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CHUATOCO, Anthony DALANON, Farlene DONIEGO, Joanne FULGUERAS, Alyssa Marie  LAGRADA, Rabbie Group 8 Unit Operations  4 ChE - A
Problem 4.1-1 Problem #16 (Click on the following to view the solutions) Problem Set 2 Geankoplis Problem 5.3-6 Problem #8 GROUP 8
Problem #8 A  spherical   furnace has an inside radius of  1 m , and an outside radius of  1.2 m . The thermal conductivity of the wall is  0.5 W/m · K . The inside furnace temperature is  1100 ° C  and the outside surface is at  80 ° C . a) Calculate the  total heat loss  for  24 hrs  operation; b) What is the  heat flux  and  temperature  at a radius of  1.1 m ?
Problem #8 Given: Required: 1 m 1.2 m 1.1 m 80 ° C 1100 ° C 0.5 W/m · K T a)  total heat loss (q) for 24 hrs b)  heat flux (q/A) & T at 1.1m radius
Solution: q  =  q i   =  q o  = -  Σ T R T R T   =  Δ x K m A m = T i  - T R i = T - T o R o A m   =  4 π   ·  r i  · r o Problem #8
Solution: R T   =  Δ x K m A m =  1m – 1.2m =  Problem #8 - 0.0265 K/W q   = -  Σ T R T =  - (1100°C – 80°C) - 0.0265 K/W =  38453.09 W or J/s  q  =  3.322 x 10 9  J  a)  total heat loss (q) for 24 hrs
Solution: Problem #8 b)  heat flux (q/A) & T at 1.1m radius q  =  q i   = T i  - T R i 1m – 1.1m ( 0.5 W/m·K)  [ 4 π  (1m)   (1.1m)] - ( 1100°C –  T  ) 38453.09 W  =  T  =  543.64 °C  q/A  =  2781.82 W/m 2
Problem #16 (US) A large  slab   1m thick  is initially at a uniform temperature of  150 o C .  Suddenly its front face is exposed to a fluid maintained at  250 ° C , but its rear face remained insulated.  The fluid has a convective coefficient of  40 W/m 2 · K .  Assume the solid has a thermal diffusivity of  0.000025 m 2 /s  and a thermal conductivity of  20 W/m · K .   Using a  numerical finite difference method  with  M=5  and  4 slices , construct a  table for the temperature profile  of the slab up to a time of  4000 sec .
Problem #16 Given: Required: Slab:  Thickness = 1m  0 T n  = 150 °C   Front Face: T a  = 250 °C h  = 40 W/m 2 K κ   = 20 W/mK  α   = 0.000025 m 2 /s  Rear Face: Insulated t = 4000s  4 slices M = 5 Δ x = 1m/4 = 0.25 m table for the temperature profile Using a  numerical finite difference method
Problem #16 Solution: Δ t  = 500s N  = 0.5 q 1 2 3 4 f Δ x  = 0.25m insulation T a  = 250 °C
Problem #16 Solution: Front Face: for n=1 General:  for n=2 to n=4 Rear Face: for n=f
Problem #16 Solution: t n
Problem 4.1-1 Insulation in a Cold Room:  Calculate the  heat loss  per m 2  of surface area for a temporary insulating wall of a food cold storage room where the outside temperature is  299.9 K  and the inside temperature  276.5 K . The wall is composed of  25.4 mm  of corkboard having a  k   of  0.0433 W/m∙K.
Problem 4.1-1 Given: Required: Wall:  T o  = 299.9 K T i  = 276.5 K Side = 25.4 mm   k   =  0.0433 W/m∙K heat loss (q) per m 2
Solution: q  = -  Σ T R T R T   =  Δ x K m A m Problem 4.1-1 Basis:  1 m 2 q  = 299.9 K -276.5 K R T   =  0.0254m (0.0433 W/m∙K)(1m 2 ) =  - 0.587 K/W - 0.587 K/W q  =  39.89 W/ m 2
Problem 5.3-6 Unsteady-State Conduction in a Brick Wall: A flat brick wall  1.0 ft thick  is the lining on one side of a furnace. If the wall is at uniform temperature of  100°F  and one side is suddenly exposed to a gas at  1100°F , calculate the time for the furnace wall at point  0.5 ft  from the surface to reach  500°F . The rear side of the wall is insulated. The convection coefficient is  2.6 Btu/h·ft 2 ° F  and the physical properties of the brick are  k =0.65 Btu/h·ft ° F  and  0.02 ft 2 /h .
Problem 5.3-6 Given: Required: Flat brick wall: T = 500 °F   T 1  = 1100 °F h  =  2.6 Btu/h·ft 2 F   κ   =  0.65 Btu/h·ft ° F α   =  0.02 ft 2 /h t = ? (at 0.5 ft)  T 0  = 100 °F 0.5 ft
Solution: Problem 5.3-6 From the graph (Heisler): X = 6.5 t  =  81.25 hrs

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4A Group 8 - Problem Set #2

  • 1. CHUATOCO, Anthony DALANON, Farlene DONIEGO, Joanne FULGUERAS, Alyssa Marie LAGRADA, Rabbie Group 8 Unit Operations 4 ChE - A
  • 2. Problem 4.1-1 Problem #16 (Click on the following to view the solutions) Problem Set 2 Geankoplis Problem 5.3-6 Problem #8 GROUP 8
  • 3. Problem #8 A spherical furnace has an inside radius of 1 m , and an outside radius of 1.2 m . The thermal conductivity of the wall is 0.5 W/m · K . The inside furnace temperature is 1100 ° C and the outside surface is at 80 ° C . a) Calculate the total heat loss for 24 hrs operation; b) What is the heat flux and temperature at a radius of 1.1 m ?
  • 4. Problem #8 Given: Required: 1 m 1.2 m 1.1 m 80 ° C 1100 ° C 0.5 W/m · K T a) total heat loss (q) for 24 hrs b) heat flux (q/A) & T at 1.1m radius
  • 5. Solution: q = q i = q o = - Σ T R T R T = Δ x K m A m = T i - T R i = T - T o R o A m = 4 π · r i · r o Problem #8
  • 6. Solution: R T = Δ x K m A m = 1m – 1.2m = Problem #8 - 0.0265 K/W q = - Σ T R T = - (1100°C – 80°C) - 0.0265 K/W = 38453.09 W or J/s q = 3.322 x 10 9 J a) total heat loss (q) for 24 hrs
  • 7. Solution: Problem #8 b) heat flux (q/A) & T at 1.1m radius q = q i = T i - T R i 1m – 1.1m ( 0.5 W/m·K) [ 4 π (1m) (1.1m)] - ( 1100°C – T ) 38453.09 W = T = 543.64 °C q/A = 2781.82 W/m 2
  • 8. Problem #16 (US) A large slab 1m thick is initially at a uniform temperature of 150 o C . Suddenly its front face is exposed to a fluid maintained at 250 ° C , but its rear face remained insulated. The fluid has a convective coefficient of 40 W/m 2 · K . Assume the solid has a thermal diffusivity of 0.000025 m 2 /s and a thermal conductivity of 20 W/m · K .   Using a numerical finite difference method with M=5 and 4 slices , construct a table for the temperature profile of the slab up to a time of 4000 sec .
  • 9. Problem #16 Given: Required: Slab: Thickness = 1m 0 T n = 150 °C Front Face: T a = 250 °C h = 40 W/m 2 K κ = 20 W/mK α = 0.000025 m 2 /s Rear Face: Insulated t = 4000s 4 slices M = 5 Δ x = 1m/4 = 0.25 m table for the temperature profile Using a numerical finite difference method
  • 10. Problem #16 Solution: Δ t = 500s N = 0.5 q 1 2 3 4 f Δ x = 0.25m insulation T a = 250 °C
  • 11. Problem #16 Solution: Front Face: for n=1 General: for n=2 to n=4 Rear Face: for n=f
  • 13. Problem 4.1-1 Insulation in a Cold Room: Calculate the heat loss per m 2 of surface area for a temporary insulating wall of a food cold storage room where the outside temperature is 299.9 K and the inside temperature 276.5 K . The wall is composed of 25.4 mm of corkboard having a k of 0.0433 W/m∙K.
  • 14. Problem 4.1-1 Given: Required: Wall: T o = 299.9 K T i = 276.5 K Side = 25.4 mm k = 0.0433 W/m∙K heat loss (q) per m 2
  • 15. Solution: q = - Σ T R T R T = Δ x K m A m Problem 4.1-1 Basis: 1 m 2 q = 299.9 K -276.5 K R T = 0.0254m (0.0433 W/m∙K)(1m 2 ) = - 0.587 K/W - 0.587 K/W q = 39.89 W/ m 2
  • 16. Problem 5.3-6 Unsteady-State Conduction in a Brick Wall: A flat brick wall 1.0 ft thick is the lining on one side of a furnace. If the wall is at uniform temperature of 100°F and one side is suddenly exposed to a gas at 1100°F , calculate the time for the furnace wall at point 0.5 ft from the surface to reach 500°F . The rear side of the wall is insulated. The convection coefficient is 2.6 Btu/h·ft 2 ° F and the physical properties of the brick are k =0.65 Btu/h·ft ° F and 0.02 ft 2 /h .
  • 17. Problem 5.3-6 Given: Required: Flat brick wall: T = 500 °F T 1 = 1100 °F h = 2.6 Btu/h·ft 2 F κ = 0.65 Btu/h·ft ° F α = 0.02 ft 2 /h t = ? (at 0.5 ft) T 0 = 100 °F 0.5 ft
  • 18. Solution: Problem 5.3-6 From the graph (Heisler): X = 6.5 t = 81.25 hrs