Law of Heat Transfer

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1 Law of Heat Transfer The Fundamental Laws which are used in broad area of applications are: 1. The law of conversion of mass 2. Newton s second law of motion 3. First and second laws of thermodynamics The Subsidiary laws which are based on experimental facts are: 4. Fourier Law of Heat conduction 5. Newton s law cooling 6. Stefan Boltzmann law for thermal radiation 7. Equation of State 1

2 Basic modes of heat transfer Conduction is the transfer of heat through solids or stationary fluids. Fourier s law of heat conduction Convection uses the movement of fluids to transfer heat. Newton s law of cooling Radiation require a medium for transferring heat; this mode uses the electromagnetic radiation emitted by an exchanging heat. Stefan Boltzmann law = W/m 2 K 4 Stefan Boltzmann constant 2

3 Fourier s Law When x 0 Fourier s law of heat conduction Heat conduction through a large plane wall of thickness x and area A 3

4 Newton s Law Convection uses the movement of fluids to transfer heat. q= h A T Where q = average rate of heat transfer by convection (watt or J/s) A = heat transfer area (m 2 ) T = Difference between the temperature of the surface and the fluid at some specified location ( 0 C) h = an average vale of the proportionality constant called convective heat transfer coefficient (watt/ m 2 0 C) h : knowledge of fluid mechanics Newton s law of cooling Proposed in 1701 h depends on geometry of surface, the velocity, properties of the fluid and also the temperature difference T 4

5 Stefan Boltzmann Law The heat exchange by radiation was calculated experimentally by Stefan who proposed that the energy radiated by a body is proportional to the fourth power of absolute temperature. It was confirmed by Boltzmann in 1884 by therefore resulting in the Stefan Boltzmann which may be stated as Q= б A T 4 Where Stefan Boltzmann law q = maximum rate of heat emission by a body at the given temperature (black body emission) (watt) A = area of the body (m 2 ) T = absolute temperature (k) σ = Stefan Boltzmann constant = W/m 2 K 4 = BTU/h ft 2 R 4 = kcal/h m 2 k 4 5

6 Stefan Boltzmann Law Net rate of heat radiation from a black of area A 1 at absolute temperature T 1 to another black body at a lower temperature T 2 will therefore be given by: q A 1 T 4 1 T 4 2 For the case of real bodies this equation becomes q A F 12 T 1 T 2 Where q = net rate of heat exchange by radiation(watt) F 12 = a shape factor depending upon the geometry, emissivities and relative location of the two surfaces 6

7 Conduction and Radiation: Depend on temperature difference Convection: Needs assistance of mechanical mass transport also and is therefore governed by fluid motion as well Conduction and Convection: heat flux is directly linearly related to temperature difference Radiation: Heat flux is related to the difference in the fourth power of the absolute temperatures 7

8 Variation in Heat transfer with reference to time Steady state Steady State means the state of the system that does not change with time. The temperature at each point of the system (at any location) remains constant in the course of time and it is a function of space coordinates. and T = f(x, y, z) Unsteady (transient) State Unsteady State means the state of the system that does change with time. When temperature at any point in a system changes with time, process is unsteady state heat transfer and T = f(x, y, z, time) The heat flux at any location remains constant or invariant with respect to time. Internal energy does not change in such a process e.g. Heat transfer to boiling tubes from the hot gases, from hot fluid to cold fluid in a heat exchanger, large furnaces The heat flux at any location does not remain constant Internal energy changes in such a process e.g. Cooling of castings in a foundry or hot steel job on a blacksmith s anvil, heat transfer from hot coffee 8 left in a room, cooling or heating process

9 Variation in Heat transfer with reference to time Periodic or Quasi steady state The variation in temperature of an unsteady state system undergoes particular cycle, the process is called a periodic or quasi steady state heat transfer process. The temperature at each point return periodically to the same value. The rate of heat flow and that of energy storage undergoes periodic variation. Ex. Heating or cooling of a building wall during 24 hour cycle of the day or that of the walls of an Internal combustion engine. 9

10 SIMULTANEOUS HEAT TRANSFER MECHANISMS Heat transfer is only by conduction in opaque solids, but by conduction and radiation in semitransparent solids. A solid may involve conduction and radiation but not convection. A solid may involve convection and/or radiation on its surfaces exposed to a fluid or other surfaces. Heat transfer is by conduction and possibly by radiation in a still fluid (no bulk fluid motion) and by convection and radiation in a flowing fluid. In the absence of radiation, heat transfer through a fluid is either by conduction or convection, depending on the presence of any bulk fluid motion. Convection = Conduction + Fluid motion Heat transfer through a vacuum is by radiation. Most gases between two solid surfaces do not interfere with radiation. Liquids are usually strong absorbers of radiation. Although there are three mechanisms of heat transfer, a medium may involve only two of them simultaneously. 10

11 When radiation and convection occur simultaneously between a surface and a gas: Combined heat transfer coefficient h combined Includes the effects of both convection and radiation 11

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