{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6 - FLUIDISATION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 298 Example 6.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Galileo number = 1.004  *10**5\n",
      "\n",
      "Value of Remf is 40\n",
      "\n",
      "minimum fluidisation velocity is 36.4 mm/sec\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Calculating minimum fluidisation velocity\n",
    "\n",
    "#Calculating Galileo number\n",
    "def Galileo_number():\n",
    "    d = 3*10**(-3)#  #particle size is in meters\n",
    "    p = 1100#       #density of liquid is in kg/m**3\n",
    "    ps = 4200#      #density of spherical particles is in kg/m**3\n",
    "    g = 9.81#       #acceleration due to gravity is in m/sec**2\n",
    "    u = 3*10**(-3)#  #viscosity is in Ns/m**2\n",
    "    Ga = d**3*p*(ps-p)*g/u**2#\n",
    "    return Ga\n",
    "Ga = Galileo_number()#\n",
    "print\"\\nGalileo number = %.3f  *10**5\"%(Ga*10**(-5))\n",
    "\n",
    "#Calculating Re mf\n",
    "Remf = 25.7*(sqrt(1+5.53*10**(-5)*(1.003*10**5))-1)#\n",
    "print\"\\nValue of Remf is %d\"%(Remf)#\n",
    "\n",
    "umf = Remf*(3*10**(-3))/(3*10**(-3)*1100)#\n",
    "print\"\\nminimum fluidisation velocity is %.1f mm/sec\"%(umf*1000)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 299 Example 6.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " (a)\n",
      "\n",
      "voidage = 0.48\n",
      "\n",
      "minimum fluidisation velocity is 0.057 kg/m**2sec\n",
      "\n",
      " (b)\n",
      "\n",
      "terminal velocity is 0.0031m/sec\n",
      "\n",
      "Reynlds no =0.093\n",
      "\n",
      "The required mass flow rate is 2.78 kg/m**2sec\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "#Calculating voidage by considering eight closely packed spheres of diameter d in a cube of size 2d\n",
    "print\"\\n (a)\"\n",
    "def voidage():\n",
    "    d = 1*10**(-4)#    #diameter is in meters\n",
    "    meu = 3*10**(-3)#  #viscosity is in Ns/m**2\n",
    "    ps = 2600#        #density is in kg/m**3\n",
    "    p = 900#         #density is in kg/m**3\n",
    "    e = (8*d**(3)-8*(pi/6)*d**(3))/(8*d**(3))#\n",
    "    return e\n",
    "e = voidage()#\n",
    "print\"\\nvoidage = %.2f\"%(e)#\n",
    "\n",
    "#Calculating minimum fluidisation mass flow rate\n",
    "\n",
    "def min_fluidis_vel():\n",
    "    e = voidage()#\n",
    "    d = 1*10**(-4)#    #diameter is in meters\n",
    "    meu = 3*10**(-3)#  #viscosity is in Ns/m**2\n",
    "    ps = 2600#        #density is in kg/m**3\n",
    "    p = 900#         #density is in kg/m**3  \n",
    "    g = 9.81#         #acceleration due to gravity is in m/sec**2\n",
    "    Gmf = 0.0055*(e)**(3)/(1-e)*(d**2)*p*(ps-p)*g/meu#\n",
    "    return Gmf\n",
    "Gmf = min_fluidis_vel()#\n",
    "print\"\\nminimum fluidisation velocity is %.3f kg/m**2sec\"%(Gmf)#\n",
    "\n",
    "\n",
    "print\"\\n (b)\"\n",
    "def terminal_velocity():\n",
    "    e = voidage()#\n",
    "    d = 1*10**(-4)#    #diameter is in meters\n",
    "    meu = 3*10**(-3)#  #viscosity is in Ns/m**2\n",
    "    ps = 2600#        #density is in kg/m**3\n",
    "    p = 900#         #density is in kg/m**3  \n",
    "    g = 9.81#         #acceleration due to gravity is in m/sec**2\n",
    "    u = d**(2)*g*(ps-p)/(18*meu)#\n",
    "    return u\n",
    "print\"\\nterminal velocity is %.4fm/sec\"%(terminal_velocity())#\n",
    "\n",
    "#Reynolds no for this Terminal velocity is\n",
    "Re = (10**(-4)*0.0031*900)/(3*10**(-3))#\n",
    "print\"\\nReynlds no =%.3f\"%(Re)#\n",
    "print\"\\nThe required mass flow rate is %.2f kg/m**2sec\"%(terminal_velocity()*900)#\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Page 305 Example 6.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Galileo number = 9.42*10**5\n",
      "\n",
      " The Reynolds no is 1798\n",
      "\n",
      "velocity = 0.45 m/sec\n",
      "\n",
      "value of n is 2.42\n",
      "\n",
      "Voidage is 0.784\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols,solve\n",
    "# to calculate voidage of the bed\n",
    "\n",
    "def Galileo_number():\n",
    "    d = 4*10**(-3)#  #particle size is in meters\n",
    "    p = 1000#       #density of water is in kg/m**3\n",
    "    ps = 2500#      #density of glass is in kg/m**3\n",
    "    g = 9.81#       #acceleration due to gravity is in m/sec**2\n",
    "    u = 1*10**(-3)#  #viscosity is in Ns/m**2\n",
    "    Ga = d**3*p*(ps-p)*g/u**2#\n",
    "    return Ga\n",
    "\n",
    "print\"\\nGalileo number = %.2f*10**5\"%(Galileo_number()*10**(-5))#\n",
    "\n",
    "def Reynolds_no():\n",
    "    Ga = Galileo_number()#\n",
    "    Re = (2.33*Ga**(0.018)-1.53*Ga**(-0.016))**(13.3)#\n",
    "    return Re\n",
    "print\"\\n The Reynolds no is %d\"%(Reynolds_no())#\n",
    "v = Reynolds_no()*(1*10**(-3))/(0.004*1000)#\n",
    "print\"\\nvelocity = %.2f m/sec\"%(v)#\n",
    "\n",
    "n = symbols('n')\n",
    "z = solve((4.8-n)-0.043*(Galileo_number())**(0.57)*(n-2.4))[0]\n",
    "print\"\\nvalue of n is %.2f\"%(z)#\n",
    "\n",
    "#voidage at a velocity is 0.25m/sec\n",
    "e=0.1#\n",
    "while 1:\n",
    "    enew = e -((0.25/0.45)-e**(2.42))/(-2.42*e**1.42)#\n",
    "    if (enew == e):\n",
    "        print\"\\nVoidage is %.3f\"%(e)#\n",
    "        break#\n",
    "    \n",
    "    e=enew#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 345 Example 6.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Bp58OP/6xk4iZWWf0+L62nn8+PTPy4ot5R2Jm1jXlViKRdIyk5yU9I+mcVtbZ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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ca037f9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "From the graph the value of slope is -0.002  \n",
      "\n",
      " b = 0.0873 kmol/kg\n"
     ]
    }
   ],
   "source": [
    "from numpy import arange,log\n",
    "from sympy import symbols,solve\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n",
    "t = arange(250,2001,250) # #time is in secs\n",
    "y = [0.00223, 0.00601, 0.00857, 0.0106, 0.0121, 0.0129, 0.0134 ,0.0137]\n",
    "\n",
    "i =0#\n",
    "yo = 0.01442#\n",
    "z=[];\n",
    "\n",
    "x=[]\n",
    "while i<8:\n",
    "    z.append(y[(i)]/yo)\n",
    "    \n",
    "    x.append(log(y[(i)]))\n",
    "    i=i+1#\n",
    "\n",
    "title(\"slope of adsorption isotherm\")\n",
    "xlabel(\"Time(sec)\")\n",
    "ylabel(\"log(1-(y/yo))\")\n",
    "plot(t,x)\n",
    "show()\n",
    "print\"\\nFrom the graph the value of slope is %.3f  \"%(-0.00167)#\n",
    "Gm = 0.679*10**(-6)#  #units are in kmol/sec\n",
    "W = 4.66#            #units are in gram\n",
    "b = symbols('b')\n",
    "s = solve(-0.00167*4.66*b+0.679*10**(-6))[0]\n",
    "print\"\\n b = %.4f kmol/kg\"%(s*10**3)#0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 349 Example 6.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KlPBF2skdXn01JP7p02HatPB/9mzYZJOwA0juDFZfPe2Ipdkp4Yt0so8/hmee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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2ca03fb090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " heat transferred = 1.28 kw/m**2 of bed cross sectional area\n",
      "\n",
      " Volume of particles is 0.43 m**3\n",
      "\n",
      " Volume of 1 particle is 8.18*10**(-12) m**3\n",
      "\n",
      " number of particles is 5.26*10**(10)\n",
      "\n",
      " heat transfer coefficient = 12.1 W/m**2\n",
      "\n",
      " h = 61.6 W/m**2 K\n"
     ]
    }
   ],
   "source": [
    "from numpy import arange,log,pi\n",
    "from sympy import symbols,solve\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n",
    "\n",
    "gas_flow_rate =0.2#       #units are in kg/m**2\n",
    "c = 0.88#                 #specific heat capacity of air is kj/kg K\n",
    "viscosity = 0.015*10**(-3)##viscosity is in Ns/m**2\n",
    "d = 0.25*10**(-3)#         #particle size is in meters\n",
    "k = 0.03#                 #thermal conductivity is in W/m K\n",
    "e = 0.57#                 #e is voidage\n",
    "\n",
    "T = [339.5, 337.7, 335.0, 333.6, 333.3, 333.2]# #temperature is in kelvins\n",
    "deltaT=[]\n",
    "for t in T:\n",
    "    deltaT.append(t - 333.2)\n",
    "h = [0, 0.64, 1.27, 1.91, 2.54, 3.81]#\n",
    "title(\"temperature rise as a function of bed height\")\n",
    "xlabel(\"height above bed support(mm))\")\n",
    "ylabel(\"deltaT(K)\")\n",
    "plot(h,deltaT)\n",
    "show()\n",
    "\n",
    "#Area under the curve gives the value of  the heat teansfer integral =8.82mm K\n",
    "\n",
    "q = 0.2*0.88*(339.5-332.2)#\n",
    "print\"\\n heat transferred = %.2f kw/m**2 of bed cross sectional area\"%(q)#\n",
    "\n",
    "#Assuming 1m**3 volume\n",
    "Vp = (1-0.57)#       #Volume of particles is in m**3\n",
    "print\"\\n Volume of particles is %.2f m**3\"%(Vp)\n",
    "v1 = (pi/6)*d**3#    #Volume of 1 particle in m**3\n",
    "print\"\\n Volume of 1 particle is %.2f*10**(-12) m**3\"%(v1*10**(12))#\n",
    "print\"\\n number of particles is %.2f*10**(10)\"%(Vp/v1*10**(-10))#\n",
    "\n",
    "x =symbols('x')#\n",
    "h = solve(1100 - x*(1.03*10**4)*(8.82*10**(-3)))[0]\n",
    "print\"\\n heat transfer coefficient = %.1f W/m**2\"%(h)#\n",
    "\n",
    "#Nu = 0.11Re**(1.28)\n",
    "Re = (0.2*0.25*10**(-3))/(0.015*10**(-3))#\n",
    "h1 = 0.11*(Re)**(1.28)*k/d#\n",
    "print\"\\n h = %.1f W/m**2 K\"%(h1)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page 350 Example 6.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0dedb77e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      " Coefficient for heat transfer between the gas and the particles= 14.1W/m**2 K\n",
      "\n",
      " Let the evaporation rate be 0.1 kg/sec at a temp difference = 50 degK\n",
      "\n",
      " The heat flow = 2.6*10**5 W\n",
      "\n",
      " the effective area of the bed A = 368 m**2\n",
      "\n",
      " The surface area of the bed = 1200 m**2\n",
      "\n",
      " hence the fraction of the bed = 0.31\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from sympy import symbols,solve\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n",
    "\n",
    "cp = 0.85#                              #specific heat capacity of the air\n",
    "h = [0, 0.625, 1.25, 1.875, 2.5, 3.75]#                       #height in mm  \n",
    "T=[339.5, 337.7, 335.0 ,333.6 ,333.3, 333.2]##temperature in K\n",
    "\n",
    "deltaT=[]\n",
    "for t in T:\n",
    "    deltaT.append(t - 333.2)\n",
    "                     #temperature difference in kelvins\n",
    "plot(h,deltaT)\n",
    "title(\"deltaT as a function of bed height\")\n",
    "xlabel(\"Height above bed support z(mm)\")\n",
    "ylabel(\"Temperature difference deltaT (K)\")\n",
    "show()\n",
    "#From the plot area under the curve is 6.31 K mm \n",
    "sp = (6/(0.25*10**(-3)))*(0.5)#  #sp is surface area per unit volume in m**2/m**3\n",
    "G = 0.2#                        #in kg/m**2sec\n",
    "Cp = 850#                       #Cp is in J/kg K\n",
    "h1 = symbols('h1')\n",
    "s = solve(0.2*850*6.3-h1*1.2*10**(4)*6.31*10**(-3))[0]\n",
    "print\" \\n Coefficient for heat transfer between the gas and the particles= %.1fW/m**2 K\"%(s)#\n",
    "\n",
    "print\"\\n Let the evaporation rate be 0.1 kg/sec at a temp difference = 50 degK\"\n",
    "mdot = 0.1#         #evaporation rate is 0.1 kg/sec\n",
    "Latent_heat = 2.6*10**(6)#\n",
    "print\"\\n The heat flow = %.1f*10**5 W\"%(mdot*Latent_heat*10**(-5))#\n",
    "A=(2.6*10**5)/(14.1*50)#\n",
    "print\"\\n the effective area of the bed A = %d m**2\"%(A)#\n",
    "print\"\\n The surface area of the bed = %d m**2\"%(0.1*1.2*10**4)#\n",
    "print\"\\n hence the fraction of the bed = %.2f\"%(369/1200)#\n"
   ]
  }
 ],
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