The partial differential equation for distribution of temperature in an aliminium rod is given by Here, k=0.835. For t=0 the temperature is zero, boundary conditions are given as T(0) = 100°C and T(10) = 50°C. Find the temperature distribution in interior nodes for two time levels by finite difference method by taking Ax = 2 cm and At = 0.1. Finite difference equation for heat equation is: Tij+1 = A Ti+1,j + (1 – 22)T;j + 2 T¡-1,j where 2 = kat Ax2"

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Chapter2: Second-order Linear Odes
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numerical analysis

The partial differential equation for distribution of temperature in an aliminium rod is given by
k-
Here, k=0.835. For t=0 the temperature is zero, boundary conditions are given as T(0) = 100°C
at
and T(10) = 50°C. Find the temperature distribution in interior nodes for two time levels by finite difference
method by taking Ax = 2 cm and At = 0.1.
Finite difference equation for heat equation is:
Τj+1 λ Τi+1.j + (1-2 λ) Τij +λ T-1.j
kat
where 1 =
Ax2
Transcribed Image Text:The partial differential equation for distribution of temperature in an aliminium rod is given by k- Here, k=0.835. For t=0 the temperature is zero, boundary conditions are given as T(0) = 100°C at and T(10) = 50°C. Find the temperature distribution in interior nodes for two time levels by finite difference method by taking Ax = 2 cm and At = 0.1. Finite difference equation for heat equation is: Τj+1 λ Τi+1.j + (1-2 λ) Τij +λ T-1.j kat where 1 = Ax2
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