Esfera de aluminio, fenomenos de transporte 2
Propiedades del aluminio | | | |
k = | 210 | w/m°C | Radio (R) = | 0.015 | m |
C = | 0.085| J/gm°C | h = | 20 | w/m^2°C |
ρ= | 2.72 | gm/cm^3 | | | |
| | | | | |
Bi = | 0.00142857 | < 0.1 | | | |
Como el “Bi” es menor que 0.1 se puede utilizar el análisis de parámetros concentrados.
1τ=hAρCV=hρC*4πR243πR3=3hρCR
3h/ρCR | = | 0.00164312 | s^-1 |
Realizando los cálculos correspondientes y obtener el tiempo necesario, para que la esfera alcancelas distintas temperaturas con intervalos de “cinco”. Y graficar:
a) Tiempo-Temperatura
b) t* - θ*
Con | 101 | °C | |
T = | 101 | °C | |
T∞ = | 100 | °C | |
To = | 200 | °C | |
| | | |
θ^* = | 0.01 | = | 99% |
t^* = | (hA/ρCV)*t | | |
t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | |
| | | |
Sustitución | | | |
0.5 =e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |
| | | |
Despejando | | | |
Ln(0.5)/(0.001643) = | 2802.70658 | seg. |
t = | 46.7117763 | min | |
Con | 105 | °C | |
T = | 105 | °C | |
T∞ = | 100 | °C | |
To = | 200 | °C | |
| | | |
θ^* = | 0.05 | = | 95% |
| | | |
t^* = | (hA/ρCV)*t | | |
t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | || | | |
Sustitución | | | |
0.5 = e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |
| | | |
Despejando | | | |
Ln(0.5)/(0.001643) = | 1823.20266 | seg. |
t = | 30.386711 | min | |
Con | 110 | °C | |
T = | 110 | °C | |
T∞ = | 100 | °C | |
To = | 200 | °C | |
| | | |
θ^* = | 0.1 | = | 90% |
| | | |
t^* = | (hA/ρCV)*t | | |t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | |
| | | |
Sustitución | | | |
0.5 = e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |
| | | |
Despejando | | | |
Ln(0.5)/(0.001643) = | 1401.35329 | seg. |
t = | 23.3558881 | min | |
Con | 115 | °C | |
T = | 115 | °C | |
T∞ = | 100 | °C | |
To = | 200 | °C | |
| | | |
θ^* = | 0.15 |= | 85% |
| | | |
t^* = | (hA/ρCV)*t | | |
t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | |
| | | |
Sustitución | | | |
0.5 = e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |
| | | |
Despejando | | | |
Ln(0.5)/(0.001643) = | 1154.58722 | seg. |
t = | 19.2431204 | min | |
Con | 120 | °C | |
T = | 120 | °C | |
T∞ = | 100 | °C | |To = | 200 | °C | |
| | | |
θ^* = | 0.2 | = | 80% |
| | | |
t^* = | (hA/ρCV)*t | | |
t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | |
| | | |
Sustitución | | | |
0.5 = e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |
| | | |
Despejando | | | |
Ln(0.5)/(0.001643) = | 979.503914 | seg. |
t = | 16.3250652 | min | |
Con |125 | °C | |
T = | 125 | °C | |
T∞ = | 100 | °C | |
To = | 200 | °C | |
| | | |
θ^* = | 0.25 | = | 75% |
| | | |
t^* = | (hA/ρCV)*t | | |
t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | |
| | | |
Sustitución | | | |
0.5 = e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |
| | | |
Despejando | | | |
Ln(0.5)/(0.001643) = |843.698748 | seg. |
t = | 14.0616458 | min | |
Con | 130 | °C | |
T = | 130 | °C | |
T∞ = | 100 | °C | |
To = | 200 | °C | |
| | | |
θ^* = | 0.3 | = | 70% |
| | | |
t^* = | (hA/ρCV)*t | | |
t^* = | 0.001643 s^-1*(t) | |
θ^* = | |
| | |
| | | |
Sustitución | | | |
0.5 = e^-(0.001643)*t | | |
In(0.5)=-0.001643*t | | |...
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