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Correlations for heat transfer and pressure drop

Nomenclature:

D - Hydraulic diameter
L - Flow length
vel - Fluid velocity
Dens - Density
CP - Specific heat capacity
DV - Dynamic viscosity
KV - Kinematic viscosity = DV/Dens
TC - Thermal conductivity
Beta - Thermal expansion coefficient
T,Surf - Surface temperature
T,Amb - Ambient temperature
dT = T,Surf - T,Amb
Grav - Gravity acceleration
Re - Reynolds number = vel*D/KV
Gr - Grashof number = Grav*Beta*abs(dT)*D^3/KV^2
Pr - Prandtl number = KV*CP/TC
Ra - Rayleigh number = Gr*Pr
Nu - Nusselt number = HTC*D/TC
HTC - Heat transfer coefficient
rlRough - Relative coarseness
rFrict - Friction coefficient for fluid flow pressure drop
Lam - Laminar
Tr - Transient
Turb - Turbulent

General forced convection heat transfer:

Re > 10000: HTC = HTCTurb = 0.027*(TC/D)*Re^0.8*Pr^(1/3)
Re < 2300: HTC = HTCLam = 1.86*(TC/D)*Re*Pr*D/L)^(1/3)
2300 < Re < 10000: HTC = HTCTurb*(1-(1-1.86*(L/D)^(-1/3​)*(2300/Re)^(3/2))

Laminar forced convection (Kreith & Black):

Nu = 0.664*sqrt(Re)*Pr^(1/3);

Turbulent forced convection (Kreith & Black):

Nu = 0.036*(Re^0.8-23200)*Pr^(1/3);

Forced convection heat transfer for external cross flow over single pipe (Churchill & Bernstein, 1977):

Nu = 0.3 + 0.62*Re^(1/2)*Pr^(1/3)/(1+(0.4​/Pr)^(2/3))^0.25*(1+(Re/282000​)^(5/8))^(4/5)

Turbulent forced convection heat transfer inside smooth pipes (Sieder & Tate, 1936):

Nu = 0.027*Re^0.8*Pr^(1/3)*(DV/DV,w​all)^0.14, Re > 10,000, 0.5 < Pr < 1E6

Turbulent forced convection heat transfer inside smooth pipes (Dittus & Boelter, 1930):

Nu = 0.023*Re^0.8*Pr^0.4, dT > 0, 2500 < Re < 1.24E5, 0.7 < Pr < 120, L/D > 60

Turbulent forced convection heat transfer inside smooth pipes (Dittus & Boelter, 1930):

Nu = 0.023*Re^0.8*Pr^0.3, dT < 0, 2500 < Re < 1.24E5, 0.7 < Pr < 120, L/D > 60

General vertical plate free convection (Churchill & Chu, 1975):

Nu = [0.825 + 0.387*Ra^(1/6)/[1 + (0.492/Pr)^(9/16)]^(8/27)]^2, 0.1 < Ra < 1E12

Vertical plate laminar free convection (Kreith & Black):

Nu = 0.59*Ra^(1/4)

Vertical plate turbulent free convection (Kreith & Black):

Nu = 0.10*Ra^(1/3)

Vertical, short pipe external free convection heat transfer (LeFevre & Ede, 1956):

Nu = 4/3*[7*Ra*Pr/[5*(20 + 21*Pr)]]^(1/4) + 4*(272 + 315*Pr)*L/[35*(64 + 63*Pr)*D]

Vertical long pipe internal free convection heat transfer (A. Bejan, 1984):

Nu = Ra/128, L/D > Ra

Horizontal plate stable free convection (Incropera & DeWitt, 1990):

Nu = 0.27*Ra^(1/4), 1E5 < Ra < 1E10

Horizontal plate unstable laminar free convection (Lloyd & Moran, 1974):

Nu = 0.54*Ra^(1/4), 1E4 < Ra < 1E7

Horizontal plate unstable turbulent free convection (Lloyd & Moran, 1974):

Nu = 0.15*Ra^(1/3), 1E7 < Ra < 1E9

Horizontal pipe external free convection heat transfer (Churchill & Chu, 1975):

Nu = [0.6 + 0.387*Ra^(1/6)/[1 + (0.559/Pr)^(9/16)]^(8/27)]^2, 1E-5 < Ra < 1E12

Correlations for pressure drop:
rlRoughMin interpolated in the following table with respect to the Reynolds number Re:

Re: 0 20,000 20,000 100,000 1,000,000 10,000,000 100,000,000
rlRoughMin: 1 1 0.067 0.014 0.0017 0.00019 0.000025

Smooth pipes: (rlRough < rlRoughMin)

Re < 2,000: rFrict = 64/Re,
2,000 < Re < 100,000: rFrict = 0.3164*Re^(-0.25),
Re > 100,000: rFrict = 0.0032+0.221*Re^(-0.237)

Coarse pipes: (rlRough > rlRoughMin)

Re < 2,000: rFrict = 64/Re = rFrict,Lam
2,000 < Re < 3,000: rFrict,Tr = rFrict,Lam+(rFrict, Turb-rFrict​,Lam)*(0.001*Re-2)
3,000 < Re < 20,000: rFrict,0 = 0.3164*Re^(-0.25),
rLam,0 = sqrt(rFrict,0)
rLam,n = 1/(1.14-0.868589*ln(rlRough+9.​3/(Re*rLam,n-1)))
rFrict = rLam,n*rLam,n = rFrict, Turb
Re > 20,000: rLam = 1/(1.14+0.868589*ln(1/rlRough)​)
rFrict = rLam*rLam

Correlations for heat transfer and pressure drop

Nomenclature:

D - Hydraulic diameter
L - Flow length
vel - Fluid velocity
Dens - Density
CP - Specific heat capacity
DV - Dynamic viscosity
KV - Kinematic viscosity = DV/Dens
TC - Thermal conductivity
Beta - Thermal expansion coefficient
T,Surf - Surface temperature
T,Amb - Ambient temperature
dT = T,Surf - T,Amb
Grav - Gravity acceleration
Re - Reynolds number = vel*D/KV
Gr - Grashof number = Grav*Beta*abs(dT)*D^3/KV^2
Pr - Prandtl number = KV*CP/TC
Ra - Rayleigh number = Gr*Pr
Nu - Nusselt number = HTC*D/TC
HTC - Heat transfer coefficient
rlRough - Relative coarseness
rFrict - Friction coefficient for fluid flow pressure drop
Lam - Laminar
Tr - Transient
Turb - Turbulent

General forced convection heat transfer:

Re > 10000: HTC = HTCTurb = 0.027*(TC/D)*Re^0.8*Pr^(1/3)
Re < 2300: HTC = HTCLam = 1.86*(TC/D)*Re*Pr*D/L)^(1/3)
2300 < Re < 10000: HTC = HTCTurb*(1-(1-1.86*(L/D)^(-1/3​)*(2300/Re)^(3/2))

Laminar forced convection (Kreith & Black):

Nu = 0.664*sqrt(Re)*Pr^(1/3);

Turbulent forced convection (Kreith & Black):

Nu = 0.036*(Re^0.8-23200)*Pr^(1/3);

Forced convection heat transfer for external cross flow over single pipe (Churchill & Bernstein, 1977):

Nu = 0.3 + 0.62*Re^(1/2)*Pr^(1/3)/(1+(0.4​/Pr)^(2/3))^0.25*(1+(Re/282000​)^(5/8))^(4/5)

Turbulent forced convection heat transfer inside smooth pipes (Sieder & Tate, 1936):

Nu = 0.027*Re^0.8*Pr^(1/3)*(DV/DV,w​all)^0.14, Re > 10,000, 0.5 < Pr < 1E6

Turbulent forced convection heat transfer inside smooth pipes (Dittus & Boelter, 1930):

Nu = 0.023*Re^0.8*Pr^0.4, dT > 0, 2500 < Re < 1.24E5, 0.7 < Pr < 120, L/D > 60

Turbulent forced convection heat transfer inside smooth pipes (Dittus & Boelter, 1930):

Nu = 0.023*Re^0.8*Pr^0.3, dT < 0, 2500 < Re < 1.24E5, 0.7 < Pr < 120, L/D > 60

General vertical plate free convection (Churchill & Chu, 1975):

Nu = [0.825 + 0.387*Ra^(1/6)/[1 + (0.492/Pr)^(9/16)]^(8/27)]^2, 0.1 < Ra < 1E12

Vertical plate laminar free convection (Kreith & Black):

Nu = 0.59*Ra^(1/4)

Vertical plate turbulent free convection (Kreith & Black):

Nu = 0.10*Ra^(1/3)

Vertical, short pipe external free convection heat transfer (LeFevre & Ede, 1956):

Nu = 4/3*[7*Ra*Pr/[5*(20 + 21*Pr)]]^(1/4) + 4*(272 + 315*Pr)*L/[35*(64 + 63*Pr)*D]

Vertical long pipe internal free convection heat transfer (A. Bejan, 1984):

Nu = Ra/128, L/D > Ra

Horizontal plate stable free convection (Incropera & DeWitt, 1990):

Nu = 0.27*Ra^(1/4), 1E5 < Ra < 1E10

Horizontal plate unstable laminar free convection (Lloyd & Moran, 1974):

Nu = 0.54*Ra^(1/4), 1E4 < Ra < 1E7

Horizontal plate unstable turbulent free convection (Lloyd & Moran, 1974):

Nu = 0.15*Ra^(1/3), 1E7 < Ra < 1E9

Horizontal pipe external free convection heat transfer (Churchill & Chu, 1975):

Nu = [0.6 + 0.387*Ra^(1/6)/[1 + (0.559/Pr)^(9/16)]^(8/27)]^2, 1E-5 < Ra < 1E12

Correlations for pressure drop:
rlRoughMin interpolated in the following table with respect to the Reynolds number Re:

Re: 0 20,000 20,000 100,000 1,000,000 10,000,000 100,000,000
rlRoughMin: 1 1 0.067 0.014 0.0017 0.00019 0.000025

Smooth pipes: (rlRough < rlRoughMin)

Re < 2,000: rFrict = 64/Re,
2,000 < Re < 100,000: rFrict = 0.3164*Re^(-0.25),
Re > 100,000: rFrict = 0.0032+0.221*Re^(-0.237)

Coarse pipes: (rlRough > rlRoughMin)

Re < 2,000: rFrict = 64/Re = rFrict,Lam
2,000 < Re < 3,000: rFrict,Tr = rFrict,Lam+(rFrict, Turb-rFrict​,Lam)*(0.001*Re-2)
3,000 < Re < 20,000: rFrict,0 = 0.3164*Re^(-0.25),
rLam,0 = sqrt(rFrict,0)
rLam,n = 1/(1.14-0.868589*ln(rlRough+9.​3/(Re*rLam,n-1)))
rFrict = rLam,n*rLam,n = rFrict, Turb
Re > 20,000: rLam = 1/(1.14+0.868589*ln(1/rlRough)​)
rFrict = rLam*rLam

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vuran cephe bizim parti cephemiz

cüret direniş savaş
önderimiz dursun karataş

o değil de panpalar

umudun adı dhkp-c

das kapital okumadan burda ahkam kesenin hariçten gazel okuyanın gelmişini geçmişini yedi ceddini devri devranını izzeti ikrdıbını gibeyim.

Correlations for heat transfer and pressure drop

Nomenclature:

D - Hydraulic diameter
L - Flow length
vel - Fluid velocity
Dens - Density
CP - Specific heat capacity
DV - Dynamic viscosity
KV - Kinematic viscosity = DV/Dens
TC - Thermal conductivity
Beta - Thermal expansion coefficient
T,Surf - Surface temperature
T,Amb - Ambient temperature
dT = T,Surf - T,Amb
Grav - Gravity acceleration
Re - Reynolds number = vel*D/KV
Gr - Grashof number = Grav*Beta*abs(dT)*D^3/KV^2
Pr - Prandtl number = KV*CP/TC
Ra - Rayleigh number = Gr*Pr
Nu - Nusselt number = HTC*D/TC
HTC - Heat transfer coefficient
rlRough - Relative coarseness
rFrict - Friction coefficient for fluid flow pressure drop
Lam - Laminar
Tr - Transient
Turb - Turbulent

General forced convection heat transfer:

Re > 10000: HTC = HTCTurb = 0.027*(TC/D)*Re^0.8*Pr^(1/3)
Re < 2300: HTC = HTCLam = 1.86*(TC/D)*Re*Pr*D/L)^(1/3)
2300 < Re < 10000: HTC = HTCTurb*(1-(1-1.86*(L/D)^(-1/3​)*(2300/Re)^(3/2))

Laminar forced convection (Kreith & Black):

Nu = 0.664*sqrt(Re)*Pr^(1/3);

Turbulent forced convection (Kreith & Black):

Nu = 0.036*(Re^0.8-23200)*Pr^(1/3);

Forced convection heat transfer for external cross flow over single pipe (Churchill & Bernstein, 1977):

Nu = 0.3 + 0.62*Re^(1/2)*Pr^(1/3)/(1+(0.4​/Pr)^(2/3))^0.25*(1+(Re/282000​)^(5/8))^(4/5)

Turbulent forced convection heat transfer inside smooth pipes (Sieder & Tate, 1936):

Nu = 0.027*Re^0.8*Pr^(1/3)*(DV/DV,w​all)^0.14, Re > 10,000, 0.5 < Pr < 1E6

Turbulent forced convection heat transfer inside smooth pipes (Dittus & Boelter, 1930):

Nu = 0.023*Re^0.8*Pr^0.4, dT > 0, 2500 < Re < 1.24E5, 0.7 < Pr < 120, L/D > 60

Turbulent forced convection heat transfer inside smooth pipes (Dittus & Boelter, 1930):

Nu = 0.023*Re^0.8*Pr^0.3, dT < 0, 2500 < Re < 1.24E5, 0.7 < Pr < 120, L/D > 60

General vertical plate free convection (Churchill & Chu, 1975):

Nu = [0.825 + 0.387*Ra^(1/6)/[1 + (0.492/Pr)^(9/16)]^(8/27)]^2, 0.1 < Ra < 1E12

Vertical plate laminar free convection (Kreith & Black):

Nu = 0.59*Ra^(1/4)

Vertical plate turbulent free convection (Kreith & Black):

Nu = 0.10*Ra^(1/3)

Vertical, short pipe external free convection heat transfer (LeFevre & Ede, 1956):

Nu = 4/3*[7*Ra*Pr/[5*(20 + 21*Pr)]]^(1/4) + 4*(272 + 315*Pr)*L/[35*(64 + 63*Pr)*D]

Vertical long pipe internal free convection heat transfer (A. Bejan, 1984):

Nu = Ra/128, L/D > Ra

Horizontal plate stable free convection (Incropera & DeWitt, 1990):

Nu = 0.27*Ra^(1/4), 1E5 < Ra < 1E10

Horizontal plate unstable laminar free convection (Lloyd & Moran, 1974):

Nu = 0.54*Ra^(1/4), 1E4 < Ra < 1E7

Horizontal plate unstable turbulent free convection (Lloyd & Moran, 1974):

Nu = 0.15*Ra^(1/3), 1E7 < Ra < 1E9

Horizontal pipe external free convection heat transfer (Churchill & Chu, 1975):

Nu = [0.6 + 0.387*Ra^(1/6)/[1 + (0.559/Pr)^(9/16)]^(8/27)]^2, 1E-5 < Ra < 1E12

Correlations for pressure drop:
rlRoughMin interpolated in the following table with respect to the Reynolds number Re:

Re: 0 20,000 20,000 100,000 1,000,000 10,000,000 100,000,000
rlRoughMin: 1 1 0.067 0.014 0.0017 0.00019 0.000025

Smooth pipes: (rlRough < rlRoughMin)

Re < 2,000: rFrict = 64/Re,
2,000 < Re < 100,000: rFrict = 0.3164*Re^(-0.25),
Re > 100,000: rFrict = 0.0032+0.221*Re^(-0.237)

Coarse pipes: (rlRough > rlRoughMin)

Re < 2,000: rFrict = 64/Re = rFrict,Lam
2,000 < Re < 3,000: rFrict,Tr = rFrict,Lam+(rFrict, Turb-rFrict​,Lam)*(0.001*Re-2)
3,000 < Re < 20,000: rFrict,0 = 0.3164*Re^(-0.25),
rLam,0 = sqrt(rFrict,0)
rLam,n = 1/(1.14-0.868589*ln(rlRough+9.​3/(Re*rLam,n-1)))
rFrict = rLam,n*rLam,n = rFrict, Turb
Re > 20,000: rLam = 1/(1.14+0.868589*ln(1/rlRough)​)
rFrict = rLam*rLam

bursayı gibtik ondan geç kaldık panpalar.

sanat düşmanı amcık ağızlı. züt veren radikal feminist.

valeria amcık ağızlının tekiydi panpalar en sevdiğim ressamı öldürdü kevaşe.

eftane züttepenin cenaze namazına katılmayan gerçekten gibtirsin gitsin beyler

hadi elinize belinize kuvvet

panpalar bu kullanıcı hesaplarını bi deneyin olmazsa yenilerini paylaşıcam.

Correlations for heat transfer and pressure drop

Nomenclature:

D - Hydraulic diameter
L - Flow length
vel - Fluid velocity
Dens - Density
CP - Specific heat capacity
DV - Dynamic viscosity
KV - Kinematic viscosity = DV/Dens
TC - Thermal conductivity
Beta - Thermal expansion coefficient
T,Surf - Surface temperature
T,Amb - Ambient temperature
dT = T,Surf - T,Amb
Grav - Gravity acceleration
Re - Reynolds number = vel*D/KV
Gr - Grashof number = Grav*Beta*abs(dT)*D^3/KV^2
Pr - Prandtl number = KV*CP/TC
Ra - Rayleigh number = Gr*Pr
Nu - Nusselt number = HTC*D/TC
HTC - Heat transfer coefficient
rlRough - Relative coarseness
rFrict - Friction coefficient for fluid flow pressure drop
Lam - Laminar
Tr - Transient
Turb - Turbulent

kapış kapış gidecek panpalar. hadi toplaşın bakalım.

@10 dokuz kat tabi panpa sokak arasında elinde yarım ekmekle top sektirdiğin top buydu.

bu yazıdan birşey anladıysam makina mühendisiyim aq!

correlations for heat transfer and pressure drop

nomenclature:

d - hydraulic diameter
l - flow length
vel - fluid velocity
dens - density
cp - specific heat capacity
dv - dynamic viscosity
kv - kinematic viscosity = dv/dens
tc - thermal conductivity
beta - thermal expansion coefficient
t,surf - surface temperature
t,amb - ambient temperature
dt = t,surf - t,amb
grav - gravity acceleration
re - reynolds number = vel*d/kv
gr - grashof number = grav*beta*abs(dt)*d^3/kv^2
pr - prandtl number = kv*cp/tc
ra - rayleigh number = gr*pr
nu - nusselt number = htc*d/tc
htc - heat transfer coefficient
rlrough - relative coarseness
rfrict - friction coefficient for fluid flow pressure drop
lam - laminar
tr - transient
turb - turbulent

general forced convection heat transfer:

re > 10000: htc = htcturb = 0.027*(tc/d)*re^0.8*pr^(1/3)
re < 2300: htc = htclam = 1.86*(tc/d)*re*pr*d/l)^(1/3)
2300 < re < 10000: htc = htcturb*(1-(1-1.86*(l/d)^(-1/3)*(2300/re)^(3/2))

laminar forced convection (kreith & black):

nu = 0.664*sqrt(re)*pr^(1/3);

turbulent forced convection (kreith & black):

nu = 0.036*(re^0.8-23200)*pr^(1/3);

forced convection heat transfer for external cross flow over single pipe (churchill & bernstein, 1977):

nu = 0.3 + 0.62*re^(1/2)*pr^(1/3)/(1+(0.4/pr)^(2/3))^0.25*(1+(re/282000)^(5/8))^(4/5)

turbulent forced convection heat transfer inside smooth pipes (sieder & tate, 1936):

nu = 0.027*re^0.8*pr^(1/3)*(dv/dv,wall)^0.14, re > 10,000, 0.5 < pr < 1e6

turbulent forced convection heat transfer inside smooth pipes (dittus & boelter, 1930):

nu = 0.023*re^0.8*pr^0.4, dt > 0, 2500 < re < 1.24e5, 0.7 < pr < 120, l/d > 60

turbulent forced convection heat transfer inside smooth pipes (dittus & boelter, 1930):

nu = 0.023*re^0.8*pr^0.3, dt < 0, 2500 < re < 1.24e5, 0.7 < pr < 120, l/d > 60

general vertical plate free convection (churchill & chu, 1975):

nu = [0.825 + 0.387*ra^(1/6)/[1 + (0.492/pr)^(9/16)]^(8/27)]^2, 0.1 < ra < 1e12

vertical plate laminar free convection (kreith & black):

nu = 0.59*ra^(1/4)

vertical plate turbulent free convection (kreith & black):

nu = 0.10*ra^(1/3)

vertical, short pipe external free convection heat transfer (lefevre & ede, 1956):

nu = 4/3*[7*ra*pr/[5*(20 + 21*pr)]]^(1/4) + 4*(272 + 315*pr)*l/[35*(64 + 63*pr)*d]

vertical long pipe internal free convection heat transfer (a. bejan, 1984):

nu = ra/128, l/d > ra

horizontal plate stable free convection (incropera & dewitt, 1990):

nu = 0.27*ra^(1/4), 1e5 < ra < 1e10

horizontal plate unstable laminar free convection (lloyd & moran, 1974):

nu = 0.54*ra^(1/4), 1e4 < ra < 1e7

horizontal plate unstable turbulent free convection (lloyd & moran, 1974):

nu = 0.15*ra^(1/3), 1e7 < ra < 1e9

horizontal pipe external free convection heat transfer (churchill & chu, 1975):

nu = [0.6 + 0.387*ra^(1/6)/[1 + (0.559/pr)^(9/16)]^(8/27)]^2, 1e-5 < ra < 1e12

correlations for pressure drop:
rlroughmin interpolated in the following table with respect to the reynolds number re:

re: 0 20,000 20,000 100,000 1,000,000 10,000,000 100,000,000
rlroughmin: 1 1 0.067 0.014 0.0017 0.00019 0.000025

smooth pipes: (rlrough < rlroughmin)

re < 2,000: rfrict = 64/re,
2,000 < re < 100,000: rfrict = 0.3164*re^(-0.25),
re > 100,000: rfrict = 0.0032+0.221*re^(-0.237)

coarse pipes: (rlrough > rlroughmin)

re < 2,000: rfrict = 64/re = rfrict,lam
2,000 < re < 3,000: rfrict,tr = rfrict,lam+(rfrict, turb-rfrict,lam)*(0.001*re-2)
3,000 < re < 20,000: rfrict,0 = 0.3164*re^(-0.25),
rlam,0 = sqrt(rfrict,0)
rlam,n = 1/(1.14-0.868589*ln(rlrough+9.3/(re*rlam,n-1)))
rfrict = rlam,n*rlam,n = rfrict, turb
re > 20,000: rlam = 1/(1.14+0.868589*ln(1/rlrough))
rfrict = rlam*rlam

beni yaz!

"3 akçe aldı ya çakal!"

kenan komutan, vefa

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http://2.bp.blogspot.com/...UdrgdqwPvw/s400/kames.jpg

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:(((((((

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panpa bu çizgi filmi hatırlayan var mı?

http://www.youtube.com/wa...bru8s&feature=related

panpa bu çizgi filmi hatırlayanınız var mı?

http://www.youtube.com/watch?v=3JjhQ1Oi_3k

misket sezonundan gazoz kapağı sezonuna ne zaman geçileceğine kimin karar verdiğini hep merak ederdim panpa

correlations for heat transfer and pressure drop

nomenclature:

d - hydraulic diameter
l - flow length
vel - fluid velocity
dens - density
cp - specific heat capacity
dv - dynamic viscosity
kv - kinematic viscosity = dv/dens
tc - thermal conductivity
beta - thermal expansion coefficient
t,surf - surface temperature
t,amb - ambient temperature
dt = t,surf - t,amb
grav - gravity acceleration
re - reynolds number = vel*d/kv
gr - grashof number = grav*beta*abs(dt)*d^3/kv^2
pr - prandtl number = kv*cp/tc
ra - rayleigh number = gr*pr
nu - nusselt number = htc*d/tc
htc - heat transfer coefficient
rlrough - relative coarseness
rfrict - friction coefficient for fluid flow pressure drop
lam - laminar
tr - transient
turb - turbulent

general forced convection heat transfer:

re > 10000: htc = htcturb = 0.027*(tc/d)*re^0.8*pr^(1/3)
re < 2300: htc = htclam = 1.86*(tc/d)*re*pr*d/l)^(1/3)
2300 < re < 10000: htc = htcturb*(1-(1-1.86*(l/d)^(-1/3)*(2300/re)^(3/2))

laminar forced convection (kreith & black):

nu = 0.664*sqrt(re)*pr^(1/3);

turbulent forced convection (kreith & black):

nu = 0.036*(re^0.8-23200)*pr^(1/3);

forced convection heat transfer for external cross flow over single pipe (churchill & bernstein, 1977):

nu = 0.3 + 0.62*re^(1/2)*pr^(1/3)/(1+(0.4/pr)^(2/3))^0.25*(1+(re/282000)^(5/8))^(4/5)

turbulent forced convection heat transfer inside smooth pipes (sieder & tate, 1936):

nu = 0.027*re^0.8*pr^(1/3)*(dv/dv,wall)^0.14, re > 10,000, 0.5 < pr < 1e6

turbulent forced convection heat transfer inside smooth pipes (dittus & boelter, 1930):

nu = 0.023*re^0.8*pr^0.4, dt > 0, 2500 < re < 1.24e5, 0.7 < pr < 120, l/d > 60

turbulent forced convection heat transfer inside smooth pipes (dittus & boelter, 1930):

nu = 0.023*re^0.8*pr^0.3, dt < 0, 2500 < re < 1.24e5, 0.7 < pr < 120, l/d > 60

general vertical plate free convection (churchill & chu, 1975):

nu = [0.825 + 0.387*ra^(1/6)/[1 + (0.492/pr)^(9/16)]^(8/27)]^2, 0.1 < ra < 1e12

vertical plate laminar free convection (kreith & black):

nu = 0.59*ra^(1/4)

vertical plate turbulent free convection (kreith & black):

nu = 0.10*ra^(1/3)

vertical, short pipe external free convection heat transfer (lefevre & ede, 1956):

nu = 4/3*[7*ra*pr/[5*(20 + 21*pr)]]^(1/4) + 4*(272 + 315*pr)*l/[35*(64 + 63*pr)*d]

vertical long pipe internal free convection heat transfer (a. bejan, 1984):

nu = ra/128, l/d > ra

horizontal plate stable free convection (incropera & dewitt, 1990):

nu = 0.27*ra^(1/4), 1e5 < ra < 1e10

horizontal plate unstable laminar free convection (lloyd & moran, 1974):

nu = 0.54*ra^(1/4), 1e4 < ra < 1e7

horizontal plate unstable turbulent free convection (lloyd & moran, 1974):

nu = 0.15*ra^(1/3), 1e7 < ra < 1e9

horizontal pipe external free convection heat transfer (churchill & chu, 1975):

nu = [0.6 + 0.387*ra^(1/6)/[1 + (0.559/pr)^(9/16)]^(8/27)]^2, 1e-5 < ra < 1e12

correlations for pressure drop:
rlroughmin interpolated in the following table with respect to the reynolds number re:

re: 0 20,000 20,000 100,000 1,000,000 10,000,000 100,000,000
rlroughmin: 1 1 0.067 0.014 0.0017 0.00019 0.000025

smooth pipes: (rlrough < rlroughmin)

re < 2,000: rfrict = 64/re,
2,000 < re < 100,000: rfrict = 0.3164*re^(-0.25),
re > 100,000: rfrict = 0.0032+0.221*re^(-0.237)

coarse pipes: (rlrough > rlroughmin)

re < 2,000: rfrict = 64/re = rfrict,lam
2,000 < re < 3,000: rfrict,tr = rfrict,lam+(rfrict, turb-rfrict,lam)*(0.001*re-2)
3,000 < re < 20,000: rfrict,0 = 0.3164*re^(-0.25),
rlam,0 = sqrt(rfrict,0)
rlam,n = 1/(1.14-0.868589*ln(rlrough+9.3/(re*rlam,n-1)))
rfrict = rlam,n*rlam,n = rfrict, turb
re > 20,000: rlam = 1/(1.14+0.868589*ln(1/rlrough))
rfrict = rlam*rlam