Conduction Calculators

Analyze steady-state heat conduction through various geometries. All calculations powered by Fortran for high-precision results.

Steady Heat Conduction in Plane Walls

Calculate heat transfer through single and multilayer plane walls. Includes thermal resistance network analysis and temperature profile visualization across wall layers.

Multi-layer Thermal Resistance Temperature Profile
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Composite Wall Conduction with Convection

Evaluate overall heat transfer coefficients ($U$-value) and thermal resistances for multi-layer walls under convective and radiative ambient environments. Evaluates condensation risks.

Convection Boundaries Overall U-Value Condensation Check
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Variable Conductivity k = f(T)

Analyze steady heat conduction with variable thermal conductivity across plane walls, cylinders, and spheres using the Kirchhoff transformation.

Kirchhoff Transform Variable Properties T Profile Overlay
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Multilayered Cylinders & Spheres

Analyze heat conduction through multilayered cylindrical and spherical geometries. Compute radial temperature distribution and total heat transfer rate.

Cylindrical Spherical Radial Distribution
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Critical Radius of Insulation

Determine the critical insulation radius for cylinders and spheres. Analyze the trade-off between conduction resistance and convection resistance.

Critical Radius Insulation Analysis
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Straight Rectangular Fins

Calculate fin efficiency, effectiveness, and total heat dissipation for straight rectangular fin geometries with various tip conditions.

Fin Efficiency Fin Effectiveness Heat Dissipation
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Annular (Circular) Fin Efficiency

Calculate efficiency and heat transfer for annular fins on tubes using exact Bessel function solutions. Includes radial temperature profile and material comparison.

Bessel Functions Fin Efficiency Heat Exchangers
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Pin Fin & Spine Calculator

Calculate efficiency, effectiveness, and dissipation for cylindrical, conical, parabolic, and rectangular pin fins or spines under multiple boundary conditions.

Pin Fins & Spines Tapering Profiles Thermal Efficiency
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Heat Sink & Fin Array Calculator

Evaluate plate fin and pin fin heat sinks. Calculate overall thermal resistance, base plate operating temperature, overall efficiency, optimal fin spacing, and pressure drop.

Heat Sinks Plate & Pin Arrays Optimal Spacing
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Lumped System Analysis

Transient heat conduction using the lumped capacitance method. Compute Biot number, time constant, and cooling/heating curves for various geometries.

Biot Number Time Constant Cooling Curve
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Transient Conduction 1D (Heisler)

One-term approximation for transient conduction in plane walls, long cylinders, and spheres. Interactive Heisler-style charts and temperature profiles.

Heisler Charts Fourier Number One-Term Approx.
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Conduction with Heat Generation

Temperature distribution in plane walls, cylinders, and spheres with uniform internal heat generation. Compute Tmax, surface temperature, and safety margins.

Heat Source T_max Temperature Profile
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Thermal Contact Resistance

Calculate microscale contact resistance and conductance using Mikic-Rohsenow and CMY correlations. Evaluate joint performance with and without TIM.

Mikic-Rohsenow Contact Conductance TIM Analysis
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2D Conduction Shape Factors

Calculate conduction shape factors (S) and heat rates for 12+ configurations, including buried pipes, eccentric cylinders, wall edges, and floor heating arrays.

Shape Factors Buried Pipes Eccentric Cylinders
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Semi-Infinite Solid Conduction

Calculate transient heat penetration, temperature profiles, and surface heat rates in semi-infinite media under constant temperature, heat flux, or convection boundary conditions.

Transient Conduction Penetration Depth Error Function
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Stefan Problem — Phase Change

Calculate interface position s(t), growth constant λ, phase change time for thickness d, multi-phase temperature profiles, and total energy released or absorbed.

Phase Change Solidification/Melting Moving Boundary
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2D Thermal Bridge Calculator (Pont Thermique)

Evaluate linear transmittance (ψ) and point transmittance (χ) for balcony slabs, corners, window frames, floors, and columns. Interactive 2D isothermal contours.

ISO 10211 Linear & Point Transmittance Isothermal Heatmap
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Multidimensional Transient Conduction

Calculate 2D and 3D transient temperature distributions using product solutions of standard 1D conduction geometries (cylinders and walls).

Product Solution Multidimensional Heatmap Viz
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1D Transient Conduction Numerical Solver (FDM)

Solve transient 1D heat equation numerically using Explicit, Implicit BE, or Crank-Nicolson finite difference schemes. Supports temperature-dependent properties.

Finite Difference Explicit/Implicit FDM Simulation
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About Heat Conduction

Heat conduction (or thermal conduction) is the transfer of thermal energy through a material without bulk motion. It is governed by Fourier's Law: q = -k × dT/dx, where k is the thermal conductivity, and dT/dx is the temperature gradient. Our calculators use the thermal resistance network method for composite walls and the analytical solutions for cylindrical and spherical geometries.

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