# Heat Exchanger LMTD and Required Surface Area Calculator

> Source: https://netray.co/tools/heat-exchanger-lmtd-area-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Find heat duty, LMTD, cold stream flow and the area needed for a given overall U value.

## Category

engineering-plm

## Industry

Chemical Manufacturing

## Audience

- Process engineer
- Mechanical engineer
- Maintenance engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Hot stream flow

**Key:** mh

**Type:** number

**Default:** 2

**Min:** 0

**Step:** 0.1

**Unit:** kg/s

#### Hot stream specific heat

**Key:** cph

**Type:** number

**Default:** 3.5

**Min:** 0.1

**Step:** 0.1

**Unit:** kJ/kg.K

#### Hot inlet temperature

**Key:** thi

**Type:** number

**Default:** 120

**Step:** 1

**Unit:** deg C

#### Hot outlet temperature

**Key:** tho

**Type:** number

**Default:** 70

**Step:** 1

**Unit:** deg C

#### Cold inlet temperature

**Key:** tci

**Type:** number

**Default:** 25

**Step:** 1

**Unit:** deg C

#### Cold outlet temperature

**Key:** tco

**Type:** number

**Default:** 60

**Step:** 1

**Unit:** deg C

#### Cold stream specific heat

**Key:** cpc

**Type:** number

**Default:** 4.18

**Min:** 0.1

**Step:** 0.01

**Unit:** kJ/kg.K

#### Overall heat transfer coefficient U

**Key:** u

**Type:** slider

**Default:** 500

**Min:** 100

**Max:** 1500

**Step:** 50

**Unit:** W/m2.K

**Help:** Water to organics in shell and tube is often 250 to 750. Plate exchangers reach higher.

#### LMTD correction factor F

**Key:** f

**Type:** number

**Default:** 1

**Min:** 0.5

**Max:** 1

**Step:** 0.01

**Help:** 1.0 for pure counter-current. Use the chart value for multi-pass shell and tube.

**Outputs:**

#### Heat duty

**Key:** duty

**Expr:** mh * cph * (thi - tho)

**Format:** decimal

**Primary:** true

**Description:** kW.

#### Delta T at hot end

**Key:** dt1

**Expr:** thi - tco

**Format:** decimal

#### Delta T at cold end

**Key:** dt2

**Expr:** tho - tci

**Format:** decimal

#### LMTD (counter-current)

**Key:** lmtd

**Expr:** if(eq(dt1, dt2), dt1, (dt1 - dt2) / ln(dt1 / dt2))

**Format:** decimal

#### Required area

**Key:** area

**Expr:** duty * 1000 / (u * f * lmtd)

**Format:** decimal

**Primary:** true

**Description:** m2.

#### Cold stream flow needed

**Key:** mc

**Expr:** duty / (cpc * (tco - tci))

**Format:** decimal

**Description:** kg/s.

**Chart:**

#### Required area vs overall U

**Type:** line

**X:** u

**From:** 100

**To:** 1500

**Steps:** 28

**Series:**

- area

**Disclaimer:** Preliminary sizing only. Valid when both temperature differences are positive (no temperature cross for counter-current). Fouling allowance, pressure drop and mechanical design need a full rating.

## Content

**Intro:** Sizing or checking a heat exchanger starts with duty and the log mean temperature difference. Enter the stream temperatures and U, and you get the heat duty, the required surface area and the cold stream flow in one step.

**Sections:**

#### How to use it

**Body:** Fill in the hot stream flow, specific heat and both temperatures, then the cold inlet and outlet temperatures. Choose an overall heat transfer coefficient based on your fluids and exchanger type, and the correction factor F if the unit is multi-pass. The result gives the area to specify or compare with your existing unit. The chart sweeps U to show how sensitive the area is to fouling.

#### The equations

**Body:** Duty Q = m x cp x (T hot in minus T hot out). The two terminal differences for counter-current flow are delta T1 = Thi - Tco and delta T2 = Tho - Tci. LMTD equals (delta T1 minus delta T2) divided by the natural log of their ratio. Area A = Q / (U x F x LMTD). If both differences are equal, LMTD is simply that value, which the calculator handles.

**Bullets:**

- Counter-current gives the highest LMTD and smallest area
- Co-current flow needs a different delta T definition
- F below about 0.8 signals a poor arrangement
- Add 10 to 25 percent area for fouling where appropriate

#### Reading the result

**Body:** With the defaults, the duty is 350 kW and the LMTD about 52 K, so a 500 W/m2.K exchanger needs roughly 13 square metres. If the cold stream flow shown is more than your utility can supply, relax the cold outlet temperature or accept a larger area. Check that both differences stay positive, otherwise the stated outlet temperatures are physically impossible.

**Bullets:**

- Heat balance: hot duty must equal cold duty
- Check metallurgy for chloride or acid service
- Verify pressure drop against pump capability
- Cleaning intervals drive the real fouling margin

**Cta:** If your equipment register and maintenance plans sit in an ERP, Netray can help tie exchanger cleaning history to performance checks. Ask for a review.

**Faq:**

#### Why use LMTD instead of the average temperature difference?

**Answer:** The temperature difference between the streams changes along the exchanger. The log mean is the correct average for constant U and specific heats, and the arithmetic mean overstates it when the two ends differ a lot.

#### What F factor should I use?

**Answer:** Use 1.0 for pure counter-current or double-pipe units. For multi-pass shell and tube, read F from standard charts using the R and P parameters, or from your rating software, and aim for 0.8 or higher.

#### How do I choose U?

**Answer:** Use vendor data or past units in similar service. Typical clean values range from about 250 W/m2.K for gas-liquid to over 1000 for water-water in plate exchangers. Include fouling in the effective U.

#### What if the temperatures cross?

**Answer:** A cold outlet hotter than the hot outlet is not possible in pure counter-current flow only if the second differential turns negative. Here, the second end must remain positive. A cross needs multi-pass analysis and an F correction.

## Search terms

LMTD calculator, heat exchanger area calculation, log mean temperature difference, shell and tube sizing calculator, heat duty calculator, overall heat transfer coefficient, counter current exchanger design

---
Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json