{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 4 : Forced Convection"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.2 Page No : 112"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The rate of heat loss is 5328 W\n"
]
}
],
"source": [
"# Variables\n",
"l = 2. \t\t\t#m, length of flat surface\n",
"T1 = 150. \t\t\t#C, surface temp.\n",
"p = 1. \t\t\t#atm, pressure\n",
"T2 = 30. \t\t\t#C, bulk air temp.\n",
"V = 12. \t\t\t#m/s, air velocity\n",
"\n",
"#Calculation\n",
"Tf = (T1+T2)/2 \t\t\t#C, mean air film temp.\n",
"mu = 2.131*10**-5 \t\t\t#m**2/s, vismath.cosity\n",
"k = 0.031 \t\t\t#W/m C, thermal conductivity\n",
"rho = 0.962 \t\t\t#kg/m**3, density of air\n",
"cp = 1.01 \t\t\t#kj/kg C, specific heat of air\n",
"Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n",
"Remax = l*V*rho/mu \t\t\t#maximum Reynold no.\n",
"Re = 5.*10**5 \t\t\t#Reynold no. during transition to turbulent flow \n",
"L_ = (Re*mu)/(V*rho) \t\t\t#m,dismath.tance from the leading edge\n",
"#for laminar flow heat transfer coefficient h, \n",
"#h16.707*x**-(1/2)\n",
"#(a)\n",
"#h2 = 31.4*x**(-1/5)\n",
"#b\n",
"hav = 22.2\n",
"#c\n",
"Q = hav*l*p*(T1-T2)\n",
"\n",
"# Results\n",
"print \"The rate of heat loss is %.0f W\"%(Q)\n",
"\n",
"# rounding off error."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.3 Page No : 114"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The steady state temprature is 230 C\n",
"The recalculated value is almost equal to previous one.\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"d = 7.24*10**-4 \t\t\t#m, diameter of wire\n",
"l = 1. \t\t\t#m, length of wire\n",
"I = 8.3 \t\t\t#A, current in a wire\n",
"R = 2.625 \t\t\t#ohm/m, electrical resistance\n",
"V = 10. \t\t\t#m/s, air velocity\n",
"Tb = 27. \t\t\t#C, bulk air temp.\n",
"#the properties at bulk temp.\n",
"mu = 1.983*10**-5 \t\t\t#m**2/s, vismath.cosity\n",
"k = 0.02624 \t\t\t#W/m C, thermal conductivity\n",
"rho = 1.1774 \t\t\t#kg/m**3, density of air\n",
"cp = 1.0057 \t\t\t#kj/kg C, specific heat of air\n",
"\n",
"# Calculations and Results\n",
"Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n",
"Re = d*V*rho/mu \t\t\t# Reynold no.\n",
"#from eq. 4.19, nusslet no.\n",
"Nu = 0.3+(0.62*Re**(1./2)*Pr**(1./3)/(1+(0.4/Pr)**(2./3))**(1./4))*(1+(Re/(2.82*10**5))**(5./8))**(4./5)\n",
"hav = Nu*k/d \t\t\t#W/m**2 C, average heat transfer coefficient\n",
"Q = I**2*R \t\t\t#W, rate of electrical heat generation\n",
"A = math.pi*d*l\n",
"dt = Q/(hav*A) \t\t\t#C,temp. difference\n",
"T = dt+Tb \t\t\t#C, steady state temp.\n",
"print \"The steady state temprature is %.0f C\"%(T)\n",
"\n",
"Tm = (T+Tb)/2 \t\t\t#C, mean air film temp.\n",
"#the properties at Tm temp.\n",
"mu1 = 2.30*10**-5 \t\t\t#m**2/s, vismath.cosity\n",
"k1 = 0.0338 \t\t\t#W/m C, thermal conductivity\n",
"rho1 = 0.878 \t\t\t#kg/m**3, density of air\n",
"cp1 = 1.014 \t\t\t#kj/kg C, specific heat of air\n",
"Re1 = d*V*rho1/mu1 \t\t\t# Reynold no.\n",
"Pr1 = (1.014*10**3*2.30*10**-5)/k1 \t\t\t#Prandtl no.\n",
"#from eq. 4.19, nusslet no.\n",
"Nu1 = 0.3+(0.62*Re1**(1./2)*Pr1**(1./3)/(1+(0.4/Pr1)**(2./3))**(1./4))*(1+(Re1/(2.82*10**5))**(5./8))**(4./5)\n",
"hav1 = Nu1*k1/d \t\t\t#W/m**2 C, average heat transfer coefficient\n",
"dt1 = Q/(hav1*A) \t\t\t#C,temp. difference\n",
"T1 = dt1+Tb \t\t\t#C, steady state temp.\n",
"print \"The recalculated value is almost equal to previous one.\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.4 Page No : 116"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"initial rate of melting of ice is 0.0109 g/s\n",
"The required time is is 1665 s\n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"di = 0.04 \t\t\t#m, diameter of ice ball\n",
"V = 2. \t\t\t#m/s, air velocity\n",
"T1 = 25. \t\t\t#C, steam temp.\n",
"T2 = 0.\n",
"#the properties of air\n",
"mu = 1.69*10**-5 \t\t\t#kg/ms, vismath.cosity\n",
"k = 0.026 \t\t\t#W/m C, thermal conductivity\n",
"rho = 1.248 \t\t\t#kg/m**3, density \n",
"cp = 1.005 \t\t\t#kj/kg C, specific heat \n",
"#propertice of ice\n",
"lamda = 334. \t\t\t#kj/kg, heat of fusion\n",
"rhoice = 920. \t\t\t#kg/m**3 density of ice\n",
"\n",
"# Calculations and Results\n",
"Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n",
"Re = di*V*rho/mu \t\t\t# Reynold no.\n",
"#from eq. 4.19, nusslet no.\n",
"Nu = 2+(0.4*Re**0.5+0.06*Re**(2./3))*Pr**0.4\n",
"hav = Nu*k/di \t\t\t#W/m**2 C, average heat transfer coefficient\n",
"Ai = math.pi*di**2 \t\t\t#initial area of sphere\n",
"Qi = Ai*hav*(T1-T2) \t\t\t#W = J/s, initial rate of heat transfer\n",
"Ri = Qi/lamda \t\t\t#initial rate of melting of ice\n",
"print \"initial rate of melting of ice is %.4f g/s\"%(Ri)\n",
"\n",
"#(b)\n",
"#mass of ice ball 4/3*math.pi*r**3\n",
"#Rate of melting = Rm = -d/dt(m)\n",
"#Rate of heat input required = -lamda*Rate of melting\n",
"#heat balance equation\n",
"# -lamda*(Rm) = h*4*math.pi*r**2*dt\n",
"#integrating and solving\n",
"rf = ((di/2)**3/2.)**(1./3)\n",
"#solving eq. 3\n",
"t1 = 1.355*10**-4/(8.136*10**-8)\n",
"print \"The required time is is %.0f s\"%(t1)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.5 Page No : 121"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the required contact time is 1.43 s\n"
]
}
],
"source": [
"from scipy.integrate import quad \n",
"# Variables\n",
"Vo = 0.5 \t\t\t#m/s air velocity\n",
"T1 = 800. \t\t\t#C, initial temp.\n",
"T2 = 550. \t\t\t#C, final temp.\n",
"Tam = 500. \t\t\t#C, air mean temp.\n",
"P = 1.2 \t\t\t#atm, pressure\n",
"#the properties of solid particles.\n",
"dp = 0.65*10**-3 \t\t\t#m, average particle diameter\n",
"cps = 0.196 \t\t\t#kcal/kg C, specific heat\n",
"rhos = 2550. \t\t\t#kg/m**3, density \n",
"#Properties of air\n",
"mu = 3.6*10**-5 \t\t\t#kg/ms, vismath.cosity\n",
"k = 0.05 \t\t\t#kcal/hm C, thermal conductivity\n",
"rho = 0.545 \t\t\t#kg/m**3, density of air\n",
"cp = 0.263 \t\t\t#kcal/kg C, specific heat of air\n",
"\n",
"#calculation\n",
"Pr = cp*mu*3600/k \t\t\t#Prandtl no.\n",
"Redp = dp*Vo*rho/mu \t\t\t# Reynold no.\n",
"#from eq. 4.29(b) heat transfer coefficient\n",
"h = (k/dp)*(2+0.6*(Redp)**(1./2)*(Pr)**(1./3))\n",
"Tg = 500 \t\t\t#C, gas temp.\n",
"#from heat balance equation\n",
"# -(dTs/dt) = 6h/(dp*rhos*cps)*(Ts-Tg)\n",
"\n",
"def f2(Ts): \n",
" return (1/(Ts-Tg))\n",
"\n",
"t = (dp*rhos*cps/(6*h))* quad(f2,550,800)[0]\n",
"\n",
"# Results\n",
"print \"the required contact time is %.2f s\"%(t*3600)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.6 Page No : 126"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the required rate of flow of water is 1053 kg/h \n",
"the overall heat transfer coefficient is 300 W/m**2 C\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"mo_ = 1000. \t\t\t#kg/h, cooling rate of oil\n",
"cpo = 2.05 \t\t\t#kj/kg C, specific heat of oil\n",
"T1 = 70. \t\t\t#C, initial temp. of oil\n",
"T2 = 40. \t\t\t#C, temp. of oil after cooling\n",
"cpw = 4.17 \t\t\t#kj/kg C, specific heat of water\n",
"T3 = 42. \t\t\t#C, initial temp. of water\n",
"T4 = 28. \t\t\t#C, temp. of oil after cooling\n",
"A = 3. \t\t\t#m**2, heat exchange area\n",
"\n",
"# Calculation and Results\n",
"mw_ = mo_*cpo*(T1-T2)/(cpw*(T3-T4))\n",
"print \"the required rate of flow of water is %.0f kg/h \"%(mw_)\n",
"Q = mo_*cpo*(T1-T2)/3600 \t\t\t#kw, heat duty\n",
"dt1 = T1-T3 \t\t\t#C, hot end temp. difference\n",
"dt2 = T2-T4 \t\t\t#C, cold end temp. difference\n",
"LMTD = (dt1-dt2)/(math.log(dt1/dt2)) \t\t\t#math.log mean temp. difference\n",
"dtm = LMTD\n",
"U = Q*10**3/(A*dtm)\n",
"print \"the overall heat transfer coefficient is %.0f W/m**2 C\"%(round(U,-1))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.7 Page No : 126"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The inlet temprature is Ti = 26 C\n",
"The outlet temprature is To = 107 C\n"
]
}
],
"source": [
"from scipy.optimize import fsolve \n",
"import math\n",
"\n",
"# Variables\n",
"Q = 38700. \t\t\t#kcal/h, heat duty\n",
"W = 2000. \t\t\t#kg/h gas flow rate\n",
"cp = 0.239 \t\t\t#kcal/kg C, specific heat of nitrogen\n",
"A = 10. \t\t\t#m**2 ,heat exchanger area\n",
"U = 70. \t\t\t#kcal/hm**2 C, overall heat transfer coefficient\n",
"n = 0.63 \t\t\t#fin efficiency\n",
"\n",
"#Calculation\n",
"dt = Q/(W*cp) \t\t\t#C, temp. difference\n",
"#To-Ti = dt.........................(i)\n",
"dtm = Q/(U*A*n)\n",
"#(To-Ti)/(math.log((160-Ti)/(160-To))) = 87.8........(2)\n",
"#solving 1 and 2\n",
"def f(To): \n",
" return (To-(To-dt))/(math.log((160-(To-dt))/(160-To)))-87.8\n",
"\n",
"To = fsolve(f,100)\n",
"Ti = To-dt\n",
"\n",
"# Results\n",
"print \"The inlet temprature is Ti = %.0f C\"%(Ti)\n",
"print \"The outlet temprature is To = %.0f C\"%(To)\n",
"\n",
"# note : answers are slightly different because of fsolve function of python."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.8 Page No : 127"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The outlet eater temp. is 109.8 C\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"V = 1.8 \t\t\t#m/s, velocity of hot water\n",
"T1 = 110. \t\t\t#C, initial temp.\n",
"l = 15. \t\t\t#m, length of pipe\n",
"t = 0.02 \t\t\t#m, thickness of insulation\n",
"kc = 0.12 \t\t\t#W/mC,thermal conductivity of insulating layer\n",
"ho = 10. \t\t\t#Wm**2 C, outside film coefficient\n",
"T2 = 20. \t\t\t#C, ambient temp.\n",
"#the properties of water at 110 C\n",
"mu = 2.55*10**-4 \t\t\t#m**2/s, vismath.cosity\n",
"k = 0.685 \t\t\t#W/m C, thermal conductivity\n",
"rho = 950. \t\t\t#kg/m**3, density of air\n",
"cp = 4.23 \t\t\t#kj/kg C, specific heat of air\n",
"di = 0.035 \t\t\t#m, actual internal dia. of pipe\n",
"ri = di/2. \t\t\t#m,internal radius\n",
"t1 = 0.0036 \t\t\t#m, actual thickness of 1-1/4 schedule 40 pipe\n",
"ro = ri+t1 \t\t\t#m, outer radius of pipe\n",
"r_ = ro+t \t\t\t#m, outer radius of insulation\n",
"kw = 43. \t\t\t#W/mC, thermal conductivity of steel\n",
"\n",
"#calculation\n",
"Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n",
"Re = di*V*rho/mu \t\t\t# Reynold no.\n",
"#from eq. 4.9, Nusslet no.\n",
"Nu = 0.023*(Re)**0.88*Pr**0.3\n",
"hi = Nu*k/di \t\t\t#W/m**2 C, average heat transfer coefficient\n",
"#the overall coefficient inside area basis Ui\n",
"Ui = 1./(1/hi+(ri*math.log(ro/ri))/kw+(ri*math.log(r_/ro))/kc+ri/(r_*ho)) \n",
"Ai = math.pi*di*l \t\t\t#m**2, inside area basis\n",
"W = math.pi*ri**2*V*rho \t\t\t#kg/s, water flow rate\n",
"#from the relation b/w LMTD and rate of heat loss\n",
"\n",
"def f(To): \n",
" return (W*cp*10**3)/(Ui*Ai)*(T1-To)-((T1-To)/math.log((T1-T2)/(To-T2)))\n",
"To = fsolve(f,100)\n",
"\n",
"# Results\n",
"print \"The outlet eater temp. is %.1f C\"%(To)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.9 Page No : 129"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The exit water temp is 36 C\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"T1 = 28. \t\t\t#C, inlet temp. \n",
"T2 = 250. \t\t\t#C,bulk temp.\n",
"V = 10. \t\t\t#m/s, gas velocity\n",
"l = 20. \t\t\t#m, length of pipe\n",
"mw = 1.*3600 \t\t\t#kg/h, water flow rate\n",
"di = 4.1*10**-2 \t\t\t#m, inlet diameter\n",
"Tm = (T1+T2)/2 \t\t\t#C, mean temp.\n",
"ro = 0.0484 \t\t\t#m, outside radius\n",
"#properties of water\n",
"mu = 8.6*10**-4 \t\t\t#kg/ms, vismath.cosity\n",
"kw = 0.528 \t\t\t#kcal/h m C, thermal conductivity\n",
"kw_ = 0.528*1.162 \t\t\t#W/ m C, thermal conductivity\n",
"rho = 996. \t\t\t#kg/m**3, density of air\n",
"cp = 1*4.18 \t\t\t#kj/kg C, specific heat of air\n",
"cp_ = 1. \t\t\t#kcal/kg C\n",
"#properties of flue gas\n",
"mu1 = 2.33*10**-5 \t\t\t#kg/ms, vismath.cosity\n",
"ka = 0.0292 \t\t\t#kcal/h m C, thermal conductivity\n",
"rho1 = 0.891 \t\t\t#kg/m**3, density of air\n",
"cp1 = 0.243 \t\t\t#kcal/kg C, specific heat of air\n",
"Pr = 0.69\n",
"\n",
"#calculation\n",
"A = math.pi/4*di**2 \t\t\t#m**2, cross section of pipe\n",
"Vw = 1/(rho*A) \t\t\t#m/s, velocity of warer\n",
"Re = di*Vw*rho/mu \t\t\t# Reynold no.\n",
"Pr1 = cp*10**3*mu/kw_ \t\t\t#Prandtl no. for water\n",
"Nu = 0.023*Re**0.8*Pr1**0.4 \t\t\t#Nusslet no.\n",
"#water side heat transfer coefficient hi\n",
"hi = 206*kw/di\n",
"#gas side heat transfer coefficient ho\n",
"a = 41 \t\t\t#mm, i.d. schedule\n",
"Tw = 3.7 \t\t\t#mm, wall thickness\n",
"do = a+2*Tw \t\t\t#mm, outer diameter of pipe\n",
"Re1 = do*10**-3*V*rho1/mu1 \t\t\t# Reynold no\n",
"#from eq. 4.19, nusslet no.\n",
"Nu1 = 0.3+(0.62*Re1**(1./2)*Pr**(1./3)/(1+(0.4/Pr)**(2./3))**(1/4.))*(1+(Re1/(2.82*10**5))**(5./8))**(4/5.)\n",
"ho = (Nu1*ka/do)*10**3 \t\t\t#kcal/h m**2 C\n",
"Uo = 1/(ro/(di/2*hi)+1/ho) \t\t\t#kcal/h m**2 C, overall heat transfer coefficient\n",
"\n",
"#Heat balance\n",
"A1 = math.pi*ro*l \t\t\t#m62, outside area of pipe\n",
"#from the formula of LMTD\n",
"def f(T2_): \n",
" return mw*cp_*(T2_-T1)-Uo*A1*((T2_-T1)/math.log((T2-T1)/(T2-T2_)))\n",
"T2_ = fsolve(f,1)\n",
"\n",
"# Results\n",
"print \"The exit water temp is %.0f C\"%(T2_)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.10 Page No : 131"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The tube length is 123 m\n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"dti = 0.0212 \t\t\t#m inner tube\n",
"dto = 0.0254 \t\t\t#cm, outer tube\n",
"dpi = 0.035 \t\t\t#cm, outer pipe\n",
"mo_ = 500. \t\t\t#kh/h, cooling rate of oil\n",
"To2 = 110. \t\t\t#C, initial temo. of oil\n",
"To1 = 70. \t\t\t#C, temp. after cooling of oil\n",
"Tw2 = 40. \t\t\t#C, inlet temp. of water\n",
"Tw1 = 29. \t\t\t#C, outlet temp. of water\n",
"#properties of oil\n",
"cpo = 0.478 \t\t\t#kcal/kg C\n",
"ko = 0.12 \t\t\t#kcal/h m C, thermal conductivity\n",
"rho = 850. \t\t\t#kg/m**3, density of oil\n",
"#properties of water\n",
"kw = 0.542 \t\t\t#kcal/h m C, thermal conductivity\n",
"kw_ = (kw*1.162) \t\t\t#kj/kg C\n",
"muw = 7.1*10**-4 \t\t\t#kg/ms, vismath.cosity of water\n",
"cpw = 1. \t\t\t#kcal/kg C\n",
"cpw_ = cpw*4.17 \t\t\t#kcal/kg C\n",
"rhow = 1000. \t\t\t#kg/m**3, density\n",
"\n",
"#calculation\n",
"HL = mo_*cpo*(To2-To1) \t\t\t#kcal/h, heat load of exchanger\n",
"mw_ = HL/(cpw*(Tw2-Tw1)) \t\t\t#kg/h water flow rate\n",
"mw_1 = mw_/(3600*10**3) \t\t\t#m**3/s water flow rate\n",
"A1 = (math.pi/4)*(dti)**2 \t\t\t#m**2, flow area of tube\n",
"Vw = mw_1/A1 \t\t\t#m/s water velocity\n",
"Rew = dti*Vw*rhow/muw \t\t\t#Reynold no.\n",
"Prw = cpw_*10**3*muw/kw_ \t\t\t#Prandtl no.\n",
"Nuw = 0.023*Rew**0.8*Prw**0.4 \t\t\t#nusslet no.\n",
"#water side heat transfer coefficient hi\n",
"hi = Nuw*kw/dti\n",
"\n",
"#oil side heat transfer coefficient\n",
"A2 = math.pi/4*(dpi**2-dto**2) \t\t\t#m**2, flow area of annulus\n",
"Vo = mo_/(3600*rho*A2) \t\t\t#m/s velocity of oil\n",
"de = (dpi**2-dto**2)/dto \t\t\t#m, equivalent dia of annulus\n",
"Tmo = (To2+To1)/2 \t\t\t#C,mean oil temp.\n",
"muoil = math.exp((5550./(Tmo+273))-19) \t\t\t#kg/ms, vismath.cosity of oil\n",
"Reo = de*Vo*rho/muoil\n",
"Pro = cpo*muoil*3600/ko \t\t\t#prandtl no. for oil \n",
"\n",
"#assume (1st approximation)\n",
"Nuo = 3.66\n",
"ho = Nuo*ko/de \t\t\t#kcal/h m**2 c\n",
"L = 1 \t\t\t#assume length of tube\n",
"Ai = math.pi*dti*L\n",
"Ao = math.pi*dto*L\n",
"#overall heat transfer coefficient 1st approximation\n",
"Uo = 1/(1/ho+Ao/(Ai*hi))\n",
"LMTD = ((To2-Tw2)-(To1-Tw1))/(math.log((To2-Tw2)/(To1-Tw1)))\n",
"Ao1 = HL/(Uo*LMTD) \t\t\t #m**2, heat transfer area\n",
"Lt = Ao1/(math.pi*dto) \t\t\t #m, tube length\n",
"#from eq. 4.8\n",
"Nuo1 = 1.86*(Reo*Pro/(Lt/de))**(1./3) \t\t\t#Nusslet no. \n",
"ho1 = Nuo1*ko/de\n",
"Tmw = (Tw1+Tw2)/2 \t\t\t#C, mean water temp.\n",
"#balancing heat transfer rate of oil and water\n",
"\n",
"#average wall temp. Twall\n",
"Twall = ((hi*dti*(-Tmw))-(ho1*dto*Tmo))/(-65.71216)\n",
"#vismath.cosity of oil at this temp.\n",
"muwall = math.exp((5550/(Twall+273))-19) \t\t\t#kg/ms, vismath.cosity of oil\n",
"#Nusslet no. \n",
"Nuo2 = 1.86*(Reo*Pro/(Lt/de))**(1./3)*(muoil/muwall)**0.14\n",
"ho2 = Nuo2*ko/de\n",
"Uo2 = 1/((1/ho2)+(Ao/(Ai*hi)))\n",
"Ao2 = HL/(Uo2*LMTD)\n",
"Lt_ = Ao2/(math.pi*dto)\n",
"\n",
"# Results\n",
"print \"The tube length is %d m\"%(Lt_)\n",
"\n",
"# rounding off error."
]
},
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"metadata": {},
"source": [
"## Example 4.11 Page No : 135"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" the rate of heat transfer to water.is 6.93e+05 kcal/h\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"Ti = 260. \t\t\t#C, initial temp.\n",
"Ts = 70. \t\t\t#C, skin temp.\n",
"St = 0.15 \t\t\t#m,space between tubes in equilateral triangular arrangement\n",
"Sd = St \t\t\t#space between tubes\n",
"mu = 4.43*10**-5 \t\t\t#m**2/s, momentum diffusity\n",
"k = 0.0375 \t\t\t#W/m C, thermal conductivity\n",
"rho = 0.73 \t\t\t#kg/m**3, density of air\n",
"cp = 0.248 \t\t\t#kj/kg C, specific heat of air\n",
"V = 16. \t\t\t#m/s, velociity \n",
"d = 0.06 \t\t\t#m, outside diameter of tube\n",
"Nt = 15. \t\t\t#no. of tubes in transverse row\n",
"Nl = 14. \t\t\t#no. of tubes in longitudinal row\n",
"N = Nl*Nt \t\t\t#total no. of tubes\n",
"L = 1. \t\t\t#m, length\n",
"#Calculation\n",
"Sl = (math.sqrt(3)/2)*St\n",
"Pr = cp*mu*3600*rho/k \t\t\t#Prandtl no. of bulk air\n",
"Pr = 0.62\n",
"Prw = 0.70 \t\t\t#Prandtl no. of air at wall temp. 70 C\n",
"#from eq. 4.25\n",
"Vmax = (St/(St-d))*V\n",
"#from eq. 4.26\n",
"Vmax1 = (St/(2*(St-d)))*V\n",
"Redmax = d*Vmax/mu\n",
"p = St/Sl \t\t\t#pitch ratio\n",
"#from table 4.3\n",
"m = 0.6\n",
"C = 0.35*(St/Sl)**0.2\n",
"h = round((k/d)*C*(36163)**m*(Pr)**(0.36)*(Pr/Prw)**(0.25))\n",
"#from eq. 4.28\n",
"dt = round(190*math.exp(-math.pi*d*N*h/(rho*V*3600*Nt*St*cp)))\n",
"LMTD = ((Ti-Ts)-(dt))/math.log((Ti-Ts)/dt)\n",
"A = round(math.pi*d*L*N,1) \t\t\t#m**2, heat transfer area\n",
"Q = h*A*LMTD\n",
"\n",
"# Results\n",
"print \" the rate of heat transfer to water.is %.2e kcal/h\"%(Q)\n",
"\n",
"# Note : Value of LMTD is wrong in book please check."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.12 Page No : 140"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Outlet temp. of water for one pass through the tubes is 51 C\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"W = 0.057 \t\t\t#m**3/min/tube, flow rate of water\n",
"W_ = W*16.66 \t\t\t#kg/s. water flow rate\n",
"di = 0.0212 \t\t\t#m,inside diameter\n",
"Ti = 32. \t\t\t#C, inlet water temp.\n",
"Tw = 80. \t\t\t#C, wall temp.\n",
"L = 3. \t\t\t#m, length of pip\n",
"\n",
"#Calculation\n",
"V = (W/60)*(1/((math.pi/4)*di**2)) \t\t\t#m/s, water velocity\n",
"#the properties of water at mean liquid temp..\n",
"mu = 7.65*10**-4 \t\t\t#m**2/s, vismath.cosity\n",
"k = 0.623 \t\t\t#W/m C, thermal conductivity\n",
"rho = 995. \t\t\t#kg/m**3, density of air\n",
"cp = 4.17 \t\t\t#kj/kg C, specific heat of air\n",
"\n",
"Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n",
"Re = di*V*rho/mu \t\t\t# Reynold no.\n",
"#from eq. 4.19, nusslet no.\n",
"#from dittus boelter eq.\n",
"Nu = 0.023*Re**0.8*Pr**0.4 \t\t\t#Prandtl no.\n",
"f = 0.0014+0.125*Re**-0.32 \t\t\t#friction factor\n",
"#Reynold anamath.logy\n",
"St = f/2 \t\t\t#Smath.tanton no.\n",
"Nu1 = Re*Pr*St\n",
"#Prandtl anamath.logy\n",
"St1 = (f/2)/(1+5*(Pr-1)*math.sqrt(f/2))\n",
"Nu2 = St1*Re*Pr \n",
"#colburn analogy\n",
"Nu3 = Re*Pr**(1./3)*(f/2)\n",
"h = Nu3*k/(di) \t\t\t#W/m**2 C av heat transfer coefficient\n",
"#Q = W_*cp*10**3*(To-Ti) = h*A*LMTD\n",
"A = math.pi*di*L \t\t\t#m**2\n",
"def f(To): \n",
" return W_*cp*10**3*(To-Ti)-h*A*((To-Ti)/math.log((Tw-Ti)/(Tw-To)))\n",
"To = fsolve(f,1)\n",
"#Revised calculation\n",
"Tm = (Ti+To)/2 \t\t\t#C, mean liquid temp.\n",
"#the properties of water at new mean liquid temp..\n",
"mu1 = 6.2*10**-4 \t\t\t#m**2/s, vismath.cosity\n",
"k1 = 0.623 \t\t\t#W/m C, thermal conductivity\n",
"rho1 = 991. \t\t\t#kg/m**3, density of air\n",
"cp1 = 4.17 \t\t\t#kj/kg C, specific heat of air\n",
"\n",
"Pr1 = cp1*10**3*mu1/k1 \t\t\t#Prandtl no.\n",
"Re1 = di*V*rho1/mu1 \t\t\t# Reynold no.\n",
"#from dittus boelter eq.\n",
"f1 = 0.0014+0.125*Re1**(-0.32) \t\t\t#friction factor\n",
"#colburn anamath.logy\n",
"Nu4 = Re1*Pr1**(1./3)*(f1/2)\n",
"h1 = Nu4*k1/(di) \t\t\t#W/m**2 C av heat transfer coefficient\n",
"def f(To_): \n",
" return W_*cp*10**3*(To_-Ti)-h1*A*((To_-Ti)/math.log((Tw-Ti)/(Tw-To_)))\n",
"To_ = fsolve(f,1)\n",
"\n",
"print \"Outlet temp. of water for one pass through the tubes is %.0f C\"%(To_)\n",
"\n"
]
}
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