対数平均温度差 (LMTD) は、熱交換器、特に向流および並流配置における熱伝達の有効平均温度差です。これは、両端の高温流体と低温流体の温度差の対数平均です。LMTD は次の式を使用して計算されます。[latex]Delta T_{LM} = frac{Delta T_A – Delta T_B}{ln(Delta T_A / Delta T_B)}[/latex]。
対数平均温度差（LMTD）
1910
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The LMTD method is a cornerstone of heat exchanger analysis. It arises from the integration of the heat transfer rate equation along the length of the exchanger, assuming constant fluid properties and overall heat transfer coefficient. The fundamental heat transfer equation is [latex]Q = U A \Delta T_{LM}[/latex], where Q is the rate of heat transfer, U is the overall heat transfer coefficient, and A is the heat transfer surface area. The LMTD correctly accounts for the non-linear temperature profile of the fluids as they flow through the exchanger. For a counter-current flow exchanger, [latex]\Delta T_A[/latex] and [latex]\Delta T_B[/latex] are the temperature differences at the two ends of the exchanger. For a parallel flow exchanger, the same formula applies, but the temperature differences are calculated differently based on the inlet and outlet positions. The counter-flow arrangement is generally more efficient as it yields a higher LMTD for given inlet and outlet temperatures, allowing for a smaller required surface area A for the same heat duty Q. However, when the temperature difference at one end is equal to the other, the LMTD is simply that temperature difference. If one of the temperature differences is zero, the LMTD is mathematically undefined, but in practice, this represents a limit where heat transfer ceases to be effective. For more complex geometries like cross-flow or multi-pass shell-and-tube exchangers, a correction factor F is applied to the LMTD, such that [latex]\Delta T_{eff} = F \cdot \Delta T_{LM, counterflow}[/latex].
UNESCO Nomenclature: 3328
熱力学
タイプ
抽象システム
混乱
増分
使用法
広く普及している
前駆物質
- フーリエの熱伝導の法則（1822年）
- 第一法則 熱力学の（エネルギー保存の法則)
- ニュートンの冷却法則
- 積分と対数関数のための微積分学の発展
アプリケーション
- design and performance analysis of shell and tube heat exchangers
- 工業用ボイラーおよび凝縮器のサイズ決定
- HVACシステムの最適化
- 発電所における熱管理
- 化学プロセス 工学的計算
特許:
NA
潜在的なイノベーションのアイデア
- AI-driven optimization of multi-stage heat exchanger networks using real-time LMTD calculations
- development of compact heat exchangers with complex flow paths optimized via computational fluid dynamics to maximize the lmtd correction factor
- smart hvac systems that dynamically adjust fluid flow rates to maintain an optimal lmtd for energy efficiency
- miniaturized lmtd sensors for microfluidic heat exchangers in electronics cooling
- software for predicting and mitigating thermal stresses in exchangers based on lmtd profiles
- phase-change material (pcm) integrated heat exchangers where the lmtd model is adapted for 潜熱 transfer periods
- self-cleaning heat exchangers that use controlled flow reversals to disrupt fouling, monitored by lmtd performance drops
- lmtd-based control algorithms for waste heat recovery systems in automotive applications
- 3d-printed heat exchangers with customized geometries designed to enhance the lmtd
- educational virtual reality simulations for demonstrating the impact of flow arrangements on the lmtd and overall efficiency
関連キーワード：LMTD、対数平均温度差、熱交換器、熱力学、熱伝達、対向流、並流、熱工学、ヌッセルト数、総括熱伝達係数。
歴史的背景
対数平均温度差（LMTD）
（日付が不明または関連性がない場合、例えば「流体力学」などでは、その注目すべき出現時期の概算値が提示されます。）
