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## Heat Transfer

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**Heat Transfer**Muhammad Rashid Usman Institute of Chemical Engineering and Technology University of the Punjab, Lahore. Figure taken from: http://heatexchanger-design.com/2011/10/06/heat-exchangers-6/ Dated: 17-Jan-2012**Text Book [1]**Please read to know and learn. Geankoplis, C.J. (2003). Transport processes and separation process principles: includes unit operations. 4th ed. Prentice-Hall International, Inc. 3**Transfer processes-1**For a transfer or rate process Conductance is called transport property. Compare the above equations with Ohm’s law of electrical conductance**Transfer processes-1**Compare the above equations with Ohm’s law of electrical conductance 5**Transfer processes-2**In chemical engineering, we study three transfer processes (rate processes), namely • Momentum transfer or Fluid flow • Heat transfer • Mass transfer**Transfer processes-4**Transfer processes are either: Molecular (rate of transfer is only a function of molecular activity), or Convective (rate of transfer is mainly due to fluid motion or convective currents) We now start “principles of heat transfer”.**Introduction to heat transfer-1**Heat transfer is a science which deals with the energy transfer between two given locations as a result of temperature difference. Thermodynamics encompasses systems at equilibrium and does not give any information about rate of a quantity, here, rate of heat transfer. Time is not a thermodynamic variable. Thermodynamics predicts only the maximum possible amount of a quantity that can be transferred. Heat transfer, on the other hand, deals with rates and predicts how fast or slow the heat will flow from one point to the other. Therefore it helps in sizing the heat transfer equipment. 9**Introduction to heat transfer-2(Applications)**Knowledge of heat transfer is important in designing refrigeration systems, power plants, vehicles, major pieces of equipment for petroleum refinery and chemical plants. Think of daily life examples. What about wearing warm cloths in winter? 10**Introduction to heat transfer-2(Applications)**Car radiator [3] Cooling fins in an electronic device [2] Boiler Heat exchanger [3] 11 Figure on for right is taken from http://www.lenntech.com/applications/process/boiler/boiler-feed-water.htm**Units of energy and heat Transfer**• SI units of heat is J (Joule), while in English system units are British thermal unit (Btu). • SI units of rate of heat transfer = J·s–1, while in English system units are Btu·h–1. 1.0 cal (thermochemical) = 4.1840 J 1.0 cal (IT) = 4.1868 J 1.0 Btu = 1055.06 J = 252.16 cal (TC) 1.0 J·s–1 = 1.0 W (Watt) 1.0 Btu·h–1 = 0.29307 W 12**Modes of heat transfer-1**Unlike momentum transfer (fluid flow) and mass transfer, heat energy is transferred by three modes: Conduction Convection Radiation 13**Modes of heat transfer-2**http://www.beodom.com/en/education/entries/principles-of-thermal-insulation- heat-transfer-via-conduction-convection-and-radiation 14**Conduction heat transfer**T2 T1 Direction of heat T1 > T2 • Heat conduction is applied to the mechanism of internal exchange from one body to another in contact, or from one part of a single body to another part by exchange of activity at molecular level. This exchange is the kinetic energy exchange by vibration of the atomic lattice, by movement of free electrons, or by molecular activity. Convection is important in fluids. 15 Left figure is taken from http://www.educationalelectronicsusa.com/p/heat-IV.htm**Convection heat transfer-1**Heat transfer by convection is due to fluid motion on a macroscopic scale i.e. heat transfer mechanism occurs in a fluid by mixing of one portion of the fluid with another portion due to gross movement of the mass of the fluid. The actual process of energy transfer from one fluid particle or molecule to another is still one of conduction, but energy may be transported from one point to the other by displacement of fluid itself. 16**Convection heat transfer-2**In which of the following cases heat transfer will be higher in heating a fluid? a) Conduction or b)Convection 17**Radiation heat transfer**Electromagnetic radiation spectrum [3] • Radiation is unique as it does not require any physical medium for heat transfer. Energy transfer by radiation occurs by means of electromagnetic radiations. 18**Fourier’s law of heat conduction**The rate of flow of heat through a single homogeneous solid is directly proportional to the area of the section at right angles to the direction of heat flow, and to the change of temperature with respect to the length of the path of the heat flow (temperature gradient). Joseph Fourier**Thermal conductivity-1**In Eq. 1, “k” is called Fourier’s law proportionality factor and known as “thermal conductivity” of a material through which heat is flowing. It is the quantitative measure of the heat conducting ability of a material. Define thermal conductivity from Fourier’s law of heat conduction (Eq. 1).**Thermal conductivity-2**SI units of thermal conductivity are J·s–1·m–1·°C–1 or J·s–1·m–1·K–1 Or W·m–1·°C–1 or W·m–1·K–1 What will the units in English system? 1.0 Btu·h–1·ft–1·°F–1 = 1.73073 W·m–1·°C–1 23**Effect of temperature, pressure, and composition on thermal**conductivity-1 • Unlike specific volume, specific heat capacity, specific volume, thermal conductivity is a non-additive property. • Gases: • Thermal conductivity increases with increasing pressure. The effect is small at low pressures and near 1.0 bar the effect is ignorable. • Generally, thermal conductivity increases with increase in temperature. • Thermal conductivity increases nearly as square root of the absolute temperature upto few atmospheres. • At high pressures, increasing temperature, decreases the value. 29**Effect of temperature, pressure, and composition on thermal**conductivity-2 • Liquids: • Generally speaking, thermal conductivity of liquids are relatively not affected by pressure. • Raising the temperature , usually decreases the thermal conductivity, and the variation may be expressed as linear. • Solids: • Thermal conductivity of pure metals decreases with an increase in temperature. Explain Why? 30**Estimation of thermal conductivity**• When experimental thermal conductivity data is not available in the literature, we need to do experiments to find the value and when not possible we use a reliable estimation method. Students are referred to Poling, B.E., Prausnitz, J.M., O’Connell, J.P. (2001) The properties of gases and liquids. 5th ed. McGraw-Hill. Singapore. • Further discussion on thermal conductivity is beyond the scope of this course. Students are expected to go through 9th chapter of Bird, R.B., Stewart, W.E., Lightfoot, E.N. (2000) Transport Phenomena. 2nd ed. John Wiley & Sons, Inc. Singapore in higher semesters to have more insight knowledge. 33**Heat conduction through a plane wall-1**What is the direction of heat? 36**Heat conduction through a plane wall-2: Temperature Profile**What about variation of temperature with distance? 37**Heat conduction through a plane wall-3: Temperature Profile**38**Heat conduction through a plane wall-4**, J/s , W/m2 , °C/W , J/s or W 39**Heat conduction through a plane wall-5: Problem-1**The wall of an industrial furnace is constructed from 0.15 m thick fireclay brick having a thermal conductivity of 1.7 W/m·K. Measurements made during steady-state operation reveal temperatures of 1400 and 1150 K at the inner and outer surfaces, respectively. What is the rate of heat loss through a wall that is 0.5 m by 1.2 m on a side? [4] 40 http://forevermaterial.en.made-in-china.com/product/BqRmDZYynbpH/China-Low-Porosity-Fireclay-Brick.html http://www.directindustry.com/prod/sistem-teknik-industrial-furnaces/roller-hearth-furnaces-26280-577854.html**Heat conduction through a plane wall-6: Problem-2**Calculate the heat loss per m2 of surface area for an insulating wall composed of 25.4 mm thick fiber insulating board, where the inside temperature is 352.7 K and the outside temperature is 297.1 K. Thermal conductivity of the material is 0.048 W/m·K. [1] Answer: 105.1 W/m2 41 http://forevermaterial.en.made-in-china.com/product/BqRmDZYynbpH/China-Low-Porosity-Fireclay-Brick.html http://www.directindustry.com/prod/sistem-teknik-industrial-furnaces/roller-hearth-furnaces-26280-577854.html**Heat conduction through a plane wall with variable thermal**conductivity-1 In the previous problem, thermal conductivity is assumed to constant with temperature. Taking thermal conductivity as a linear function of temperature, it may be shown If it is a polynomial of second degree, it may be shown as below: Where, a,b, and c are constants. 42**Heat conduction through a plane wall with variable thermal**conductivity-2 • It can be any function of temperature, and in each case one has to integrate it while keeping within the integral on the right side of the Fourier’s equation. • If you are given T vs k data, you can develop your own suitable function by fitting the given data which may be used with Fourier’s law. Always keep temperatures of interest in your mind. • When thermal conductivity is a linear function of temperature, use two point linear interpolation to find the thermal conductivity at arithmetic mean of the temperatures of interest and incorporate the interpolated value of the thermal conductivity in Fourier’s law. 43**Heat conduction through a plane wall with variable thermal**conductivity-3 What are isotropic and anisotropic materials? Think about wood! Think about an aluminum block! 44**Heat conduction through a plane wall with variable thermal**conductivity-4 What if thermal conductivity even varies in a single direction? How can we introduce the variation of thermal conductivity along the direction of flow in Fourier’s law? 45**Heat conduction through a hollow cylinder-3: Temperature**profile What about temperature profile in radial direction? Any idea about temperature profile in axial direction! The answer is straight forward. Think! 48**Heat conduction through a hollow cylinder-4: Temperature**profile 49**Heat conduction through a hollow cylinder-5: Problem-3**A glass pipe has an outside diameter of 6 in, and an inside diameter of 5 in, it will be used to transport a fluid which maintains the inner surface at 200 °F, the outside temperature of the pipe is 175 °F. What will be the rate of heat flow? k = 0.63 Btu/h·ft·°F. [p. 16, 5] Answer: 542.78 Btu/h·ft 50