Английская Википедия:Forced convection in porous media

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Forced convection is type of heat transport in which fluid motion is generated by an external source like a (pump, fan, suction device, etc.). Heat transfer through porus media is very effective and efficiently. Forced convection heat transfer in a confined porous medium has been a subject of intensive studies during the last decades because of its wide applications.

The basic problem in heat convection through porous media consists of predicting the heat transfer rate between a deferentially heated, solid impermeable surface and a fluid-saturated porous medium. Beginning with constant wall temperature.

In 2D steady state system

<math>\partial u/\partial x+\partial v/\partial y=0 </math>

According to Darcy's law

<math>u=-(K/\mu)\partial P/\partial x </math>

<math>v=-(K/\mu)\partial P/\partial y </math>

<math>u\partial T/\partial x+v\partial T/\partial y = \boldsymbol{\alpha}{\partial^2\over\partial x^2}T </math>

<math>u=</math><math>U_\infty</math> <math>v=0</math>

<math>P(x)= -(\mu/K)U\infty x+ constant</math>

<math>\delta_t</math> is the thickness of the slender layer of length x that affects the temperature transition from <math>T_0</math> to <math>T_\infty</math>.

Balancing the energy equation between enthalpy flow in the x direction and thermal diffusion in the y direction

<math>U_\infty\partial T/\partial x\sim \alpha\Delta T/\delta_t^2</math>

boundary is slender so <math>\delta_t<<x</math>

<math>\delta_t/x \sim Pe_x^-.5</math>

<math>Nu = hx/K \sim x/\delta_t \sim Pe_x^0.5</math>

The Peclet number is a dimensionless number used in calculations involving convective heat transfer. It is the ratio of the thermal energy convected to the fluid to the thermal energy conducted within the fluid.

<math>Pe_x</math> <math>=</math> Advective transport rate <math>/</math> Diffusive transport rate

<math>Pe_x = U_\infty x/\alpha</math>

See also

• Darcy's law
• Nusselt Number
• Porous media
• Convective heat transfer
• Heat transfer coefficient
• Porous media

External links

• https://web.archive.org/web/20091211060057/http://www.me.ust.hk/~mezhao/pdf/20.PDF