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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,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
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