Thermal Resistance Calculator
Calculate thermal resistance for plates, hollow cylinders, and hollow spheres with critical radius analysis
Calculate Thermal Resistance
Thermal Resistance Results
Formula used: R = t / (k × A)
Thermal conductivity: 237 W/m·K
Example Calculation
Aluminum Container Example
Material: Aluminum (k = 237 W/m·K)
Geometry: Hollow Cylinder
Length: 500 mm
Inner radius: 100 mm
Outer radius: 200 mm
Calculation
R = ln(r₂/r₁) / (2π × L × k)
R = ln(200/100) / (2π × 0.5 × 237)
R = ln(2) / (745.15)
R = 9.31 × 10⁻⁴ K/W
Material Comparison
Higher thermal resistance means better insulation properties
Thermal Resistance Tips
Higher thermal resistance = better insulation
Units are K/W (Kelvins per Watt)
Critical radius determines optimal insulation thickness
Lower thermal conductivity = higher resistance
Understanding Thermal Resistance
What is Thermal Resistance?
Thermal resistance is a measure of how much an object resists the flow of heat. It's defined as the ratio of temperature difference to heat flow rate: R = ΔT / Q. Higher thermal resistance means better insulation properties.
Applications
- •Building insulation design
- •Electronic component cooling
- •Pipe insulation systems
- •Thermal barrier design
Thermal Resistance Formulas
Plate
R = t / (k × A)
t = thickness, k = thermal conductivity, A = area
Hollow Cylinder
R = ln(r₂/r₁) / (2π × L × k)
r₁, r₂ = inner/outer radius, L = length
Hollow Sphere
R = (r₂-r₁) / (4π × r₁ × r₂ × k)
r₁, r₂ = inner/outer radius
Critical Radius of Insulation
For hollow geometries, there exists a critical radius beyond which adding more insulation actually improves thermal resistance. Below this critical radius, adding insulation may increase heat transfer due to increased surface area for convection.
Cylinder Critical Radius
r_cr = k / h
Sphere Critical Radius
r_cr = 2k / h
Where k is thermal conductivity and h is the heat transfer coefficient between the object and surrounding medium.