#### Heat equation

## What is meant by heat equation?

noun Mathematics, Thermodynamics. a partial differential equation the solution of which gives the distribution of temperature in a region as a function of space and time when the temperature at the boundaries, the initial distribution of temperature, and the physical properties of the medium are specified.

## What is heat equation in PDE?

The equation governing this setup is the so-called one-dimensional heat equation: ∂u∂t=k∂2u∂x2, where k>0 is a constant (the thermal conductivity of the material). That is, the change in heat at a specific point is proportional to the second derivative of the heat along the wire.

## What is Laplace equation for heat flow?

Laplace’s equation and Poisson’s equation are the simplest examples of elliptic partial differential equations. In the study of heat conduction, the Laplace equation is the steady-state heat equation. In general, Laplace’s equation describes situations of equilibrium, or those that do not depend explicitly on time.

## Is heat an elliptic equation?

If b2 − 4ac > 0, we say the equation is hyperbolic. If b2 − 4ac = 0, we say the equation is parabolic. If b2 − 4ac < 0, we say the equation is elliptic. The heat equation ut − uxx = 0 is parabolic.

## How do I calculate specific heat?

Calculate specific heat as c = Q / (mΔT) . In our example, it will be equal to c = -63,000 J / (5 kg * -3 K) = 4,200 J/(kg·K) . This is the typical heat capacity of water.

## What is steady state heat transfer?

Steady-state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant, so that (after an equilibration time), the spatial distribution of temperatures (temperature field) in the conducting object does not change any further.

## Which equation is Laplace equation?

Laplace’s equation, second-order partial differential equation widely useful in physics because its solutions R (known as harmonic functions) occur in problems of electrical, magnetic, and gravitational potentials, of steady-state temperatures, and of hydrodynamics.

## How do you calculate heat flow rate?

So the rate of heat transfer to an object is equal to the thermal conductivity of the material the object is made from, multiplied by the surface area in contact, multiplied by the difference in temperature between the two objects, divided by the thickness of the material.