Does Negative Divergence of Gradient Temperature Lead to the Laplace Equation?

Thread starter range.rover
Start date Aug 5, 2014
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Divergence Gradient

In summary, the divergence of gradient is a mathematical operation that describes the rate of change of a vector field in a given direction. It is calculated by taking the dot product of the gradient vector and the vector field, resulting in a scalar value. A positive divergence indicates expansion or divergence of the vector field, while a negative divergence indicates contraction or convergence. In physics and engineering, the divergence of gradient is used to calculate flux and is important in understanding fluid flow, heat transfer, and electromagnetic fields. It is possible for the divergence of gradient to be negative at a point, indicating a local minimum in the vector field.

Aug 5, 2014

range.rover

does negative divergence of gradient tempearature gives to lalace equation...?

-div(∇T) = [∂^2T/∂x^2+∂^2T/∂y^2]

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Aug 5, 2014

SteamKing

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It's the Laplace equation:

http://en.wikipedia.org/wiki/Laplacian

The Laplacian operator is defined as the divergence of the gradient.

1. What is the definition of divergence of gradient?

The divergence of gradient is a mathematical operation that describes the rate of change of a vector field in a given direction. It is also known as the dot product of the gradient and the vector field.

2. How is the divergence of gradient calculated?

The divergence of gradient is calculated by taking the dot product of the gradient vector (which contains the partial derivatives of the vector field with respect to each variable) and the vector field itself. This results in a scalar value.

3. What does a positive or negative divergence of gradient indicate?

A positive divergence of gradient indicates that the vector field is expanding or diverging, meaning that the magnitude of the vector is increasing in all directions. A negative divergence of gradient indicates that the vector field is contracting or converging, meaning that the magnitude of the vector is decreasing in all directions.

4. How is the divergence of gradient used in physics and engineering?

In physics and engineering, the divergence of gradient is used to calculate the flux of a vector field through a given surface. This is important in understanding the flow of fluids, heat transfer, and electromagnetic fields.

5. Can the divergence of gradient be negative at a point?

Yes, the divergence of gradient can be negative at a point. This indicates that the vector field is contracting at that specific point, while it may still be expanding or diverging in other areas. This is known as a local minimum in the vector field.