Search results
Results from the WOW.Com Content Network
The Crank–Nicolson stencil for a 1D problem. The Crank–Nicolson method is based on the trapezoidal rule, giving second-order convergence in time.For linear equations, the trapezoidal rule is equivalent to the implicit midpoint method [citation needed] —the simplest example of a Gauss–Legendre implicit Runge–Kutta method—which also has the property of being a geometric integrator.
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions.A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient).
Atmospheric thermodynamics is the study of heat-to-work transformations (and their reverse) that take place in the Earth's atmosphere and manifest as weather or climate. . Atmospheric thermodynamics use the laws of classical thermodynamics, to describe and explain such phenomena as the properties of moist air, the formation of clouds, atmospheric convection, boundary layer meteorology, and ...
In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of the convection–diffusion equation when bulk velocity is zero.
Another form of convection is forced convection. In this case, the fluid is forced to flow by using a pump, fan, or other mechanical means. Convective heat transfer , or simply, convection, is the transfer of heat from one place to another by the movement of fluids , a process that is essentially the transfer of heat via mass transfer .
In computational physics, the term advection scheme refers to a class of numerical discretization methods for solving hyperbolic partial differential equations.In the so-called upwind schemes typically, the so-called upstream variables are used to calculate the derivatives in a flow field.
In many real-life applications (e.g. heat losses at solar central receivers or cooling of photovoltaic panels), natural and forced convection occur at the same time (mixed convection). [4] Internal and external flow can also classify convection. Internal flow occurs when a fluid is enclosed by a solid boundary such as when flowing through a pipe.