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. Porous medium is defined as a material volume consisting of solid matrix with an interconnected void. Flow in porous media have revealed the Darcy law< which relates linearly the flow velocity to the pressure gradient across the porous medium. 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, including: Chemical, Environmental, Mechanical, Geological and Petroleum.

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.We begin with constant wall temperature.

In 2D steady state system

${\displaystyle \partial u/\partial x+\partial v/\partial y=0}$

According to Darcy's law

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

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

${\displaystyle u\partial T/\partial x+v\partial T/\partial y={\boldsymbol {\alpha }}{\partial ^{2} \over \partial x^{2}}T}$

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

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

Let ${\displaystyle \delta _{t}}$ be the thickness of the slender layer of length x that affects the temperature transition from ${\displaystyle T_{0}}$ to ${\displaystyle T_{\infty }}$.

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

${\displaystyle U_{\infty }\partial T/\partial x\sim \alpha \Delta T/\delta _{t}^{2}}$

boundary is slender so ${\displaystyle \delta _{t}<<x}$

${\displaystyle \delta _{t}/x\sim Pe_{x}^{-}.5}$

${\displaystyle Nu=hx/K\sim x/\delta _{t}\sim Pe_{x}^{0}.5}$

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.

${\displaystyle Pe_{x}}$ ${\displaystyle =}$ Advective transport rate ${\displaystyle /}$ Diffusive transport rate

${\displaystyle Pe_{x}=U_{\infty }x/\alpha }$

Video Forced convection in porous media

See also

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

Maps Forced convection in porous media

References

src: cdn.comsol.com

External links

• http://www.me.ust.hk/~mezhao/pdf/20.PDF

Source of the article : Wikipedia