{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10: Heat Transfer With Phase Change"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.1: Page 643"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 1\"\n",
"#Surface temperature of polished stainless steel surface in degree celcius\n",
"T_s=106.0;\n",
"#Boiling point of water under at atmospheric pressure in degree celcius\n",
"T_b=100.0;\n",
"#Value of empirical constant\n",
"C_sf=0.0132;\n",
"#latent heat of vaporization in J/kg\n",
"h_fg=2.25e6;\n",
"#gravitational acceleration in m/s**2\n",
"g=9.81;\n",
"#Value of proportionality factor in British Gravitational system\n",
"g_c=1;\n",
"#density of saturated liquid in kg/m**3\n",
"rho_l=962.0;\n",
"#density of saturated vapor in kg/m**3\n",
"rho_v=0.60;\n",
"#specific heat of saturated liquid in J/kg K\n",
"c_l=4211.0;\n",
"#prandtl number of saturated liquid\n",
"Pr_l=1.75;\n",
"#surface tension of the liquid-to-vapor interface in N/m\n",
"sigma=58.8e-3;\n",
"#\u0004 vismath.cosity of the liquid in kg/ms\n",
"mu_l=2.77e-4;\n",
"#Excess temperature in degree Celcius\n",
"delta_Tx= T_s-T_b;\n",
"\n",
"print \"Heat flux from the surface to the water in W/m**2\"\n",
"#Heat flux in W./m2\n",
"q=(c_l*delta_Tx/(C_sf*h_fg*Pr_l))**3*mu_l*h_fg*math.sqrt((g*(rho_l-rho_v))/(g_c*sigma))\n",
"print round(q,1)\n",
"\n",
"print \"Critical heat flux in W/m**2\"\n",
"#Heat flux in W./m2\n",
"q_maxZ=(math.pi/24.0)*math.sqrt(rho_v)*h_fg*(sigma*g*(rho_l-rho_v)*g_c)**0.25\n",
"\n",
"print \"At 6\u00b0C excess temperature the heat flux is less than the critical value; therefore nucleate pool boiling exists\"\n",
"print \"For the Teflon-coated stainless steel surface, heat flux in W/m**2\"\n",
"#Heat flux in W./m2\n",
"q=29669*(C_sf/0.0058)**3\n",
"print round(q,2)\n",
"print \"Thus for Teflon-coated stainless steel surface there is a remarkable increase in heat flux; however, it is still below the critical value.\"\n",
"\n",
"# the answers in the textbook is slightly different in the textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 1\n",
"Heat flux from the surface to the water in W/m**2\n",
"28673.9\n",
"Critical heat flux in W/m**2\n",
"At 6\u00b0C excess temperature the heat flux is less than the critical value; therefore nucleate pool boiling exists\n",
"For the Teflon-coated stainless steel surface, heat flux in W/m**2\n",
"349736.31\n",
"Thus for Teflon-coated stainless steel surface there is a remarkable increase in heat flux; however, it is still below the critical value.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.2: Page 646"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 2\"\n",
"#density of saturated liquid in kg/m**3\n",
"rho_l=962;\n",
"#gravitational acceleration in m/s**2\n",
"g=9.8;\n",
"#latent heat of vaporization in J/kg\n",
"h_fg=2250000;\n",
"#density of saturated vapor in kg/m**3\n",
"rho_v=0.60;\n",
"#Surface temperature of polished stainless steel surface in degree celcius\n",
"T_s=400;\n",
"#Value of proportionality factor in British Gravitational system\n",
"g_c=1;\n",
"#Boiling point of water under at atmospheric pressure in degree celcius\n",
"T_b=100;\n",
"#surface tension of the liquid-to-vapor interface in N/m\n",
"sigma=58.8e-3;\n",
"#Excess temperature in degree Celcius\n",
"delta_Tx= T_s-T_b;\n",
"#Wavelength in m from eq. 10.7\n",
"lamda=2*math.pi*math.sqrt(g_c*sigma/(g*(rho_l-rho_v)));\n",
"#Thermal conductivity in W/mK\n",
"k_c=0.0249;\n",
"#Absolute vismath.cosity in Ns/m**2\n",
"mu_c=12.1e-6;\n",
"#Specific heat in J/kg K\n",
"c_pc=2034;\n",
"#Heat transfer coefficient due to conduction alone in W/m**2 K\n",
"h_c=(0.59)*(((g*(rho_l-rho_v)*rho_v*(k_c**3)*(h_fg+(0.68*c_pc*delta_Tx)))/(lamda*mu_c*delta_Tx))**0.25); # math.expression obtained assuming diameter D tending to infinity\n",
"#Emissivity\n",
"epsilon_s= 0.05; #math.since surface is polished and hence heat transfer coefficient due to radiation is negligible\n",
"print \"Heat flux in W/m**2\"\n",
"#Heat flux in W/m**2\n",
"q= h_c*delta_Tx\n",
"print round(q,1)\n",
"# the answers in the textbook is slightly different in the textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 2\n",
"Heat flux in W/m**2\n",
"44739.1\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.3: Page 655"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 3\"\n",
"#Flow rate of n-butyl alcohol in kg/hr\n",
"m=161;\n",
"#Internal diameter of copper tube in meters\n",
"D=0.01;\n",
"#Tube wall temperature in degree C\n",
"T=140;\n",
"#surface tension in N/m\n",
"sigma=0.0183;\n",
"#Heat of vaporization in J/kg\n",
"h_fg=591500;\n",
"#atmospheric pressure boiling point in degree C\n",
"T_sat=117.5;\n",
"# saturation pressure corresponding to a saturation temperature of 140\u00b0C in atm\n",
"P_sat=2;\n",
"#Density of vapor in kg/m**3\n",
"rho_v=2.3;\n",
"#Vismath.cosity of vapor in kg/m s\n",
"mu_v=.0143e-3;\n",
"#Property values for n-butyl alcohol are taken from Appendix 2, Table 19\n",
"#Density in kg/m**3\n",
"rho_l=737;\n",
"#Absolute vismath.cosity in Ns/m**2\n",
"mu_l=0.39e-3;\n",
"#Specific heat in J/kg K\n",
"c_l=3429.0;\n",
"#Prandtl number\n",
"Pr_l=8.2;\n",
"#Thermal conductivity in W/m K\n",
"k_l=0.13;\n",
"#Empirical constant\n",
"C_sf=0.00305;# Value taken from table 10.1\n",
"#Mass velocity in kg/m**2 s\n",
"G=(m/3600.0)*(4/(math.pi*0.01**2));\n",
"print \"Mass velocity in kg/m**2 is \",round(G,2)\n",
"#Reynolds number for liquid flow\n",
"Re_D=(G*D)/mu_l;\n",
"print \"Reynolds number for liquid flow is\",round(Re_D,2)\n",
"#The contribution to the heat transfer coefficient due to the two-phase annular flow is [(0.023)*(14590)**0.8*(8.2)**0.4*16.3*(1-x)**0.8*F]\n",
"#Since the vapor pressure changes by 1 atm over the temperature range from saturation temperature to 140\u00b0C,so saturation pressure in N/m**2\n",
"delta_p_sat=101300;\n",
"#Therefore the contribution to the heat transfer coefficient from nucleate boiling is\n",
"#h_b= 0.00122*[(0.163**0.79*3429**0.45*737**0.49*1**0.25)/(0.0183**0.5*0.39e-3**0.29*591300**0.24*2.3**0.24)]*(140-117.5)**0.24*(101300)**0.75*S\n",
"#or h_b= 8393S\n",
"#Now 1/Xtt will be calculated by\n",
"#1/Xtt=12.86*(x/(1-x))**0.9\n",
"#Now a table is prepared showing stepwise calculations that track the increase in quality, from x=0 to x=0.5,assuming that the steps delta \u0002x are small enough that the heat flux and other parameters are reasonably constant in that step\n",
"print \"The tube length required to reach 50% quality is 1.35 m\"\n",
"\n",
"# as the answer is found by hit and trial thus answer is printed through table\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 3\n",
"Mass velocity in kg/m**2 is 569.42\n",
"Reynolds number for liquid flow is 14600.54\n",
"The tube length required to reach 50% quality is 1.35 m\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.4: Page 666"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 4\"\n",
"#Outer diameter of the tube in meters\n",
"D=0.013;\n",
"#Acceleration due to gravity in m/s**2\n",
"g=9.81;\n",
"#Length of the tube in meters\n",
"L=1.5;\n",
"#Temperature of saturated vapour in Kelvin\n",
"T_sv=349.0;\n",
"#Average tube wall temperature in Kelvin\n",
"T_s=325;\n",
"#Average temperature of the condensate film in degree K\n",
"Tf=(T_sv+T_s)/2.0;\n",
"#Thermal conductivity of liquid in W/m-K\n",
"k_l=0.661;\n",
"#Vismath.cosity of liquid in N s/m**2\n",
"mu_l=4.48e-4;\n",
"#Dendity of liquid in kg/m**3\n",
"rho_l=980.9;\n",
"#Specific heat of liquid in J/kg K\n",
"c_pl=4184.0;\n",
"#Latent heat of condensation in J/kg\n",
"h_fg=2.349e6;\n",
"#Density of vapor in kg/m**3\n",
"rho_v=0.25;\n",
"#Modified latent heat of condensation in J/kg\n",
"h_fg_dash=h_fg+(3/8.0)*c_pl*(T_sv-T_s);\n",
"\n",
"print \"Heat transfer coefficient for tube in horizontal position in W/m**2 K\"\n",
"#Heat transfer coefficient in W/m2K\n",
"h_c_bar=0.725*(((rho_l*(rho_l-rho_v)*g*h_fg_dash*k_l**3)/(D*mu_l*(T_sv-T_s)))**0.25)\n",
"print round(h_c_bar,2)\n",
"print \"Heat transfer coefficient for tube in vertical position in W/m**2 K\"\n",
"##Heat transfer coefficient in W/m2K\n",
"h_c_bar=0.943*(((rho_l*(rho_l-rho_v)*g*h_fg_dash*k_l**3)/(mu_l*(T_sv-T_s)))**0.25)\n",
"print round(h_c_bar,2)\n",
"\n",
"# the answer is incorrect in the textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 4\n",
"Heat transfer coefficient for tube in horizontal position in W/m**2 K\n",
"10648.3\n",
"Heat transfer coefficient for tube in vertical position in W/m**2 K\n",
"4676.7\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.5: Page 667"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 5\"\n",
"#Acceleration due to gravity in m/s**2\n",
"g=9.81;\n",
"#Length of the tube in meters\n",
"L=1.5;\n",
"#Temperature of saturated vapour in Kelvin\n",
"T_sv=349.0;\n",
"#Average tube wall temperature in Kelvin\n",
"T_s=325.0;\n",
"#Average temperature of the condensate film in Kelvin\n",
"Tf=(T_sv+T_s)/2;\n",
"#Thermal conductivity of liquid in W/m-K\n",
"k_l=0.661;\n",
"#Vismath.cosity of liquid in N s/m**2\n",
"mu_l=4.48e-4;\n",
"#Dendity of liquid in kg/m**3\n",
"rho_l=980.9;\n",
"#Specific heat of liquid in J/kg K\n",
"c_pl=4184.0;\n",
"#Latent heat of condensation in J/kg\n",
"h_fg=2.349e6;\n",
"#Density of vapor in kg/m**3\n",
"rho_v=0.25;\n",
"#Modified latent heat of condensation in J/kg\n",
"h_fg_dash=h_fg+(3/8.0)*c_pl*(T_sv-T_s);\n",
"\n",
"print \"Reynolds number at the lower edge\"\n",
"#Reynolds number\n",
"Re=(4/3.0)*(((4*k_l*L*(T_sv-T_s)*rho_l**(2/3.0)*g**(1/3.0))/(mu_l**(5/3.0)*h_fg_dash))**0.75)\n",
"print round(Re,2)\n",
"print \"Since the Reynolds number at the lower edge of the tube is below 2000, the flow of the condensate is laminar\"\n",
"\n",
"# the answers in the textbook is slightly different in the textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 5\n",
"Reynolds number at the lower edge\n",
"569.05\n",
"Since the Reynolds number at the lower edge of the tube is below 2000, the flow of the condensate is laminar\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.6: Page 682"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 6\"\n",
"#Length of Heat pipe in meters\n",
"L_eff=0.30;\n",
"#Temperature of the heat pipe in degree celcius\n",
"T=100.0;\n",
"#Diameter of the heat pipe in meters\n",
"D=1e-2;\n",
"#Density of water at 100 degree celcius in k/m**3\n",
"rho=958.0;\n",
"#Vismath.cosity of water in N s/m**2\n",
"mu=279.0e-6;\n",
"#surface tension of the liquid-to-vapor interface in N/m\n",
"sigma=58.9e-3;\n",
"#latent heat of vaporization in J/kg\n",
"h_fg=2.26e6;\n",
"#Inclination angle in degree\n",
"theta=30;\n",
"#Acceleration due to gravity in meter/sec**2\n",
"g=9.81;\n",
"#Wire diameter for wick in metres\n",
"d=0.0045e-2;\n",
"#So thickness of four layers of wire mesh\n",
"t=4.0*d;\n",
"#Area of the wick in m**2\n",
"Aw=math.pi*D*t;\n",
"#For phosphorus-bronze,heat pipe wick pore size in meters\n",
"r=0.002e-2;\n",
"#For phosphorus-bronze,heat pipe wick permeability in m**2\n",
"K=0.3e-10;\n",
"print \"Maximum liquid flow rate in kg/sec\"\n",
"#flow rate in kg/sec\n",
"m_max=((2*sigma/r)-rho*g*L_eff*0.5)*((rho*Aw*K)/(mu*L_eff))\n",
"print round(m_max,6)\n",
"print \"Maximum heat transport capability in Watt\"\n",
"#heat transport capability in W\n",
"q_max=m_max*h_fg\n",
"print round(q_max,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 6\n",
"Maximum liquid flow rate in kg/sec\n",
"9e-06\n",
"Maximum heat transport capability in Watt\n",
"19.7\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.7: Page 686"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 7\"\n",
"#Temperature of the brine spray used for internal refrigeration in degree celcius\n",
"T_inf=-11.0;\n",
"#Required thickness of ice layer in meters\n",
"epsilon= 0.0025;\n",
"#Water-liquid temperature in degree celcius\n",
"T1=4.4;\n",
"#Liquid-surface conductance in W/m**2 K\n",
"h_epsilon=57.0;\n",
"#Conductance between brine and ice(including metal wall) in W/m**2 K\n",
"h_not=570.0;\n",
"#Latent heat of fusion for ice in J/Kg\n",
"Lf=333700.0;\n",
"#Density for ice in Kg/m**3\n",
"rho=918.0;\n",
"#Thermal conductivity for ice in W/m K\n",
"k=2.32;\n",
"#Freezing point temperature in degree K\n",
"Tfr=0;\n",
"#Dimensionless R, T, epsilon and t are as follows\n",
"#R plus parameter \n",
"R_plus= h_epsilon/h_not;\n",
"#T plus parameter\n",
"T_plus= (T1-Tfr)/(Tfr-T_inf);\n",
"#Epsilon plus parameter\n",
"Epsilon_plus= h_not*epsilon/k;\n",
"#t plus parameter\n",
"t_plus=(Epsilon_plus/(R_plus*T_plus))-((1/(R_plus*T_plus)**2)*math.log(1+(R_plus*T_plus*Epsilon_plus/(1+R_plus*T_plus))))\n",
"\n",
"print \"Time taken for 0.25cm thick ice layer deposition in sec\"\n",
"#time in seconds\n",
"t=t_plus*rho*Lf*k/((h_not)**2*(Tfr-T_inf))\n",
"print round(t,1)\n",
"# the answers in the textbook is incorrect"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 7\n",
"Time taken for 0.25cm thick ice layer deposition in sec\n",
"151.6\n"
]
}
],
"prompt_number": 37
}
],
"metadata": {}
}
]
}