Contents of the Exact Analytical Conduction Toolbox

Heat Equation, Cartesian, 1D Slab Body

X11B(3,J)0T0 Power variation at x = 0 for the X11 case

X11B10T0 Slab with jump in temperature at one boundary, zero temperature at other boundary

X11B60T0 Slab body with cosine-periodic temperature variation at x=0, and zero temperature at x=L

X12B(3,J)0T0 Power variation at the surface for the X12 case

X12B10T0 Slab with jump in temperature at one boundary, zero heat flux at other boundary

X12B60T0 Slab body with cosine-periodic temperature variation at x=0, and insulated boundary at x=L.

X13B10T0 Slab with jump in temperature at one boundary, dissipating heat by convection into a zero temperature environment at x=L

X13B60T0 Slab body with cosine-periodic temperature variation at x=0 and convection at x=L.

X21B(3,J)0T0 Slab body with power law heat flux at x = 0 and fixed temperature at x = L

X21B10T0 Slab with jump in heat flux at one boundary, zero temperature at other boundary

X21B60T0 Slab with cosine-periodic heating at one boundary, zero temperature at other boundary.

X22B00T0Gx5 Slab with partial volumetric heat source and zero heat flux at both boundaries

X22B10T0 Slab with jump in heat flux at one boundary, zero heat flux at other boundary

X22B20T0 Slab subject to a linearly-in-time variable heat flux at one boundary, initially at zero temperature and thermally insulated at the other boundary

X22B60T0 Slab with cosine-periodic heating at one boundary, insulated at other boundary

X23B10T0 Slab with jump in heat flux at one boundary, dissipating heat by convection into a zero temperature environment at x=L.

X23B40T0 Slab with exponential heat flux at one boundary, convection at other boundary

X23B60T0 Slab body with cosine-periodic heat flux at x=0 and convection at x=L

X31B10T0 Slab heated by convection with jump in environment temperature at one boundary and zero temperature at other boundary

X31B60T0 Slab body with cosine-periodic fluid convection at x=0 and zero temperature at x=L.

X32B10T0 Slab heated by convection with environment at constant temperature on one boundary and thermally insulated on the other boundary

X32B20T0 Slab wall heated by convection with fluid temperature linearly increasing in time and second boundary insulated

X32B60T0 Slab body with cosine-periodic fluid convection at x=0 that is thermally insulated at x=L.

X33B00Tx4 Slab body with exponential initial condition at x=0 from laser flash and convection into ambient environment at x=0 and x=L

X33B11T1G1 Slab body with prescribed convection, surface heat flux, volumetric source, and initial temperatures

X33B50G(x5)T5 Slab body with piecewise-in-time convection at x = 0 and homogeneous convection at x = L, volumetric heating that is piecewise-in-space and constant-in-time, and piecewise initial condition.

X33B60T0 Slab body with cosine-periodic fluid convection at x=0 and convection cooling at x=L.

X33B70T0 Slab body initially at ambient temperature with flash heating at x=0 and convection into ambient environment at x=0 and x=L

X42B10T00 Slab in perfect contact with a high-conductivity surface layer with zero initial temperature and subject to a jump in boundary heat flux, initially at zero temperature and zero heat flux on the back side

X62B10T00 Slab in imperfect contact with a high-conductivity surface layer with zero initial temperature and subject to a jump in boundary heat flux, initially at zero temperature and zero heat flux on the back side