Thermophysical properties of foods and unsteady heat transfer

Transcription

1 Thermophysical properties of foods and unsteady heat transfer Questions 1. Nominate the main goals of the foods heating and nominate the basic operations having these goals 2. Define thermal conductivity, specific heat, enthalpy, density, bulk density, energy value and surface heat transfer coefficient 3. Typical numerical values of thermal conductivity, specific heat and density for water, proteins, fats and saccharides valid at temperature 20 C 4. Calculation of density and specific heat for mixtures of components 5. Present existing databases where we can find the numerical values of thermal and other physical properties of foods 6. Figure the typical curves for temperature dependence of enthalpy (specific heat) for food with prevailing water as the main component and with prevailing fat as the main component 7. Express by words the balance of rate of energy transfer 8. Nominate three basic boundary conditions for heated or chilled body 9. Typical values of heat transfer coefficient at free convection of gas and for condensing steam (drop condensation regime) 10. Nominate the basic mechanisms of energy transfer (heat transfer) 11. Onedimensional stationary heat conduction by the wall 12. Biot number (definition, limiting cases) 13. Heat transfer coefficient by the composited wall 14. Example of calculation of heating time of the content of ideally mixed vessel 15. Example of calculation of evaporating time of water from the cooking pot heated by the ohmic heater

2 Q6a. Enthalpy of the water as a function of temperature Fig. 4 Enthalpy of water (notice of values of specific heat of phases and phase transition heat of freezing and evaporation at atmospheric pressure) Typical for pure water are sharp transfer between phases (phase transition is made at given temperature). In practice we can achieve the supercooling of water or superheating of water at some conditions (super clean water) Q6b. Schema of the enthalpy of fat as a function of temperature Fig. 5 Schema of enthalpy of fat with indicated typical mean temperatures of phase transitions of fat Tf Tr Tt freezing temperature recrystallisation temperature melting temperature The broad range in temperature of phase transition is typical for fats. This is caused by the fact that each fat is the mixture of different fatty acids (tri-acid glycerols). Each pure component has its typical phase transition.

3 Q13. Heat transfer coefficient via the wall of the house isolated by the heat isolation layer Fig. 1 Hypothetical temperature profiles of air and wall of the house T 1 outer air temperature ( C) (let is 5 C) T 2 room temperature ( C) (let is +22 C) Wall surface size S (m 2 ) Wall and isolation thicknesses, let them be δ 2 = 0.3 m δ 1 = 0.2 m Thermal conductivities of wall material and heat isolation λ 2 = 0.3 W.m -1.K -1 λ 1 = 0.02 W.m -1.K -1 Q heat flux (total) (W) Surface heat transfer coefficient between outer air (wind, combination of free convection and forced convection) and the wall, let is the value of α 1 = Q/S.(T 1 T s1 ) = 100 W.m -2.K -1 Surface heat transfer coefficient between the wall and inner air (free convection near wall ) α 2 = Q/S.(T 2 T s2 ) = 10 W.m -2.K -1 Where T s1 and T s2 are the temperatures of the wall at outer and inner side Heat transfer coefficient k k = 1/[1/α 1 + δ 1 /λ 1 + δ 2 /λ 2 + 1/α 2 ] = 1/[1/ / / /10] = 1/[ ] = 1/11.11 = 0.09 W.m -2.K -1 We can see that isolation (index 1) substantially increased the heat resistence of the wall (decreased the heat transfer coefficient)

4 Total heat flux via the wall with area of 1 m 2 Q = k. S. (T 2 T 1 ) = (22 (-5)) = 2.4 W Q14. Heating of the content of the ideally mixed vessel Fig. 2 Schema of the vessel heated by steam and ideally mixed Energy ballance ignoring heat losses: dt/dt. m k. c p = - k. S. (T p T) dt/(t p T) = -k.s/m k.c p. dt Integration in ranges T 0, T a 0, t we can get after some adjustments we can get T = T 0 + (T p T 0 ).[ 1 exp (-t/τ) ], Where the time constant of heating process τ is given τ = m k.c p /k.s

5 Q15. Time for water evaporation from cooking pot Fig. 3 Schema of the cooking pot Mass of the water in pot m k = 1 kg Specific heat of the water in pot c p = 4186 J.kg -1.K -1 Initial temperature of the water T 0 =12 C Power of the pot heating coil Q = 2000 W Assumption: ideally mixed vessel (bubles, free convection around the heating coil) Heating up to boiling point 100 C Q = m k. c p.dt/dt Separating of parameters and integration we can get the relation for heating time t = m k. c p. (T-T 0 )/Q t heating = (100-12)/2000 = 184 seconds Evaporation time Q = dm/dt.r, Where r is evaporation heat at standard pressure r = J.kg -1. Separating and integrating we can get the relation for evaporating time t evaporating = m k.r/q = /2000 = 1129 seconds i.e. cca 19 minutes.