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thermal_transient_1d

Calculate transient 1-D heat conduction in a plane wall with surface convection, returning center and surface temperatures using the Heisler series.

Instructions

Analytic 1-D plane-wall transient conduction (one-term Heisler series), valid for Fourier ≳ 0.2 — the closed-form transient the Elmer thermal_transient solve is gated against, and the distributed (spatial-gradient) answer the lumped screen only approximates. A wall of half-thickness L cools/heats toward ambient by surface convection: Bi = h·L/k, Fo = α·t/L², α = k/(ρ·cₚ). Pass alpha_m2_s, or k+rho+cp, or a material (Materials DB: thermal_conductivity/Density/specific_heat); get h_conv from the h_estimate correlation screen rather than guessing.

As Bi→0 the body is isothermal and this collapses to the lumped exponential exp(−t/τ) (cross-checked via t_center_lumped_c / lumped_agrees). Returns {biot, fourier, eigenvalue_1, c1, t_center_c, t_surface_c, t_center_lumped_c, time_constant_s, one_term_valid, lumped_agrees}.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
kNo
cpNo
rhoNo
h_convYes
materialNo
alpha_m2_sNo
duration_sYes
t_ambient_cNo
t_initial_cNo
half_thickness_mmYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

A4.5/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are supplied, so the description carries the full behavioral burden, and it does so well: it discloses the underlying model, its validity range, the limiting collapse to the lumped exponential, and a cross-check flag. It stops short of stating error behavior outside the valid Fourier range beyond implying the one_term_valid flag, leaving a small gap.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Dense but front-loaded: identity of the method, then validity, then sibling relationships, then input guidance, then output keys. Every sentence carries physics or sourcing information; the only cost is density that slightly reduces scannability.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 10-parameter tool with no output schema, the description does the heavy lifting by enumerating the returned keys (biot, fourier, t_center_c, t_surface_c, etc.) and covering material/geometry interpretation. It is nearly complete, with only peripheral parameter units/roles left implicit.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate, and it largely does: it maps alpha_m2_s/k+rho+cp/material to their roles, defines α = k/(ρ·cₚ), ties Bi = h·L/k and Fo = α·t/L² to the required inputs, and points h_conv to its source. Minor inputs like t_ambient_c, t_initial_c, and duration_s are left to inference, so it is not fully compensatory.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

Names a specific method and resource: 'Analytic 1-D plane-wall transient conduction (one-term Heisler series)'. It explicitly distinguishes itself from two siblings: the Elmer 'thermal_transient solve' it is gated against, and the 'lumped screen' it improves upon via the distributed spatial-gradient answer. An agent can pick it apart from thermal_lumped and thermal_transient_submit without opening any schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

States an explicit validity domain ('valid for Fourier ≳ 0.2') and gives concrete input-sourcing rules: pass alpha_m2_s, or k+rho+cp, or a material, and 'get h_conv from the h_estimate correlation screen rather than guessing.' It also frames when the lumped alternative applies (Bi→0). This is close to full when-to-use/when-not guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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