Analyze one-dimensional conduction with clear thermal outputs. Switch geometry, enter properties, and compare steady results. Built for physics practice, engineering homework, and quick verification.
| Geometry | Key Inputs | Heat Rate | Thermal Resistance |
|---|---|---|---|
| Plane Wall | k=205 W/m·K, A=0.50 m², L=0.02 m, T1=120°C, T2=40°C | 410,000.0000 W | 0.0002 K/W |
| Hollow Cylinder | k=45 W/m·K, Length=1.20 m, r1=0.03 m, r2=0.08 m, T1=150°C, T2=50°C | 34,593.2460 W | 0.0029 K/W |
| Hollow Sphere | k=0.80 W/m·K, r1=0.10 m, r2=0.18 m, T1=80°C, T2=25°C | 124.4060 W | 0.4421 K/W |
Heat transfer rate: Q = kA(T1 - T2) / L
Heat flux: q = Q / A
Thermal resistance: R = L / (kA)
Temperature gradient: dT/dx = (T2 - T1) / L
Heat transfer rate: Q = 2πkL(T1 - T2) / ln(r2 / r1)
Thermal resistance: R = ln(r2 / r1) / (2πkL)
Inner heat flux: qi = Q / (2πr1L)
Outer heat flux: qo = Q / (2πr2L)
Heat transfer rate: Q = 4πk(T1 - T2) / [(1 / r1) - (1 / r2)]
Thermal resistance: R = [(1 / r1) - (1 / r2)] / (4πk)
Inner heat flux: qi = Q / (4πr1²)
Outer heat flux: qo = Q / (4πr2²)
These relations come from Fourier law for one-dimensional steady-state conduction. The calculator keeps geometry effects explicit, so thermal resistance and heat flux match the selected shape.
One-dimensional steady-state heat conduction describes heat flow through a body when temperature changes with position in one direction only. Time does not change the temperature field. That makes the problem stable and easier to solve. Fourier law links the heat rate to conductivity, geometry, and temperature difference. This calculator turns those relations into quick outputs for common thermal cases.
Geometry strongly affects thermal resistance. A plane wall uses area and thickness directly. A hollow cylinder uses a logarithmic radius term. A hollow sphere uses inverse radii. These differences change heat transfer rate even when conductivity and temperature difference stay the same. That is why a general conduction tool should not treat every shape the same way.
Thermal conductivity shows how easily a material carries heat. Larger conductivity means easier conduction. Boundary temperatures create the driving force. Thickness or radius gap controls path length. Area also matters because larger heat transfer surfaces carry more energy. When you combine these variables correctly, you can estimate heat rate, heat flux, thermal resistance, and temperature gradient with confidence.
This type of calculation appears in physics classes, thermal engineering homework, insulation checks, pipe analysis, furnace design, and laboratory reporting. Students use it to verify manual solutions. Designers use it to compare materials. Technicians use it to estimate conductive losses through walls, tubes, or shells. The same framework also supports quick screening before more advanced simulation work.
The calculator is useful because it places key outputs in one view. You can switch geometry, adjust values, and review direction of heat flow immediately. The built-in export options also help with documentation. The example table, formulas, and usage notes make it easier to understand the thermal model and apply it correctly in real study or design tasks.
It means temperatures do not change with time. Heat still flows, but the temperature field has already stabilized.
Use it for flat slabs, plates, and walls where heat travels through thickness in one main direction.
Cylinders have changing area with radius. That adds a logarithmic term to the thermal resistance equation.
In radial systems, surface area changes with radius. The same heat rate spreads over different areas, so flux changes.
Yes. Temperature difference is what matters for conduction equations, so Celsius works well for these calculations.
A negative sign only shows direction. Heat is flowing from boundary 2 toward boundary 1.
No. It focuses on one-dimensional steady-state conduction only. Convection and radiation need additional thermal resistance terms.
It controls how easily the material transfers heat. Higher conductivity usually means lower conduction resistance and higher heat rate.
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.