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HXD
FORMULA
SHEET

#ri7i#
1 - For plane wall

UA=

ଵ

ோ௧

=

൬

2 - For a tubular pipe

ଵ

భ
೟
భ
ା
ା
൰
೓೔ ಲ
಼ಲ ೓೚ ಲ

UA= ܷ௜ ‫ܣ‬௜ = ܷ௢ ‫ܣ‬௢ =

ଵ

ோ௧

=

ቌ

భ
ା
೓೔ ಲ

ଵ

ೝ
೗೙൬ బ ൰
ೝ೔
భ
ା
ቍ
మഏ಼೗
೓బ ಲబ

3 – For a unclean surface(Fouling /scaling)
∆ࢀ࢙
ࡽ

૚
= ࡾ࢙ = ࡭ࢎ =
࢙

ࡾࢌ

ࡾ࢙ ୀࡿࢉࢇ࢒࢏࢔ࢍ ࢘ࢋ࢙࢏࢚ࢇ࢔ࢉࢋ
∆ࢀ࢙ ୀࢀࢋ࢓࢖ ࢍ࢘ࢇࢊ࢏ࢋ࢔࢚ ࢇࢉ࢘࢕࢙࢙ ࢛࢔ࢉ࢒ࢋࢇ࢔ ࢙࢛࢘ࢌࢇࢉࢋ

࡭

4 – For a fouled surfaces
‫= ܜ܀‬

‫ܑ ۯ ܑܐ‬

۹‫ܑۯ‬

+

Q = hA [1 -

૚

+ ‫+ ܟ܀‬

஺೑

‫ܑ܎ ܀‬

R ୵ = Wall resistance

૚

‫ܐ‬૙ ‫ ۯ‬૙

5 – Overall heat transfer (taking efficiency in account)
஺

(1 - Ƞ୤ )] ∆T

6 – Overall heat transfer coefficient

ܷ௢ = ‫ܗۯ‬

૚
ା‫ܗ ۯ‬
‫ ܑ ۯ‬Ƞ౟ ‫ܑܐ‬

ଵ

‫܀‬
‫܀ ۯ‬
૚
‫ ܟ ܀‬ା ‫ ܑ܎ ܗ‬ା ܎‫ ܗ‬ା
‫ ܑ ۯ‬Ƞ౟

Ƞ౥

‫ܐ‬૙ ‫ ۯ‬૙
*a=m(table)
=

In case of multipass arrangement

Ft= Correction Factor
Temperature Effectiveness :

Series Coupling over all counter flow
ܶଵଶ

ܶଵଵ

ܶଶଶ

A

ܶଶଵ

ܲଵ஺ =
ܼଵ =

்భమ ି ்భభ
்మమ ି ்భభ

ܲଵ஻ =

ܶଵଷ

B

ଵ –ோభ ௉భಲ
ଵ –ோభ ௉భಳ

=

ଵ – ௉భಳ

்మమ ି ்భయ
்మభ ି ்భభ

்మయ ି ்భయ
்మమ ି ்భమ

ܶଶଵ

ܲଵ஼ =

்మయ ି ்భమ

்௘௠௣ ௥௔௡௚௘ ௢௙ ௖௢௠௕௜௡௘ௗ ு௑

=

ܶଶଷ

்భయ ି ்భమ

்௘௠௣ ௥௔௡௚௘ ௢௙ ௜௡ௗ௜௩௜ௗ௨௔௟ ௙௟௨௜ௗ

ଵ – ௉భಲ

ܶଵଵ

=

்భమ ି ்భభ
்భయ ି ்భభ

C

்భయ ି ்భభ
்మయ ି ்భభ

=

்మమ ି ்మభ
்మయ ି ்మభ

ܶଵଷ

ܶଶଷ
ଵ – ௉భ಴

ଵ –ோభ ௉భ಴

=

ଵ – ௉భಲ

ଵ –ோభ ௉భಲ

×

ଵ – ௉భಳ

ଵ –ோభ ௉భಳ

=

்మయ ି ்భయ
்మభ ି ்భభ

General formula for ܲଵ
ܲଵ =

For R=1

∏೙ ( ଵିோభ ௉భಲ೔ )ି ∏೙ ( ଵି௉భಲ೔ )
೔సభ
೔సభ

∏೙ ( ଵିோభ ௉భಲ೔ ) ି ோభ ∏೙ ( ଵି௉భಲ೔ )
೔సభ
೔సభ

Pଵ = ∑௡ ൥൭
௜ୀଵ

ುభಲ೔
൫భషುభಲ೔ ൯
ುభಲ೔
൨
ଵା∑೙ ൤
೔సభ ൫భషು
భಲ೔ ൯

൱൩

Series Coupling overall parallel flow
ܶଵଶ

ܶଵଵ

ܶଶଶ

ܶଶଵ

ܲଵ =

ଵ

ଵାோభ

ܶଵଷ
ܶଶଷ

ܶଵଵ
ܶଶଵ

ሼ1 − ∏௡ ሾ1 − (1 + ܴ)ܲଵ஺௜ ሿሽ
௜ୀଵ

NTU = ∑௡ ܷܰܶଵ஺௜
௜ୀଵ
DOUBLE PIPE HEAT EXCHANGER
Counter Flow
( Cold-Tube Side , Hot- Shell Side)
(ଵି௉)

=

(ଵି௉ோ)

∆ܶ௟௠ =
ଵ

ே்௎೎

=

்೓೔೙ ି ்೎೚ೠ೟

்೓೚ೠ೟ ି ்೎೔೙

(்೓೔೙ ି ்೎೔೙ ) ௉ (ோିଵ)

(ோିଵ)
݈݊ቀ1−ܲቁ
ܴܲ

௟௡ቀ

భషು
ቁ
ುೃ

NTܷ௖ =

୒୘௎೓
ோ

For n- pass heat exchangers
1- Cold fluid in parallel and hot fluid in series flow

ߠ=

భൗ
೙

భ
)
భషುೃ)

௟௡቎((

ೃ
೙

௉( ିଵ)

భ
ൗ೙

భ
቏
ൗ೙

ቌଵିೃ ቍାೃ

2- Cold fluid in series and hot fluid in parallel flow

ߠ=

௉(ଵି௡ோ)⁄௡

௟௡൥(ଵି௡ோ)ቀ

భ
ቁ
భషು

భ
೙

ା௡ோ൩
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heat exchanger design formula Sheet
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heat exchanger design formula Sheet

  • 2. 1 - For plane wall UA= ଵ ோ௧ = ൬ 2 - For a tubular pipe ଵ భ ೟ భ ା ା ൰ ೓೔ ಲ ಼ಲ ೓೚ ಲ UA= ܷ௜ ‫ܣ‬௜ = ܷ௢ ‫ܣ‬௢ = ଵ ோ௧ = ቌ భ ା ೓೔ ಲ ଵ ೝ ೗೙൬ బ ൰ ೝ೔ భ ା ቍ మഏ಼೗ ೓బ ಲబ 3 – For a unclean surface(Fouling /scaling) ∆ࢀ࢙ ࡽ ૚ = ࡾ࢙ = ࡭ࢎ = ࢙ ࡾࢌ ࡾ࢙ ୀࡿࢉࢇ࢒࢏࢔ࢍ ࢘ࢋ࢙࢏࢚ࢇ࢔ࢉࢋ ∆ࢀ࢙ ୀࢀࢋ࢓࢖ ࢍ࢘ࢇࢊ࢏ࢋ࢔࢚ ࢇࢉ࢘࢕࢙࢙ ࢛࢔ࢉ࢒ࢋࢇ࢔ ࢙࢛࢘ࢌࢇࢉࢋ ࡭ 4 – For a fouled surfaces ‫= ܜ܀‬ ‫ܑ ۯ ܑܐ‬ ۹‫ܑۯ‬ + Q = hA [1 - ૚ + ‫+ ܟ܀‬ ஺೑ ‫ܑ܎ ܀‬ R ୵ = Wall resistance ૚ ‫ܐ‬૙ ‫ ۯ‬૙ 5 – Overall heat transfer (taking efficiency in account) ஺ (1 - Ƞ୤ )] ∆T 6 – Overall heat transfer coefficient ܷ௢ = ‫ܗۯ‬ ૚ ା‫ܗ ۯ‬ ‫ ܑ ۯ‬Ƞ౟ ‫ܑܐ‬ ଵ ‫܀‬ ‫܀ ۯ‬ ૚ ‫ ܟ ܀‬ା ‫ ܑ܎ ܗ‬ା ܎‫ ܗ‬ା ‫ ܑ ۯ‬Ƞ౟ Ƞ౥ ‫ܐ‬૙ ‫ ۯ‬૙
  • 4.
  • 5. = In case of multipass arrangement Ft= Correction Factor
  • 6. Temperature Effectiveness : Series Coupling over all counter flow ܶଵଶ ܶଵଵ ܶଶଶ A ܶଶଵ ܲଵ஺ = ܼଵ = ்భమ ି ்భభ ்మమ ି ்భభ ܲଵ஻ = ܶଵଷ B ଵ –ோభ ௉భಲ ଵ –ோభ ௉భಳ = ଵ – ௉భಳ ்మమ ି ்భయ ்మభ ି ்భభ ்మయ ି ்భయ ்మమ ି ்భమ ܶଶଵ ܲଵ஼ = ்మయ ି ்భమ ்௘௠௣ ௥௔௡௚௘ ௢௙ ௖௢௠௕௜௡௘ௗ ு௑ = ܶଶଷ ்భయ ି ்భమ ்௘௠௣ ௥௔௡௚௘ ௢௙ ௜௡ௗ௜௩௜ௗ௨௔௟ ௙௟௨௜ௗ ଵ – ௉భಲ ܶଵଵ = ்భమ ି ்భభ ்భయ ି ்భభ C ்భయ ି ்భభ ்మయ ି ்భభ = ்మమ ି ்మభ ்మయ ି ்మభ ܶଵଷ ܶଶଷ
  • 7. ଵ – ௉భ಴ ଵ –ோభ ௉భ಴ = ଵ – ௉భಲ ଵ –ோభ ௉భಲ × ଵ – ௉భಳ ଵ –ோభ ௉భಳ = ்మయ ି ்భయ ்మభ ି ்భభ General formula for ܲଵ ܲଵ = For R=1 ∏೙ ( ଵିோభ ௉భಲ೔ )ି ∏೙ ( ଵି௉భಲ೔ ) ೔సభ ೔సభ ∏೙ ( ଵିோభ ௉భಲ೔ ) ି ோభ ∏೙ ( ଵି௉భಲ೔ ) ೔సభ ೔సభ Pଵ = ∑௡ ൥൭ ௜ୀଵ ುభಲ೔ ൫భషುభಲ೔ ൯ ುభಲ೔ ൨ ଵା∑೙ ൤ ೔సభ ൫భషು భಲ೔ ൯ ൱൩ Series Coupling overall parallel flow ܶଵଶ ܶଵଵ ܶଶଶ ܶଶଵ ܲଵ = ଵ ଵାோభ ܶଵଷ ܶଶଷ ܶଵଵ ܶଶଵ ሼ1 − ∏௡ ሾ1 − (1 + ܴ)ܲଵ஺௜ ሿሽ ௜ୀଵ NTU = ∑௡ ܷܰܶଵ஺௜ ௜ୀଵ
  • 8. DOUBLE PIPE HEAT EXCHANGER Counter Flow ( Cold-Tube Side , Hot- Shell Side) (ଵି௉) = (ଵି௉ோ) ∆ܶ௟௠ = ଵ ே்௎೎ = ்೓೔೙ ି ்೎೚ೠ೟ ்೓೚ೠ೟ ି ்೎೔೙ (்೓೔೙ ି ்೎೔೙ ) ௉ (ோିଵ) (ோିଵ) ݈݊ቀ1−ܲቁ ܴܲ ௟௡ቀ భషು ቁ ುೃ NTܷ௖ = ୒୘௎೓ ோ For n- pass heat exchangers 1- Cold fluid in parallel and hot fluid in series flow ߠ= భൗ ೙ భ ) భషುೃ) ௟௡቎(( ೃ ೙ ௉( ିଵ) భ ൗ೙ భ ቏ ൗ೙ ቌଵିೃ ቍାೃ 2- Cold fluid in series and hot fluid in parallel flow ߠ= ௉(ଵି௡ோ)⁄௡ ௟௡൥(ଵି௡ோ)ቀ భ ቁ భషು భ ೙ ା௡ோ൩