LECTURE 5 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS: 1.0 SOME OF THE THEORETICAL CONCEPTS INVOLVED IN HEAT FLOW. 1.1 Sensible Heat Flow

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1 LECTURE 5 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS: 1.0 SOME OF THE THEORETICAL CONCEPTS INVOLVED IN HEAT FLOW 1.1 Sensible Heat Flow 1.2 Latent heat Flow 1.3 Humidity 1.4 Thermostat Condition in the Return 2.0 OTHER SOURCES OF HEAT ADDITION TO UNDERGROUND MINE ENVIRONMENT 2.1 Auto-compression REFERENCES Page 1 of 8

2 1.0 SOME OF THE THEORETICAL CONCEPTS INVOLVED IN HEAT FLOW 1.1 Sensible Heat Flow We know that sensible heat causes rise in temperature. When cool air flows in the airway, heat is added from the strata thereby increasing its temperature. Initially, when the mine airway is in its newly driven stage, the rate of heat flow from strata is very high. The rate of heat flow decreases with time. But, one should keep in mind that it is not a matter of a day or two. It may take months or even years to acquire nearly a constant rate of heat flow. Fig. 1 shows rate of heat flow from the strata in mine airways with time. Fig. 1 Sketch showing rate of heat transfer in a mine opening with time (after Banerjee, 2003) 1.2 Latent Heat Flow We know that latent heat causes no change in temperature of air, but it adds heat to the air. This results in rise in humidity. It is very rare to find a rock surface in mine which is completely dry. Presence of water on surrounding rock surface increases the complexity of mechanism of heat flow from the strata to mine air. Let us look at Fig. 2. Page 2 of 8

3 Fig.2 Heat flow balance on a wet surface (after McPherson, 1993) We can write heat transfer balance equation as q = q sen + q L joule/sec In the above equation, sensible-heat flow, q sen can be negative also. This happens when the temperature of mine air is lower than the temperature of the wet surface (rock). In this case, the dry bulb temperature of the air will decrease. But, there will be a significant rise in wet bulb temperature of the air because of moisture addition to it. In general, both sensible heat, q sen and latent heat, q L are positive. In this case, we can observe a significant rise in dry bulb and wet-bulb temperature. This will increase the humidity. 1.3 Humidity Humidity decreases heat transfer resistance between the air-rock interface. Page 3 of 8

4 1.4 Thermostat Condition in the Return Air in the intake may have different temperature in accordance with the surface climate. But as the air travels, heat transfer between the air and the strata takes place. By the time, air reaches the main return, it establishes a thermal equilibrium with the strata. Therefore, the air in the return has almost constant temperature throughout the year. 2.0 OTHER SOURCES OF HEAT ADDITION TO UNDERGROUND MINE ENVIRONMENT 2.1 Auto-compression Air entering through a shaft or incline gets compressed by the weight of the air column in the shaft or the incline. In this process, the air gets heated up. This happens because of conversion of its potential energy into enthalpy. Increase in enthalpy either increases pressure or internal energy or both, causing temperature of air to rise. Enthalpy is related to internal energy by the relation H = PV + U Where, H = enthalpy (J) P= pressure (Pa) V= volume (m 3 ) U= internal energy (J) Let us try to express change of potential energy in terms of enthalpy. Look at Fig.3. Page 4 of 8

5 Fig.3 (after McPherson, 1993) In Fig.3, point 1 can be taken as the top of shaft and point 2 as the bottom of the shaft. Applying steady flow energy equation at point 1and point 2 we have: u Z 1g + H 1 + q 12 = u Z 2g + H 2 J/kg Where, u = velocity of air (m/s) Z = height above datum (m) H = enthalpy (J/kg) q 12 = heat added in the airway (J) Change in kinetic energy will be negligible. Hence, ignoring change in kinetic energy, we have H 2 H 1 = (Z 1 Z 2 )g + q 12 J/kg Page 5 of 8

6 The term (Z 1 Z 2)g is always positive for the downcast shaft and is unavoidable. While q 12 depend on whether the surrounding rock surface is at higher temperature or lower temperature compared to the air traveling in the airways. It also depends on whether the surface is dry or wet. If no heat is transferred with the surrounding while air travels down the shaft, it is called adiabatic auto-compression. In other words, it is also called adiabatic lapse rate. Let us calculate change in temperature of air travelling down the shaft. For a general airway surface, it is given as T d = (Z 1 Z 2 )g L X C pm Where, T d = change in dry bulb temperature of the air ( ) L = latent heat of vaporization (J/kg) Z 1, Z 2 = height above datum line (m) g = acceleration due to gravity (m/s 2 ) X = increase in water vapour content of air due to evaporation (kg/kg dry air) C pm = 1+X = 1+X C pd +C pv X X = specific heat of moist air (J/kg ) If the airway is completely dry, the term L X = 0. In wet shafts, there will be considerable cooling due to evaporation. The values obtained are likely to be affected by other sources of heat. The general estimation can be made by the following relation: T d Z = per 100 m T w Z = per 100 m Page 6 of 8

7 Another way of estimating change in temperature is using equation of adiabatic compression given by T 2 T 1 = ( p 2 p 1 ) (γ 1)/γ where, T 1 and T 2 = dry bulb temperature p 1 and p 2 = atmospheric pressure γ = ratio of specific heats of air (1.42) The reverse process of auto-compression i.e auto-decompression is observed in the upcast shaft when air escapes out the mine while moving upwards in the upcast shaft. In this process expansion of air takes place causing decrease in its temperature. Due to this, droplets of water with dust gets accumulated on fans in the upcast shaft thereby reducing its life and increasing its maintenance cost. REFERENCES Banerjee S.P. (2003); Mine Ventilation ; Lovely Prakashan, Dhanbad, India. Hartman, H. L., Mutmansky, J. M. & Wang, Y. J. (1982); Mine Ventilation and Air Conditioning ; John Wiley & Sons, New York. Le Roux, W. L. (1972); Mine Ventilation Notes for Beginners ; The Mine Ventilation Society of South Africa. McPherson, M. J. (1993); Subsurface Ventilation and Environmental Engineering ; Chapman & Hall, London. Misra G.B. Calcutta, India. (1986); Mine Environment and Ventilation ; Oxford University Press, Vutukuri, V. S. & Lama, R. D. (1986); Environmental Engineering in Mines ; Cambridge University Press, Cambridge. Page 7 of 8

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