1.3.2 Left end at temperature that depends on time. No source term, zero initial conditions

1.4 Heat PDE in 2D

1.4.1 Heat PDE in 2D inside a Disk, zero temperature at boundary (circumference) of disk.

1.4.2 Heat PDE in 2D inside a Disk, insulated boundary conditions