Tugas Perpindahan Panas (SUprapto)

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Modifkasi Soal.

Tflm + NIM

277o C + 38 = 315oC atau 588K

From tabulated data, we obtain the following properties of air

(interpolated) at 588K and 1 bar

µ = 3!1"#$ % 1!&5 'sm#

ρ = 0.593 kg/m3

cp = 1048.36 J/kg K

k = 0.04618 W/mK

Reynold Numbe b!"ed #$e pl!#e leng#$ %" #$en compu#e" !" &

Re' =

ρ. U ∞ L

μ =

0.593 x10 x0.5

3.01624 x10−5 =98301.20

Re' (5 ) 105 #$%" me!n" #$!# #$e *lo+ %" l!m%n! !long #$e pl!#e leng#$

,o +e need kno+ -!ndl numbe o !lcul!#e !e!ge nu""el# numbe &

!ble o* !%" pope#%e" g%en d!#! 0.68452 .Round up #o be 0.685

nd


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NUSSELT NUMBER

Introduction

An understanding of convection boundary layers is necessary to understanding

convective heat transfer between a surface and a fluid flowing past it. A thermal boundary layer develops if the fluid free stream temperature and the surface

temperatures differ. A temperature profile exists due to the energy exchange resulting

from this temperature difference.

Thrmal Boundar! La!r

The heat transfer rate can then be written as,

And because heat transfer at the surface is by conduction,

These two terms are equal; thus

Rearranging,

Maing it dimensionless by multiplying by representative length !,


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The right hand side is now the ratio of the temperature gradient at the surface to the

reference temperature gradient. "hile the left hand side is similar to the #iot modulus.

This becomes the ratio of conductive thermal resistance to the convective thermal

resistance of the fluid, otherwise nown as the $usselt number, $u.

"ri#ation

The $usselt number may be obtained by a non dimensional analysis of %ourier&s

law since it is equal to the dimensionless temperature gradient at the surface'

$ %hr is th hat trans&r rat$ * is th

constant thrmal conducti#it! and + th 'uid tm(ratur.

(ndeed, if' , and

we arrive at

then we define

so the equation becomes

#y integrating over the surface of the body'

,

https://en.wikipedia.org/wiki/Fourier's_lawhttps://en.wikipedia.org/wiki/Fourier's_lawhttps://en.wikipedia.org/wiki/Heat_transfer_ratehttps://en.wikipedia.org/wiki/Thermal_conductivityhttps://en.wikipedia.org/wiki/Fluidhttps://en.wikipedia.org/wiki/Temperaturehttps://en.wikipedia.org/wiki/Heat_transfer_ratehttps://en.wikipedia.org/wiki/Thermal_conductivityhttps://en.wikipedia.org/wiki/Fluidhttps://en.wikipedia.org/wiki/Temperaturehttps://en.wikipedia.org/wiki/Fourier's_lawhttps://en.wikipedia.org/wiki/Fourier's_law


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where

Em(irical Corrlations

Typically, for free convection, the average $usselt number is expressed as a functionof the Rayleigh number and the )randtl number , written as'

*therwise, for forced convection, the $usselt number is generally a function of

the Reynolds number and the )randtl number , or

+mpirical correlations for a wide variety of geometries are available that express the $usselt number in the aforementioned forms.

)r con#ction

)r con#ction at a #rtical %all

ited-/ as coming from hurchill and hu'

)r con#ction &rom hori*ontal (lats

(f the characteristic length is defined

where is the surface area of the plate and is its perimeter.

Then for the top surface of a hot ob0ect in a colder environment or bottom surface of a

cold ob0ect in a hotter environment -/

https://en.wikipedia.org/wiki/Rayleigh_numberhttps://en.wikipedia.org/wiki/Prandtl_numberhttps://en.wikipedia.org/wiki/Reynolds_numberhttps://en.wikipedia.org/wiki/Prandtl_numberhttps://en.wiktionary.org/wiki/empiricalhttps://en.wiktionary.org/wiki/empiricalhttps://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/wiki/Rayleigh_numberhttps://en.wikipedia.org/wiki/Prandtl_numberhttps://en.wikipedia.org/wiki/Reynolds_numberhttps://en.wikipedia.org/wiki/Prandtl_numberhttps://en.wiktionary.org/wiki/empiricalhttps://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3


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And for the bottom surface of a hot ob0ect in a colder environment or top surface of a

cold ob0ect in a hotter environment -/

7oced conec#%on on *l!# pl!#e

)lat (lat in laminar 'o%

The local $usselt number for laminar flow over a flat plate is given by -1/

The average $usselt number for laminar flow over a flat plate is given by -1/

-2/

)orcd con#ction in turulnt (i( 'o%

,nilinski corrlation

3nielinsi&s correlation for turbulent flow in tubes'-1/

where f is the 4arcy friction factor that can either be obtained from the Moody

chart or for smooth tubes from correlation developed by )etuhov'-1/

The 3nielinsi orrelation is valid for'-1/

https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-5https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/wiki/Darcy_friction_factorhttps://en.wikipedia.org/wiki/Moody_charthttps://en.wikipedia.org/wiki/Moody_charthttps://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-5https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/wiki/Darcy_friction_factorhttps://en.wikipedia.org/wiki/Moody_charthttps://en.wikipedia.org/wiki/Moody_charthttps://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incropera490-4


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"ittus-Boltr uation

The 4ittus5#oelter equation 6for turbulent flow7 is an explicit function for calculating

the $usselt number. (t is easy to solve but is less accurate when there is a large

temperature difference across the fluid. (t is tailored to smooth tubes, so use for rough

tubes 6most commercial applications7 is cautioned. The 4ittus5#oelter equation is'

where'

is th insid diamtr o& th circular duct

is th /randtl numr

&or hatin0 o& th 'uid$ and &or coolin0 o& th

'uid.13

The 4ittus5#oelter equation is valid for -8/

)!mple The 4ittus5#oelter equation is a good approximation where temperature

differences between bul fluid and heat transfer surface are minimal, avoiding

equation complexity and iterative solving. Taing water with a bul fluid average

temperature of 9: , viscosity


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temperature, respectively. The Cieder5Tate correlation is normally solved by an

iterative process, as the viscosity factor will change as the $usselt number changes. -=/

13

where'

is th 'uid #iscosit! at th ulk 'uid tm(ratur

is th 'uid #iscosit! at th hat-trans&r oundar! sur&ac

tm(ratur

The Cieder5Tate correlation is valid for -/

)orcd con#ction in &ull! d#lo(d laminar (i( 'o%

%or fully developed internal laminar flow, the $usselt numbers are constant5valued.

The values depend on the hydraulic diameter.

%or internal %low'

where'

Dh 4 5!draulic diamtr

k f 4 thrmal conducti#it! o& th 'uid

h 4 con#cti# hat trans&r co6cint

Con#ction %ith uni&orm sur&ac hat 'u &or circular tus

https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-7https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/wiki/Hydraulic_diameterhttps://en.wikipedia.org/wiki/Thermal_conductivityhttps://en.wikipedia.org/wiki/Convectivehttps://en.wikipedia.org/wiki/Heat_transfer_coefficienthttps://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-7https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/w/index.php?title=Nusselt_number&printable=yes#cite_note-incrop-3https://en.wikipedia.org/wiki/Hydraulic_diameterhttps://en.wikipedia.org/wiki/Thermal_conductivityhttps://en.wikipedia.org/wiki/Convectivehttps://en.wikipedia.org/wiki/Heat_transfer_coefficient


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%rom (ncropera E 4e"itt,-B/

Con#ction %ith uni&orm sur&ac tm(ratur &or circular tus

%or the case of constant surface temperature,-B/

S also

Shr%ood numr 8mass trans&r Nusslt numr9

Churchill:Brnstin uation

Biot Numr

R!nolds numr

Con#cti# hat trans&r

5at trans&r co6cint

Thrmal conducti#it!

Etrnal links

Sim(l dri#ation o& th Nusslt numr &rom N%ton;s la% o&

coolin0 89

R&rncs

?. Yunus A. Çengel (2003). Heat Transfer: a Practical Approach (2ne.). !c"ra#$Hill.

2. %. &an'icente et al. (202). *Transitional natural con'ection +o# anheat transfer in an open channel*. ,nternational -ournal of Theral&ciences 63: /10. oi:0.045.i5theralsci.202.0.00.

. ,ncropera6 7rank P. De8itt6 Da'i P. (2000). 7unaentals of Heat an!ass Transfer (th e.). 9e# York: 8ile. p. ;3. ,&


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@. ,ncropera6 7rank P. De8itt6 Da'i P. (200). 7unaentals of Heat an!ass Transfer (th e.). Ho=oken: 8ile. pp. ;06 >>. ,&2/$2.

A. Incro(ra$ )rank /. )undamntals o& hat and mass trans&r. ohn il!D Sons$ 2=??.

. Incro(ra$ )rank /.F "itt$ "a#id /. 82==79. )undamntals o& 5at andMass Trans&r 8th d.9. N% GorkH il!. (. A?@. ISBN >7-=-@7?-@A72-2.

7. *Teperature Pro?le in &tea "enerator Tu=e !etal* (PD7).@etrie'e 23 &epte=er 200;.

. ,ncropera6 7rank P. De8itt6 Da'i P. (2002). 7unaentals of Heat an!ass Transfer (>th e.). Ho=oken: 8ile. pp. /6 /. ,&0$2

https://en.wikipedia.org/wiki/Frank_P._Incroperahttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-471-45728-2https://en.wikipedia.org/wiki/Special:BookSources/978-0-471-45728-2https://en.wikipedia.org/wiki/Special:BookSources/9780471457282http://www.profjrwhite.com/math_methods/pdf_files_hw/sgtm3.pdfhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-471-38650-2https://en.wikipedia.org/wiki/Frank_P._Incroperahttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/978-0-471-45728-2https://en.wikipedia.org/wiki/Special:BookSources/978-0-471-45728-2https://en.wikipedia.org/wiki/Special:BookSources/9780471457282http://www.profjrwhite.com/math_methods/pdf_files_hw/sgtm3.pdfhttps://en.wikipedia.org/wiki/International_Standard_Book_Numberhttps://en.wikipedia.org/wiki/Special:BookSources/0-471-38650-2

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