HEAT TRANSFER Introduction There will be a transfer of heat when two systems at different temperatures are brought into contact. The rate at which heat is transferred depends on The temperature difference The resistance to the flow of heat The surface area of contact These three terms may be related       FLOW OF HEAT = AREA x TEMPERATURE DIFFERENCE  RESISTANCE Heat transfer by conduction occurs as a result of the transmission of molecular motion. Heat transfer by conduction is governed by the Fourier equation   

Where: Q = Rate of heat transfer J s-1 or W K = Thermal conductivity W m-1 K-1  A = Cross-sectional area m2  l = Length of heat transfer path m ∆ T = Temperature difference oC or K Convection Heat transfer by convection is a consequence of bulk motion of a fluid. Convection may be natural, arising out of density differences caused by temperature differences in the fluid or forced where the fluid is pumped. In either case, the bulk motion of the fluid carries the heat from the fluid surface into the bulk fluid. Convective heat transfer is governed by the following equation      Q = h A ∆T  Where: Q = Rate of heat transfer J s-1 or W h = Heat transfer coefficient W m-2 K-1 A = Surface area m2   ∆ T = Temperature difference oC or K  For unsteady state heat transfer (T2 - Ta)/(T1 – Ta) = exp( -hsAt/cpV )   

Radiation Radiant heat transfer is the transfer of heat as electromagnetic radiation. It is governed by the Stefan-Boltzmann law which states that for a black body, the radiation absorbed or emitted is proportional to the fourth power of the absolute temperature.      Where: Q = Rate of heat absorbed/emitted J s-1 or W   A = Surface area m2   e = emissivity Dimensionless   σ = Stefan-Boltzmann constant , 5.7´ 10-8 W m-2 K-4   T = Temperature  K Heat Exchangers Heat Exchangers are devices for transferring heat between two fluids. There are two common types found in the food industry. Tubular exchangers, with a bundle of small diameter tubes contained in a cylindrical shell or plate heat exchangers with a series of corrugated plates separated by gaskets to give a flow channel between each pair of plates. Plate heat exchangers are more efficient devices giving a high rate of heat transfer in a compact space. They are relatively easily dismantled for cleaning, an added advantage, though less necessary with increasing stress on cleaning in place. There are two major flow arrangements in a heat exchanger:

Parallel flow where both fluids enter at the same end of the heat exchanger and leave at the same end of the heat exchanger Counter flow where the hot and cold fluids enter at opposite ends of the heat exchanger. Heat Load in a Heat Exchanger The purpose of a heat exchanger is to transfer heat from a hot fluid to a cold fluid and the basic conservation law applies (assume no heat losses)     HEAT LOST BY HOT FLUID = HEAT GAINED BY COLD FLUID

Overall Heat Transfer Coefficients When heat is transferred from the hot fluid to the cold fluid in a heat exchanger, there are three resistances to heat transfer to be overcome Transfer from the bulk hot fluid to the tube or plate surface Transfer through the tube or plate Transfer from the tube or plate surface to the bulk cold fluid These involve heat transfer by, in turn convection, conduction and convection. The total resistance to heat transfer is then given by the sum of the three resistances. From this is defined an overall heat transfer coefficient, U.   

Overall Heat Transfer Coefficients When heat is transferred from the hot fluid to the cold fluid in a heat exchanger, there are three resistances to heat transfer to be overcome Transfer from the bulk hot fluid to the tube or plate surface Transfer through the tube or plate Transfer from the tube or plate surface to the bulk cold fluid These involve heat transfer by, in turn convection, conduction and convection. The total resistance to heat transfer is then given by the sum of the three resistances. From this is defined an overall heat transfer coefficient, U.     Assuming Heat transfer area to be equal the above expression becomes

This form is correct for a plate heat exchanger, as all surface areas are the same. The overall heat transfer coefficient, U, together with the LMTD, may then be used in the convective heat transfer equation to give the overall heat transfer for the heat exchanger    The above equation is the basic heat transfer equation for a heat exchanger.

Some commonly used Heat Exchangers in Food Processing Industry

REFRIGERATION, CHILLING FREEZING Refrigeration Cycle The basis of mechanical refrigeration is the fact that at different pressures the saturation (or the condensing) temperatures of vapours are different as clearly shown on the appropriate vapour-pressure/temperature curve. As the pressure increases condensing temperatures also increase. This fact is applied in a cyclic process, which is illustrated in Fig REFRIGERATION, CHILLING FREEZING

The evaporator; in this the pressure above the refrigerant is low enough so that evaporation of the refrigerant liquid to a gas occurs at some suitable low temperature determined by the requirements of the product. This temperature might be, for example -18°C in which case the corresponding pressures would be for ammonia 229 kPa absolute and for tetrafluoroethane (also known as refrigerant 134a) 144 kPa. Evaporation then occurs and this extracts the latent heat of vaporization for the refrigerant from the surroundings of the evaporator and it does this at the appropriate low temperature. This process of heat extraction at low temperature represents the useful part of the refrigerator.

A useful measure is the ratio of the heat taken in at the evaporator (the useful refrigeration), (Hb - Ha) , to the energy put in by the compressor which must be paid for (Hc– Hb). This ratio is called the coefficient of performance (COP).  The unit commonly used to measure refrigerating effect is the ton of refrigeration = 3.52 kW. It arises from the quantity of energy to freeze 2000 lb of water in one day (2000 lb is called 1 short ton).

EXPECTED SURFACE HEAT TRANSFER COEFFICIENTS (hs) J m-2 s-1 °C-1 Still-air freezing (including radiation to coils) 9 Still-air freezing (no radiation) 6 Air-blast freezing 3 m s-1 18 Air-blast freezing 5 m s-1 30 Liquid-immersion freezing 600 Plate freezing 120

Chilling Chilling of foods is a process by which their temperature is reduced to the desired holding temperature just above the freezing point of food, usually in the region of -2 to 2°C Many commercial chillers operate at higher temperatures, up to 10-12°C. The effect of chilling is only to slow down deterioration changes and the reactions are temperature dependent. So the time and temperature of holding the chilled food determine the storage life of the food.

Rates of chilling are governed by the laws of heat transfer Rates of chilling are governed by the laws of heat transfer. It is an example of unsteady-state heat transfer by convection to the surface of the food and by conduction within the food itself. The medium of heat exchange is generally air, which extracts heat from the food and then gives it up to refrigerant in the evaporator. The rates of convection heat transfer from the surface of food and to the evaporator are much greater if the air is in movement, being roughly proportional to v0.8. To calculate chilling rates it is therefore necessary to evaluate: (a) surface heat transfer coefficient, (b) resistance offered to heat flow by any packaging material that may be placed round the food, (c) appropriate unsteady state heat conduction equation. Although the shapes of most foodstuffs are not regular, they often approximate the shapes of slabs, bricks, spheres and cylinders.

Water makes up a substantial proportion of almost all foodstuffs Freezing Water makes up a substantial proportion of almost all foodstuffs Freezing has a marked physical effect on the food. Because of the presence of substances dissolved in the water, food does not freeze at one temperature but rather over a range of temperatures. At temperatures just below the freezing point of water, crystals that are almost pure ice form in the food and so the remaining solutions become more concentrated. Even at low temperatures some water remains unfrozen in very concentrated solutions. In the freezing process, added to chilling is the removal of the latent heat of freezing. This latent heat has to be removed from any water that is present. The latent heat of freezing of water is 335 kJ kg-1 Other latent heats, for example The heats of solidification of fats, Heats of solution of salts, Of smaller magnitude than the latent heat of freezing of water.

Cold Storage For cold storage, the requirement for refrigeration comes from the need to remove the heat:  coming into the store from the external surroundings through insulation  from sources within the store such as motors, lights and people (each worker contributing something of the order of 0.5 kW)  from the foodstuffs. Heat penetrating the walls can be estimated, knowing the overall heat-transfer coefficients including the surface terms and the conductance of the insulation, which may include several different materials. The other heat sources require to be considered and summed. Detailed calculations can be quite complicated but for many purposes simple methods give a reasonable estimate.