Model one dimensional transient heat flow across slabs accurately. Track node temperatures, stability limits, and thermal response with practical engineering outputs.
| Parameter | Example Value |
|---|---|
| Slab Length | 0.10 m |
| Nodes | 11 |
| Time Step | 1 s |
| Total Time | 60 s |
| Thermal Diffusivity | 1.2E-5 m²/s |
| Thermal Conductivity | 45 W/m·K |
| Density | 7800 kg/m³ |
| Specific Heat | 480 J/kg·K |
| Initial Temperature | 200 C |
| Ambient Temperatures | 25 C on both sides |
| Convection Coefficients | 15 W/m²·K |
| Heat Generation | 0 W/m³ |
The calculator solves one dimensional transient heat conduction in a slab using the explicit finite difference method.
Governing equation:
∂T/∂t = α(∂²T/∂x²) + q'''/(ρcp)
Interior node update:
Tin+1 = Tin + Fo(Ti+1n - 2Tin + Ti-1n) + q'''Δt/(ρcp)
Where Fo = αΔt/Δx².
Convective boundary at the left surface:
T0n+1 = T0n + 2Fo[(T1n - T0n) + BiL(T∞,L - T0n)] + q'''Δt/(ρcp)
With Bi = hΔx/k.
The right boundary uses the same form. Explicit schemes are commonly checked with Fo ≤ 0.5 for stable operation.
One dimensional transient heat conduction describes temperature changes with time and position. Engineers use it for walls, plates, insulation layers, and metal sections. This calculator estimates how heat moves through a slab. It also tracks the temperature at each computational node.
Steady models ignore time. Many real systems never stay steady. Startup heating, sudden cooling, thermal shock, quenching, and furnace loading all create transient behavior. A time dependent model helps engineers predict peak temperatures, response speed, and safe operating windows.
This tool uses geometry, time step, total duration, thermal diffusivity, conductivity, density, and specific heat. It also includes convection on both sides. That makes the model practical for real design checks. Internal heat generation is available too.
The page applies an explicit finite difference approach. The slab is divided into nodes. The program then updates each node temperature for every time step. Boundary nodes use convection relations. Interior nodes use the second spatial derivative form of the heat equation.
Transient conduction calculations must respect numerical stability. The Fourier number helps assess the selected grid and time step. If the value is too large, the solution can become unreliable. This calculator reports that check so users can refine inputs quickly.
Use this calculator for refractory walls, heat treatment parts, electronic enclosures, thermal barriers, and process equipment. It works well for training, screening studies, and first pass engineering estimates. It also helps compare materials with different thermal response rates.
It means temperature changes only through the slab thickness. Heat flow in the other two directions is assumed negligible.
Thermal diffusivity controls how quickly temperature disturbances travel through the material. Larger values usually mean faster thermal response.
The Fourier number is αΔt/Δx². It compares heat diffusion over a time step with the node spacing. It is also used in stability checks.
They model heat exchange between the slab surfaces and surrounding fluids. Different left and right values allow asymmetric boundary conditions.
Yes. Enter volumetric heat generation in W/m³. The solver adds that thermal source at each time step.
It means the chosen explicit time step may be too large for the grid spacing. Reduce the time step or use fewer nodes.
No. It is best for engineering estimates, learning, and early design studies. Critical work should include validation and higher fidelity models.
They save the final temperature profile and the visible result section. This makes reporting and sharing easier.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.