Nanoscale Heat Transfer Calculator

Effective thermal conductivity and Knudsen regime at nanoscale.

Feature Size (nm)

Phonon Mean Free Path (nm)

Bulk Conductivity (W/m·K)

Temperature Diff. (K)

Kapitza Resistance (m²K/W)

Tab to move between fields

Knudsen Number

Effective k (W/m·K)

49.33

Regime (1=Diff, 2=Trans, 3=Ball)2

Conductivity Reduction (%)66.7

Heat Flux (W/m²)24,670,000,000

Thermal Time Constant (ps)18.89

Kapitza Conductance (W/m²K)100,000,000

Mfp M0

How to Use This Calculator

Enter the feature size (nm) — the critical dimension governing heat transport.
Set the phonon mean free path (nm) for your material from bulk thermal property data.
Enter bulk thermal conductivity (W/m·K) and temperature difference across the feature (K).
Set Kapitza (interfacial thermal) resistance (m²K/W) at material boundaries if applicable.
Review Knudsen number, transport regime (diffusive, transitional, or ballistic), effective conductivity, and heat flux.

How the result changes with Feature Size (nm)

Feature Size (nm): Characteristic length of nanostructure.
Phonon Mean Free Path (nm): Bulk phonon MFP. Si~40nm at 300K, diamond~300nm.
Bulk Conductivity (W/m·K): Bulk thermal conductivity. Si=148, GaN=130, diamond=2000.
Temperature Diff. (K): Temperature difference across the feature.
Kapitza Resistance (m²K/W): Interface thermal resistance. Typical: 1e-9 to 1e-7.

Identify Input Parameters
4 parameters
Feature Size (nm) = 20, Phonon Mean Free Path (nm) = 40, Bulk Conductivity (W/m·K) = 148, Temperature Diff. (K) = 10 = 5 input(s) provided
Calculate Knudsen Number
Knudsen Number = mfpNm / featureSizeNm
2 = 2
Calculate Effective k
Effective k = bulkConductivityWmK / (1 + knudsen)
49.333 = 49.333
Calculate Regime
2 = 2
Calculate Conductivity Reduction
Conductivity Reduction = ((bulkConductivityWmK - effectiveConductivity) / bulkConductivityWmK) * 100
66.7 = 66.7