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"source": [
"# Chapter 11 : Boundary layer heat transfer"
]
},
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"metadata": {},
"source": [
"## Example 11.1 Page No : 478"
]
},
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"i) Boundary layer thickness is 0.0033 m\n",
"Local drag coefficient is 8.72e-04 \n",
"total drag force is 0.615 N \n",
"Shear stress is 0.285 N/m**2\n"
]
}
],
"source": [
"import math \n",
"#Variable\n",
"v = 1. \t\t\t#m/s\n",
"#temprature\n",
"T = 25. \t\t\t# degree celcius\n",
"#length of plate,l = 1m\n",
"l = 1. \t\t\t#m\n",
"#width of plate,w = 0.5m\n",
"w = 0.5 \t\t\t#m\n",
"#angle of incidence,theta = 0 degree\n",
"theta = 0. \t\t\t#degree\n",
"\n",
"#Calculation\n",
"#for water at 25 degree celcius ,momentum diffusivity,\n",
"MD = 8.63*(10**-7) \t\t\t# m**2/s\n",
"#local Reynold no.\n",
"x = 0.5 \t\t\t#m\n",
"Re = x*v/MD \n",
"#from Eq. 11.39,the boundary layer thickness is\n",
"t = 5*x/(Re**0.5)\n",
"\n",
"\n",
"#Results\n",
"print \"i) Boundary layer thickness is %.4f m\"%(t)\n",
"\n",
"#local drag coefficient\n",
"#CD = local drag force per unit area (F)/kinetic energy per unit volume(KE)\n",
"#F = 0.332*rho*v**2*Re**0.5 and KE = 0.5*rho*v**2\n",
"CD = 0.332*v**2*(Re**-0.5)/(0.5)*v**2\n",
"\n",
"print \"Local drag coefficient is %.2e \"%(CD)\n",
"\n",
"#From eq 11.44, the drag force acting on one side of the plate is\n",
"#kinetic viscocity\n",
"mu = 8.6*(10**-4)\n",
"fd = 0.664*mu*v*(l*v/MD)**0.5*w\n",
"#the total force acting on both sides of the plate\n",
"\n",
"tfd = 2*fd\n",
"print \"total drag force is %.3f N \"%(tfd)\n",
"\n",
"#shear stress at any point in the boundary layer\n",
"#at a point in the boundary layer,\n",
"x = 0.5 \t\t\t#m\n",
"y = t/2\n",
"# n = blasius dimensionless variable\n",
"n = y/(MD*x/v)**0.5\n",
"#From table 11.1, at n = 2.5,f\"(n) = 0.218\n",
"#shear stress = tau\n",
"fn = 0.218 \t\t\t#f\"(n) = fn\n",
"tau = (mu*v*(v/(MD*x))**0.5)*fn\n",
"print \"Shear stress is %.3f N/m**2\"%(tau)\n"
]
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"metadata": {},
"source": [
"## Example 11.2 Page No : 488"
]
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"text": [
"Thermal boundary layer thickness is 8.7 mm \n",
"heat transfer coeff is 6.9 W/m**2 C\n"
]
}
],
"source": [
"#Variable\n",
"Ts = 200. \t\t\t# C,temp. of air\n",
"Ta = 30. \t\t\t#C, temp .of surface\n",
"Va = 8. \t\t\t#m/s, velocity of air\n",
"d = 0.75 \t\t\t#m, dismath.tant from leading edge\n",
"\n",
"#Calculation and Results\n",
"Tm = (Ts+Ta)/2 \t\t\t#C, Mean temp. of boundary layer\n",
"mu = 2.5*10**-5 \t\t\t#m**2/s, vismath.cosity\n",
"P = 0.69 \t\t\t#prndatl no.\n",
"k = 0.036 \t\t\t#W/m c, thermal conductivity\n",
"Re = d*Va/mu \t\t\t#reynold no.\n",
"t = 5*d/(Re**0.5*P**(1./3)) \t\t\t#m, thermal boundary layer thickness\n",
"print \"Thermal boundary layer thickness is %.1f mm \"%(t*10**3)\n",
"\n",
"N = (0.332*Re**(0.5)*P**(1./3)) \t\t\t#Nusslet no.\n",
"h = k*N/d \t\t\t#heat transfer coefficent\n",
"print \"heat transfer coeff is %.1f W/m**2 C\"%(h)\n"
]
},
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"metadata": {},
"source": [
"## Example 11.3 Page No : 489"
]
},
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"execution_count": 1,
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"name": "stdout",
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"text": [
"Local rate of heat exchange is 235 W/m2\n",
"Plate temperature is :108 Celsius \n"
]
}
],
"source": [
"# Variables\n",
"#Free strean velocity (v1) and temp.(t1) on side 1\n",
"v1 = 6. \t\t\t#m/s\n",
"t1 = 150. \t\t\t#degree celcius\n",
"#same on side 2\n",
"v2 = 3. \t\t\t#m/s\n",
"t2 = 50. \t\t\t#degree celcius\n",
"#dismath.tant\n",
"x = 0.7 \t\t\t#m\n",
"#The plate temp. is assumed to be equal to the mean of the bulk air temp on the two sides of the plates\n",
"T = 100. \t\t\t#degree celcius\n",
"\n",
"# Calculations\n",
"#Side 1\n",
"#mean air temp.\n",
"tm1 = (T+t1)/2\n",
"#From thermophysical properties:kinetic vismath.cosity (kv),Prandtl no.(P), thermal conductivity (k)\n",
"kv1 = 2.6*10**-5 \t\t\t#m**2/s\n",
"P1 = 0.69\n",
"k1 = 0.0336 \t\t\t#W/m degree celcius\n",
"#Reynold no.\n",
"Re1 = x*v1/kv1\n",
"#Nusslet no(N1)\n",
"a = 1/3.\n",
"N1 = 0.332*(Re1)**0.5*P1**a\n",
"h1 = k1*N1/x\n",
"#Side 2 of the plate\n",
"tm2 = (T+t2)/2\n",
"#Similarly\n",
"kv2 = 2.076*(10)**-5 \t\t\t#m**2/s\n",
"P2 = 0.70\n",
"k2 = 0.03 \t\t\t#W/m degree celcius\n",
"Re2 = x*v2/kv2\n",
"N2 = 0.332*(Re2)**0.5*P2**a\n",
"h2 = k2*N2/x\n",
"#overall heat transfer coeff. \n",
"U = h1*h2/(h1+h2)\n",
"#The local rate of heat exchange\n",
"RH = U*(t1-t2)\n",
"\n",
"# Results\n",
"print \"Local rate of heat exchange is %.0f W/m2\"%(RH)\n",
"#the plate temp is given by\n",
"TP = t2+(t1-t2)*U/h2\n",
"print \"Plate temperature is :%.0f Celsius \"%(TP)\n"
]
},
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"metadata": {},
"source": [
"## Example 11.4 Page No : 490"
]
},
{
"cell_type": "code",
"execution_count": 5,
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"outputs": [
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"name": "stdout",
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"text": [
"The temprature of plate after 1 hour is 82 C\n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"T1 = 120. \t\t\t#C, initial temp.\n",
"T2 = 25. \t\t\t#C, Final temp.\n",
"Tm = (T1+T2)/2 \t\t\t#C, mean temp.\n",
"rho = 8880. \t\t\t#kg/m**3, density of plate\n",
"#Properties of air at mean temp.\n",
"mu = 2.07*10**-5 \t\t\t#m**2/s, vismath.cosity\n",
"Pr = 0.7 \t\t\t#Prandtl no.\n",
"k = 0.03 \t\t\t#W/m C, thermal conductivity\n",
"l = 0.4 \t\t\t#m, length of plate\n",
"w = 0.3 \t\t\t#m, width of plate\n",
"d = 0.0254 \t\t\t#m, thickness of plate\n",
"Vinf = 1. \t\t\t#m/s, air velocity\n",
"Re = l*Vinf/mu \t\t\t#REynold no.\n",
"\n",
"#from eq. 11.90 (b)\n",
"Nu = 0.664*(Re)**(1./2)*(Pr)**(1./3) \t\t\t#average Nusslet no.\n",
"#Nu = l*h/k\n",
"h = Nu*k/l \t\t\t#W/m**2 C, heat transfer coefficient\n",
"#Rate of change of temp. is given by\n",
"A = 2*l*w \t\t\t#m**2. area of plate\n",
"t = 1*3600. \t\t\t#s, time\n",
"cp = 0.385*10.**3 \t\t\t#j/kg K, specific heat\n",
"m = l*w*d*rho \t\t\t#kg, mass of plate\n",
"\n",
"#-d/dt(m*cp8dt) = A*hv*(T1-T2)\n",
"#appling the boundary condition \n",
"T = (T1-T2)*math.exp(-A*h*t/(m*cp))+T2\n",
"print \"The temprature of plate after 1 hour is %.0f C\"%(T)\n"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 11.5 Page No : 508"
]
},
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"execution_count": 6,
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nusslet no is: 388 \n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"#Reynold no (Re),friction factor(f),Prandlt no. (P)\n",
"Re = 7.44*(10**4)\n",
"f = 0.00485\n",
"P = 5.12\n",
"x = P-1 \t\t\t#assume\n",
"\n",
"# Calculations\n",
"#according to Von Karmen anamath.logy\n",
"N = ((f/2)*Re*P)/(1+(5*math.sqrt(f/2))*(x+math.log(1+(5./6)*x)))\n",
"\n",
"# Results\n",
"print \"Nusslet no is: %.0f \"%(N)\n",
"\n"
]
}
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