Physics: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.[1]
In 2D steady state system
[math]\displaystyle{ \partial u/\partial x+\partial v/\partial y=0 }[/math]
According to Darcy's law
[math]\displaystyle{ u=-(K/\mu)\partial P/\partial x }[/math]
[math]\displaystyle{ v=-(K/\mu)\partial P/\partial y }[/math]
[math]\displaystyle{ u\partial T/\partial x+v\partial T/\partial y = \boldsymbol{\alpha}{\partial^2\over\partial x^2}T }[/math]
[math]\displaystyle{ u= }[/math][math]\displaystyle{ U_\infty }[/math] [math]\displaystyle{ v=0 }[/math]
[math]\displaystyle{ P(x)= -(\mu/K)U\infty x+ constant }[/math]
[math]\displaystyle{ \delta_t }[/math] is the thickness of the slender layer of length x that affects the temperature transition from [math]\displaystyle{ T_0 }[/math] to [math]\displaystyle{ T_\infty }[/math].
Balancing the energy equation between enthalpy flow in the x direction and thermal diffusion in the y direction
[math]\displaystyle{ U_\infty\partial T/\partial x\sim \alpha\Delta T/\delta_t^2 }[/math]
boundary is slender so [math]\displaystyle{ \delta_t\lt \lt x }[/math]
[math]\displaystyle{ \delta_t/x \sim Pe_x^-.5 }[/math]
[math]\displaystyle{ 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]\displaystyle{ Pe_x }[/math] [math]\displaystyle{ = }[/math] Advective transport rate [math]\displaystyle{ / }[/math] Diffusive transport rate
[math]\displaystyle{ Pe_x = U_\infty x/\alpha }[/math]
See also
- Darcy's law
- Nusselt Number
- Porous media
- Convective heat transfer
- Heat transfer coefficient
- Porous media
References
- ↑ Nield, D.A; Bejan, A (2013). Convection in Porous Media. Springer Science & Business Media. ISBN 9780387290966. https://books.google.com/books?id=4qTvIixmtVkC.
External links
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