Skip to content

UA Mode

Overview

In UA mode, the user specifies the overall heat transfer coefficient-area product (\(UA\) in W/K) or the individual values of \(U\) (W/m²·K) and \(A\) (m²). The solver determines the outlet temperatures and heat duty that are consistent with the specified thermal conductance.

How It Works

2-Stream Configuration (Fully Automatic)

With 2 streams, UA mode is fully determined:

  1. Identify hot and cold streams by inlet temperature
  2. Q-bisection: iterate on total heat duty
  3. At each trial Q, compute outlet temperatures via PH flash
  4. Calculate LMTD from the temperature profiles
  5. Check: \(Q_{\text{trial}} \stackrel{?}{=} UA \cdot \text{LMTD} / 1000\)
  6. Converge when \(|UA_{\text{calc}} - UA_{\text{spec}}| / UA_{\text{spec}} < 0.001\)

3+ Stream Configuration

Same as MITA mode but convergence targets \(UA\) instead of MITA.

UA Input Modes

The UA can be specified in two ways:

Specify \(UA\) directly in W/K:

\[ UA = 1000 \;\text{W/K} \]

Use this when you have a known UA from a rating calculation or equipment datasheet.

Specify \(U\) (W/m²·K) and \(A\) (m²) separately:

\[ UA = U \times A = 500 \;\text{W/(m²·K)} \times 2.0 \;\text{m²} = 1000 \;\text{W/K} \]

Use this when you know the heat transfer area and want to explore different \(U\) values, or vice versa.

UA mode configuration
Figure 1. UA mode with U×A separate input — the overall heat transfer coefficient and area are specified independently.

Typical UA Values

Application U (W/m²·K) Typical A UA Range
Water–water (plate) 2000–5000 1–10 m² 2000–50,000 W/K
Gas–gas 10–50 10–100 m² 100–5000 W/K
Condensing steam–water 2000–10,000 1–5 m² 2000–50,000 W/K
Air–water (finned) 30–60 50–200 m² 1500–12,000 W/K

Reference

Typical overall heat transfer coefficients are tabulated in Perry's Chemical Engineers' Handbook (Green & Southard, 2019), Table 11-5, and in Incropera et al. (2007), Table 11.1.

Results

Result Description
Outlet temperatures Calculated for all streams
Total heat duty Heat transferred for the given UA
MITA calculated Resulting minimum approach temperature
Effective LMTD Computed from \(Q / UA\)
Thermal efficiency \(\varepsilon = Q / Q_{\max}\)

Relationship Between Modes

The three modes are mathematically equivalent — they specify different variables of the same system:

graph LR
    A[Outlet Temperatures] -->|"Calculates"| B[UA and MITA]
    C[MITA] -->|"Calculates"| D[Outlet T and UA]
    E[UA] -->|"Calculates"| F[Outlet T and MITA]

For a 2-stream exchanger with known inlets, specifying any one of {outlet temperatures, MITA, UA} uniquely determines the other two.