---
title: "Forced convection in porous media"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Forced_convection_in_porous_media"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:52:52.743751+00:00"
instance: "kb-cron"
---

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

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

According to Darcy's law

  
    
      
        u
        =
        −
        (
        K
        
          /
        
        μ
        )
        ∂
        P
        
          /
        
        ∂
        x
      
    
    {\displaystyle u=-(K/\mu )\partial P/\partial x}
  

  
    
      
        v
        =
        −
        (
        K
        
          /
        
        μ
        )
        ∂
        P
        
          /
        
        ∂
        y
      
    
    {\displaystyle v=-(K/\mu )\partial P/\partial y}
  

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

  
    
      
        u
        =
      
    
    {\displaystyle u=}
  

  
    
      
        
          U
          
            ∞
          
        
      
    
    {\displaystyle U_{\infty }}
  
                             
  
    
      
        v
        =
        0
      
    
    {\displaystyle v=0}
  

  
    
      
        P
        (
        x
        )
        =
        −
        (
        μ
        
          /
        
        K
        )
        U
        ∞
        x
        +
        c
        o
        n
        s
        t
        a
        n
        t
      
    
    {\displaystyle P(x)=-(\mu /K)U\infty x+constant}
  

  
    
      
        
          δ
          
            t
          
        
      
    
    {\displaystyle \delta _{t}}
  
 is the thickness of the slender layer of length x that affects the temperature transition from 
  
    
      
        
          T
          
            0
          
        
      
    
    {\displaystyle T_{0}}
  
  to 
  
    
      
        
          T
          
            ∞
          
        
      
    
    {\displaystyle T_{\infty }}
  
.
Balancing the energy equation between enthalpy flow in the x direction and thermal diffusion in the y direction

  
    
      
        
          U
          
            ∞
          
        
        ∂
        T
        
          /
        
        ∂
        x
        ∼
        α
        Δ
        T
        
          /
        
        
          δ
          
            t
          
          
            2
          
        
      
    
    {\displaystyle U_{\infty }\partial T/\partial x\sim \alpha \Delta T/\delta _{t}^{2}}
  

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

  
    
      
        
          δ
          
            t
          
        
        
          /
        
        x
        ∼
        P
        
          e
          
            x
          
          
            −
          
        
        .5
      
    
    {\displaystyle \delta _{t}/x\sim Pe_{x}^{-}.5}
  

  
    
      
        N
        u
        =
        h
        x
        
          /
        
        K
        ∼
        x
        
          /
        
        
          δ
          
            t
          
        
        ∼
        P
        
          e
          
            x
          
          
            0
          
        
        .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.

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

  
    
      
        P
        
          e
          
            x
          
        
        =
        
          U
          
            ∞
          
        
        x
        
          /
        
        α
      
    
    {\displaystyle Pe_{x}=U_{\infty }x/\alpha }
  


== See also ==
Darcy's law
Nusselt Number
Porous media
Convective heat transfer
Heat transfer coefficient
Porous media


== References ==


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