Assignment I [PDF]

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15CH403J Process Modeling and Simulation Department of Chemical Engineering SRM University, Kattankulathur Tutorial – 1 Molecular and Convective flux



1. Show that the force per unit area can be interpreted as the momentum flux. 2. The steady rate of heat loss through a plane slab, which has a surface area of 3 m2 and is 7 cm thick, is 72 W. Determine the thermal conductivity of the slab if the temperature distribution in the slab is given as T = 5x + 10 Where T is temperature in C and x is the distance measured from one side of the slab in cm (Answer: 0.048 W/m.K) 3. The inner and outer surface temperatures of a 20 cm thick brick wall are 30 C and -5 C, respectively. The surface area of the wall is 25 m2. Determine the steady rate of heat loss through the wall if the thermal conductivity is 0.72 W/m K. (Answer: 3150 W) 4. Energy is generated uniformly in a 6 cm thick wall. The steady state temperature distribution is T = 145 + 3000 z – 1500 z2 Where T is temperature in C and z is the distance measured from one side of the wall in meters. Determine the rare of heat generation per unit volume if the thermal conductivity of the wall is 15 W/m K.



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5. Estimate area averaged velocity for given data below Velocity 0.5



0.49218



0.4687



0.4296



0.375



0.3046



0.21875



0.11718



0



0



0.025



0.05



0.075



0.1



0.125



0.15



0.175



0.2



(m/s) Radius (m) (Answer: 0.25 m/s) 6. The geothermal gradient is the rate of increase of temperature with depth in the earth’s crust a) If the average geothermal gradient of the earth is about 25  C/km, estimate the steady rate of heat loss from the surface of the earth. b) One your friends claims that the amount of heat escaping from 1 m2 in 4 days is enough to heat a cup of coffee. Do you agree? Justify your answer. Take the diameter and the thermal conductivity of the earth as 1.27 x 104 km and 3 W/m. K, respectively (Answer: a) 38 x 109 kW) 7. Air at 20 C and 1 atm pressure flows over a porous plate that is soaked in ethanol. The molar concentration of ethanol in the air CA is given by CA = 4 e-1.5 z Where CA is in kmol/m3 and z is the distance measured from the surface of the plate in meters. Calculate the molar flux of ethanol from the plate. DAB = 1.45 x 10-5 m2/s



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