Question

Heat transfer through Fin: Question: An Aluminium pot is used to boil water as shown below. The handle of the pot is 20-cm long, 3-cm wide, and 0.5-cm thick. The pot is exposed to room air at 25°C, and the convection coefficient is 5 W/m² °C. Plot the temperature distribution for (x=0.05,0.1,0.15,0.2 m) and total heat transfer from the handle. If a stainless-steel handle is used, what will happen to the temperature distribution and heat transfer? Can you touch the handle when the water is boiling? (k for aluminium is 237 W/m °C,K for steel is 15 W/m°C) T? = 25 °C h = 5 W/ m² °C 100 °C x Hint: Case Tip Condition Temp. Distribution Fin heat transfer A Convection heat transfer: h?(L)=-k(d?/dx)x=L (cosh m(L - x) + (h/mk) sinh m(L - x)) / (cosh mL + (h/mk) sinh mL) M?b (sinh mL + (h/mk) cosh mL) / (cosh mL + (h/mk) sinh mL) B Adiabatic (d?/dx)x=L = 0 cosh m(L - x) / cosh mL M?b tanh mL C Given temperature: ?(L) = ?L ((?L/?b) sinh mx + sinh m(L - x)) / sinh mL M?b (cosh mL - ?L/?b) / sinh mL D Infinitely long fin ?(L) = 0 e^-mx M?b ? = T - T?, m² = hP/kAc ?b = ?(0) = Tb - T?, M = ??(hPkAc)?b

          Heat transfer through Fin:
Question: An Aluminium pot is used to boil water as shown below. The handle of the pot is 20-cm long, 3-cm wide, and 0.5-cm thick. The pot is exposed to room air at 25°C, and the convection coefficient is 5 W/m² °C. Plot the temperature distribution for (x=0.05,0.1,0.15,0.2 m) and total heat transfer from the handle. If a stainless-steel handle is used, what will happen to the temperature distribution and heat transfer? Can you touch the handle when the water is boiling? (k for aluminium is 237 W/m °C,K for steel is 15 W/m°C)

T? = 25 °C
h = 5 W/ m² °C
100 °C
x
Hint:
Case Tip Condition Temp. Distribution Fin heat transfer
A Convection heat transfer: h?(L)=-k(d?/dx)x=L (cosh m(L - x) + (h/mk) sinh m(L - x)) / (cosh mL + (h/mk) sinh mL) M?b (sinh mL + (h/mk) cosh mL) / (cosh mL + (h/mk) sinh mL)
B Adiabatic (d?/dx)x=L = 0 cosh m(L - x) / cosh mL M?b tanh mL
C Given temperature: ?(L) = ?L ((?L/?b) sinh mx + sinh m(L - x)) / sinh mL M?b (cosh mL - ?L/?b) / sinh mL
D Infinitely long fin ?(L) = 0 e^-mx M?b
? = T - T?, m² = hP/kAc
?b = ?(0) = Tb - T?, M = ??(hPkAc)?b

Heat transfer through Fin:
Question: An Aluminium pot is used to boil water as shown below. The handle of the pot is 20-cm long, 3-cm wide, and 0.5-cm thick. The pot is exposed to room air at 25°C, and the convection coefficient is 5 W/m² °C. Plot the temperature distribution for (x=0.05,0.1,0.15,0.2 m) and total heat transfer from the handle. If a stainless-steel handle is used, what will happen to the temperature distribution and heat transfer? Can you touch the handle when the water is boiling? (k for aluminium is 237 W/m °C,K for steel is 15 W/m°C)

T? = 25 °C
h = 5 W/ m² °C
100 °C
x
Hint:
Case Tip Condition Temp. Distribution Fin heat transfer
A Convection heat transfer: h?(L)=-k(d?/dx)x=L (cosh m(L - x) + (h/mk) sinh m(L - x)) / (cosh mL + (h/mk) sinh mL) M?b (sinh mL + (h/mk) cosh mL) / (cosh mL + (h/mk) sinh mL)
B Adiabatic (d?/dx)x=L = 0 cosh m(L - x) / cosh mL M?b tanh mL
C Given temperature: ?(L) = ?L ((?L/?b) sinh mx + sinh m(L - x)) / sinh mL M?b (cosh mL - ?L/?b) / sinh mL
D Infinitely long fin ?(L) = 0 e^-mx M?b
? = T - T?, m² = hP/kAc
?b = ?(0) = Tb - T?, M = ??(hPkAc)?b

Added by Marc G.

Question

Please give Ace some feedback