Forced convection in porous media

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

$\partial u/\partial x+\partial v/\partial y=0$

According to Darcy's law

$u=-(K/\mu )\partial P/\partial x$

$v=-(K/\mu )\partial P/\partial y$

$u\partial T/\partial x+v\partial T/\partial y=\mathit{\alpha }\frac{{\partial }^2}{\partial x^2}T$

$u=$$U_{\mathrm{\infty }}$ $v=0$

$P(x)=-(\mu /K)U\mathrm{\infty }x+constant$

${\delta }_t$ is the thickness of the slender layer of length x that affects the temperature transition from $T_0$ to $T_{\mathrm{\infty }}$.

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

$U_{\mathrm{\infty }}\partial T/\partial x\sim \alpha \mathrm{\Delta }T/{\delta }_t^2$

boundary is slender so ${\delta }_t<<x$

${\delta }_t/x\sim P{e}_x^{-}.5$

$Nu=hx/K\sim x/{\delta }_t\sim P{e}_x^0.5$

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.

$P{e}_x$ $=$ Advective transport rate $/$ Diffusive transport rate

$P{e}_x=U_{\mathrm{\infty }}x/\alpha$

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