Virtual Labs

\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0

Find the value of T1. Boundry conditions are given as:
The temperature of top surface is 28^oC.
The temperature of left surface is 11^oC.
The temperature of bottom surface is 50^oC.
The right surface is insulated.
Given that,
l=3, w=3. Take h=1 and k=1, where h = Δx and k = Δy.

a: T1 = 39.86, T2 = 44.78, T3 = 34.14, T4 = 37.62 Explanation

Explanation

b: T1 = 19.96, T2 = 24.78, T3 = 14.04, T4 = 17.22 Explanation

Explanation

c: T1 = 29.86, T2 = 34.34, T3 = 24.13, T4 = 27.65 Explanation

Explanation

d: T1 = 24.86, T2 = 39.48, T3 = 21.13, T4 = 22.52 Explanation

Explanation

\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0

Find the value of T1. Boundry conditions are given as:
The temperature of top surface is 97^oC.
The temperature of left surface is 85^oC.
The temperature of bottom surface is 34^oC.
The right surface is insulated.
Given that,
l=3, w=3. Take h=1 and k=1, where h = Δx and k = Δy.

a: T1 = 65.63, T2 = 61.48, T3 = 82.07, T4 = 80.65 Explanation

Explanation

b: T1 = 55.98, T2 = 69.45, T3 = 88.07, T4 = 70.84 Explanation

Explanation

c: T1 = 45.68, T2 = 41.45, T3 = 52.05, T4 = 50.64 Explanation

Explanation

d: T1 = 56.86, T2 = 36.54, T3 = 28.50, T4 = 75.46 Explanation

Explanation

Differentiation(PDE) - Elliptical equation (Laplace Equation with one end insulated)