Virtual Labs

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

Find the value of T1, T2, T3, T4. Boundry conditions are given as:
The temperature of top left surface is 51^oC.
The temperature of top right surface is 75^oC.
The temperature of left upper surface is 46^oC.
The temperature of left lower surface is 52^oC.
The temperature of bottom left surface is 74^oC.
The temperature of bottom right surface is 33^oC.
The temperature of right upper surface is 62^oC.
The temperature of right lower surface is 60^oC.
Given that,
l=3, w=3. Take h=1 and k=1, where h = Δx and k = Δy.

a: T1 = 58.29, T2 = 53.08, T3 = 54.08, T4 = 61.04 Explanation

Explanation

b: T1 = 68.29, T2 = 23.08, T3 = 14.08, T4 = 81.04 Explanation

Explanation

c: T1 = 50.78, T2 = 43.12, T3 = 54.08, T4 = 55.34 Explanation

Explanation

d: T1 = 52.29, T2 = 73.08, T3 = 64.11, T4 = 51.12 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 left surface is 71^oC.
The temperature of top right surface is 40^oC.
The temperature of left upper surface is 63^oC.
The temperature of left lower surface is 19^oC.
The temperature of bottom left surface is 65^oC.
The temperature of bottom right surface is 1^oC.
The temperature of right upper surface is 25^oC.
The temperature of right lower surface is 58^oC.
Given that,
l=3, w=3. Take h=1 and k=1, where h = Δx and k = Δy.

a: T1 = 34.17, T2 = 53.20, T3 = 35.83, T4 = 83.17 Explanation

Explanation

b: T1 = 29.34, T2 = 20.38, T3 = 95.83, T4 = 54.57 Explanation

Explanation

c: T1 = 43.29, T2 = 35.20, T3 = 53.95, T4 = 38.54 Explanation

Explanation

d: T1 = 33.27, T2 = 55.23, T3 = 76.93, T4 = 22.57 Explanation

Explanation

Differentiation(PDE) - Elliptical equation (Laplace Equation)