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mechanicalwith-tool

Lmtd Calculation

Calculates heat exchanger LMTD from hot and cold terminal temperatures for counterflow or parallel flow arrangements. The template applies an explicit correction factor, calculates corrected mean temperature difference, and estimates heat duty from U, area, and corrected MTD.

with-tool: The model is given an executable Python calculator script.

Standards

TEMA Standards

Tags

deterministicheat-dutyheat-exchangerlmtdmechanical

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

8 inputs

Always given

Included directly in every task prompt.

8
Show 8 inputs

  • Hot inlet

    hot_inlet_c

    Hot fluid inlet temperature

    30 – 400 C

  • Hot outlet

    hot_outlet_c

    Hot fluid outlet temperature

    20 – 350 C

  • Cold inlet

    cold_inlet_c

    Cold fluid inlet temperature

    -10 – 200 C

  • Cold outlet

    cold_outlet_c

    Cold fluid outlet temperature

    0 – 250 C

  • Overall u

    overall_u_kw_m2_c

    Overall heat transfer coefficient

    0.02 – 5 kW/m2.C

  • Heat transfer area

    heat_transfer_area_m2

    Heat transfer surface area

    1 – 10000 m2

  • Correction factor

    correction_factor

    LMTD correction factor

    0.5 – 1

  • Flow arrangement

    flow_arrangement

    Heat exchanger flow arrangement

    counterflowparallel

Scored outputs

6 outputs

Delta t1 c

delta_t1_c

First terminal temperature difference

Scores if within ±3% of the reference value.

Delta t2 c

delta_t2_c

Second terminal temperature difference

Scores if within ±3% of the reference value.

Lmtd c

lmtd_c

Log mean temperature difference

Scores if within ±3% of the reference value.

Corrected mtd c

corrected_mtd_c

Corrected mean temperature difference

Scores if within ±3% of the reference value.

Heat duty

heat_duty_kw

Estimated heat duty

Scores if within ±3% of the reference value.

Minimum approach c

minimum_approach_c

Minimum terminal temperature approach

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

All inputs remain visible at every tier

For this template, difficulty scales through parameter and scenario ranges rather than hidden information.

easy:
All parameters given for a counterflow process cooler
medium:
All parameters given across common heat exchanger duties
hard:
All parameters given with explicit correction factor and arrangement

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • lmtd-calculation_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior mechanical engineer specializing in heat exchanger design.2 3## Problem4 5Calculate heat exchanger LMTD, corrected mean temperature difference, heat duty, and minimum approach temperature.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Hot inlet temperature | {{ hot_inlet_c }} | C |12| Hot outlet temperature | {{ hot_outlet_c }} | C |13| Cold inlet temperature | {{ cold_inlet_c }} | C |14| Cold outlet temperature | {{ cold_outlet_c }} | C |15| Overall heat transfer coefficient U | {{ overall_u_kw_m2_c }} | kW/m2.C |16| Heat transfer area | {{ heat_transfer_area_m2 }} | m2 |17| Correction factor F | {{ correction_factor }} | - |18| Flow arrangement | {{ flow_arrangement }} | - |19 20{% if archetype_description is defined %}21### Heat Exchanger Context22 23{{ archetype_description }}24{% endif %}25 26{% if tool_available %}27## Available Tool28 29An LMTD calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:30 31```bash32python3 /workspace/{{ meta.name }}_calc.py --help33```34 35You may use this tool to verify your calculations or compute values directly.36{% endif %}37 38## Required39 40Calculate the following:41 421. Terminal temperature differences (C)432. Log mean temperature difference (C)443. Corrected mean temperature difference (C)454. Heat duty (kW)465. Minimum terminal approach (C)47 48## Constraints49 50- No internet access is available. Work from engineering knowledge and the provided tool.51- For counterflow, use delta T1 = hot inlet - cold outlet and delta T2 = hot outlet - cold inlet.52- For parallel flow, use delta T1 = hot inlet - cold inlet and delta T2 = hot outlet - cold outlet.53- Use LMTD = (delta T1 - delta T2) / ln(delta T1 / delta T2).54- Use corrected MTD = LMTD x correction factor.55- Use heat duty = U x area x corrected MTD.56 57## Output Format58 59Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:60 61```json62{63 "delta_t1_c": <numeric_value>,64 "delta_t2_c": <numeric_value>,65 "lmtd_c": <numeric_value>,66 "corrected_mtd_c": <numeric_value>,67 "heat_duty_kw": <numeric_value>,68 "minimum_approach_c": <numeric_value>69}70```71 72Write your complete solution to `/workspace/output.md`.73

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Process cooler

process_cooler

Process liquid cooler with counterflow exchanger

industrial-process-coolerplant-utility-exchanger
Parameter ranges
hot_inlet_c
120 – 180
hot_outlet_c
75 – 100
cold_inlet_c
10 – 35
cold_outlet_c
40 – 70
overall_u_kw_m2_c
0.2 – 1.5
heat_transfer_area_m2
20 – 800
correction_factor
0.75 – 1

Hot water heat exchanger

hot_water_heat_exchanger

Hot water heat exchanger for building or process service

district-heating-skidbuilding-services-heat-exchanger
Parameter ranges
hot_inlet_c
95 – 120
hot_outlet_c
75 – 85
cold_inlet_c
5 – 30
cold_outlet_c
35 – 65
overall_u_kw_m2_c
0.3 – 2
heat_transfer_area_m2
5 – 300
correction_factor
0.8 – 1

Example task

industrial-process-cooler-process-cooler-preview — hard difficulty, all inputs given.

Process liquid cooler with counterflow exchanger. industrial-process-cooler. Required outputs: delta_t1_c, delta_t2_c, lmtd_c, corrected_mtd_c, heat_duty_kw, minimum_approach_c

The model sees

Scenario context and visible inputs.

hot_inlet_c
120 to 180 C
hot_outlet_c
75 to 100 C
cold_inlet_c
10 to 35 C
cold_outlet_c
40 to 70 C
overall_u_kw_m2_c
0.2 to 1.5 kW/m2.C
heat_transfer_area_m2
20 to 800 m2
correction_factor
0.75 to 1
flow_arrangement
counterflow

Executable tool: lmtd-calculation_calc.py

The model must infer

Inputs withheld at this difficulty.

Nothing. All inputs are supplied.

The model must produce

The scored JSON answer schema.

{
  "delta_t1_c": <number>,
  "delta_t2_c": <number>,
  "lmtd_c": <number>,
  "corrected_mtd_c": <number>,
  "heat_duty_kw": <number>,
  "minimum_approach_c": <number>
}
  • delta_t1_c · scored within ±3%
  • delta_t2_c · scored within ±3%
  • lmtd_c · scored within ±3%
  • corrected_mtd_c · scored within ±3%
  • heat_duty_kw · scored within ±3%
  • minimum_approach_c · scored within ±3%