MIET2039_CL06_Sizing-Shell-Tube-Heat-Exchanger-SOLUTION.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<h3 style=\"color:#7171C6;\"> Week 06 - Sizing a shell and tube heat exchanger </h3>\n",
    "\n",
    "Water at 15<sup>o</sup>C with a mass flow rate of 8 kg/s is available to cool hot oil from 90<sup>o</sup>C to 30<sup>o</sup>C. The oil mass flow rate is 5 kg/s. A shell-and-tube heat exchanger with one-shell pass and four tube-passes is proposed for this process. Using uniform cp values of 2.5 kJ/(kg<sup>o</sup>C) and 4.2 kJ/(kg<sup>o</sup>C) for oil and water, respectively, and assuming an overall heat transfer coefficient of 250 W/(m<sup>2</sup>.<sup>o</sup>C) for the heat exchanger\n",
    "\n",
    "<img src=\"img\\1shell-2tube-heatexchanger.png\" width=\"280px\">\n",
    "\n",
    "<em>\n",
    "1. determine the surface area of the heat exchanger, and therefore a combination in the diameter of the pipe with its horizontal length (max. length of 20m due to limited space) per tube-pass.\n",
    "2. if more power is used to pump the water through more rapidly, a greater cooling effect will occur. Repeat by looking at the effect of the mass flow rate at 10kg/s, 20kg/s, 30kg/s on the size of the heat exchanger. The information will help if there are space constraints in installing the heat exchanger\n",
    "</em>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#############################\n",
    "# Define the known conditions\n",
    "#############################\n",
    "tColdIn = 15\n",
    "tHotIn = 90\n",
    "tHotOut = 30\n",
    "mfrWater = 8\n",
    "mfrOil = 5\n",
    "CpOil = 2500\n",
    "CpWater = 4200\n",
    "U = 250\n",
    "\n",
    "\n",
    "#############################\n",
    "# Using the specific heat and mass flow rate data calculate the heat capacity rates \n",
    "# Cc and Ch\n",
    "#############################\n",
    "Cc = CpWater*mfrWater \n",
    "Ch = CpOil*mfrOil\n",
    "\n",
    "\n",
    "#############################\n",
    "# Calculate the heat flux for the hot fluid (since these temperatures are known)\n",
    "#############################\n",
    "q = Ch*(tHotIn - tHotOut)\n",
    "\n",
    "\n",
    "#############################\n",
    "# The heat flux for the hot fluid must equal the heat flux for the cold fluid.\n",
    "# Use this relationship to calculate the outlet cold temperature\n",
    "#############################\n",
    "tColdOut = tColdIn + q/Cc\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have determined all four temperatures the LMTD method can be used which involves determining the correction factor. When using a formula to calculate the correction factor the dimensionless P, and R terms are defined as:\n",
    "\n",
    "P = (tColdOut - tColdIn) / (tHotIn - tColdIn)\n",
    "\n",
    "R = (tHotIn - tHotOut) / (tColdOut - tColdIn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x81cd940>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x832fc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# P, R definitions\n",
    "#############################\n",
    "P = (tColdOut - tColdIn) / (tHotIn - tColdIn)\n",
    "R = (tHotIn - tHotOut) / (tColdOut - tColdIn)\n",
    "\n",
    "\n",
    "# The correction factor equations for 1-shell 2n-tube passes is given below in a\n",
    "# function F12\n",
    "import math\n",
    "def F12(P,R):\n",
    "    s = math.sqrt(1+R**2)\n",
    "    a = s/(1-R)*math.log((1-R*P)/(1-P))\n",
    "    b = math.log((2-P*(1+R-s))/(2-P*(1+R+s)))\n",
    "    f = a/b\n",
    "    return(f)\n",
    "\n",
    "# Similary the correction factor equations for 2-shell 2n-tube passes is given \n",
    "# below in a # function F24\n",
    "def F24(P,R):\n",
    "    s = math.sqrt(1+R**2)\n",
    "    ss = math.sqrt((1-P)*(1-P*R))\n",
    "    a = s/(2*(R-1))*math.log((1-P)/(1-P*R))\n",
    "    numer = 2/P - 1 - R + 2/P*ss + s\n",
    "    denom = 2/P - 1 - R + 2/P*ss - s\n",
    "    b = math.log(numer/denom)\n",
    "    f = a/b\n",
    "    return(f)\n",
    "\n",
    "#############################\n",
    "# Simply call either function based on the number of shell passes to obtain\n",
    "# the correction factor\n",
    "f = F12(P,R)\n",
    "#############################\n",
    "\n",
    "#############################\n",
    "# Determine the heat exchanger area required using q = UA*LMTD \n",
    "# (you have to calculate LMTD first)\n",
    "dt1 = tHotIn - tColdOut\n",
    "dt2 = tHotOut - tColdIn\n",
    "LMTD = (dt1-dt2)/math.log(dt1/dt2)\n",
    "A = q/(U*LMTD*f)\n",
    "#############################\n",
    "\n",
    "\n",
    "#############################\n",
    "# plot the diameter of pipe vs length of pipe from 1m to 20m length per pass\n",
    "# import our favourite modules numpy and matplotlib\n",
    "#############################\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline  # use this command to plot the graph inside python notebook\n",
    "L = np.arange(1,21)\n",
    "D = A /(math.pi*L) / 4 # divide by 4 again because I have 4-passes\n",
    "plt.plot(L,D)\n",
    "\n",
    "# what does the plot tell us? \n",
    "# It tells us for a given length we need x-diameter pipe\n",
    "# e.g. at 20m in length we need a 40cm diameter pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We need to repeat the analysis with the mass flow rate changing.\n",
    "A simple way to do this is to simply use a for loop to repeat the calculations iterating through different mass flow rates. We would also only need to recalculate the equations that are affected by the mass flow rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[126.88375010441409, 103.36255882770828, 95.83855570833623, 92.062548595039331, 89.782970706511747, 88.25509983297853, 87.159001696411678]\n"
     ]
    },
    {
     "data": {
      "image/png": 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E/fffwueLPuPen/RkcN58Xh/VjeKpDm7bv4c5CxZg9/ngrrvguus4bi7nxQ0v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\nbFjMVizmih8Osw2L2Y7FZDP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      "text/plain": [
       "<matplotlib.figure.Figure at 0x930e7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up a for loop to loop over the mass flow rate change. During each set of\n",
    "# calculations, you should store the data and plot the data at the same time.\n",
    "# Use numpy.arange(start, stop, step) function to create a list of mass flow rates\n",
    "# e.g. numpy.arange(10, 60, 10) will create an array([10, 20, 30, 40, 50])\n",
    "# You can print multiple plots by plotting each set of results at the end of each\n",
    "# iteration\n",
    "\n",
    "areaChange=[]\n",
    "for i in np.arange(10,41,5):\n",
    "    mfrWater = i\n",
    "    Cc = CpWater*mfrWater \n",
    "    tColdOut = tColdIn + q/Cc\n",
    "    P = (tColdOut - tColdIn) / (tHotIn - tColdIn)\n",
    "    R = (tHotIn - tHotOut) / (tColdOut - tColdIn)\n",
    "    f = F12(P,R)\n",
    "    dt1 = tHotIn - tColdOut\n",
    "    dt2 = tHotOut - tColdIn\n",
    "    LMTD = (dt1-dt2)/math.log(dt1/dt2)\n",
    "    A = q/(U*LMTD*f)\n",
    "    areaChange.append(A)\n",
    "    D = A /(math.pi*L) / 4\n",
    "    plt.plot(L,D)\n",
    "    \n",
    "print(areaChange)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}