Abstract
Steady and pulsatile flow and heat transfer in a channel lined with two porous layers subject to constant wall heat flux under local thermal non-equilibrium (LTNE) condition is numerically investigated. To do this, a physical boundary condition in the interface of porous media and clear region of the channel is derived. The objective of this work is, first, to assess the effects of local solid-to-fluid heat transfer (a criterion indicating on departure from local thermal equilibrium (LTE) condition), solid-to-fluid thermal conductivity ratio and porous layer thickness on convective heat transfer in steady condition inside a channel partially filled with porous media; second, to examine the impact of pulsatile flow on heat transfer in the same channel. The effects of LTNE condition and thermal conductivity ratio in pulsatile flow are also briefly discussed. It is observed that Nusselt number inside the channel increases when the problem is tending to LTE condition. Therefore, careless consideration of LTE may lead to overestimation of heat transfer. Solid-to-fluid thermal conductivity ratio is also shown to enhance heat transfer in constant porous media thickness. It is also revealed that an increase in the amplitude of pulsation may result in enhancement of Nusselt number, while Nusselt number has a minimum in a certain frequency for each value of amplitude.
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Abbreviations
- A :
-
Amplitude
- a sf :
-
Specific solid–fluid interface area
- Bi :
-
Modified Biot number
- C F :
-
Forchheimer coefficient
- c p :
-
Specific heat capacity of fluid
- Da :
-
Darcy number
- d p :
-
Diameter of particles forming porous medium
- e :
-
Thickness of porous layer
- f :
-
Frequency
- h :
-
Solid-to-fluid heat transfer coefficient
- H :
-
Channel’s half width
- k :
-
Thermal conductivity
- K :
-
Permeability
- Nu :
-
Nusselt number
- p :
-
Pressure
- Pr :
-
Prandtl number
- Q :
-
Rate of heat transfer
- R eff :
-
Ratio of thermal diffusivity
- R :
-
Radius of pipe
- Re :
-
Reynolds number
- T :
-
Dimensional temperature
- u :
-
Axial velocity
- U :
-
Velocity
- x, y:
-
Dimensional coordinates
- X, Y:
-
Dimensionless coordinates
- β :
-
Womersley number
- ε :
-
Porosity
- Φ:
-
Phase lag
- γ :
-
Experimental constant
- μ :
-
Viscosity
- θ :
-
Dimensionless temperature
- ρ :
-
Density
- σ :
-
Thermal capacity ratio
- ave:
-
Time-averaged value
- e:
-
Effective value
- f:
-
Fluid
- in:
-
Inlet
- p:
-
Pressure
- r:
-
Ratio
- s:
-
Solid
- S:
-
Steady
- sf:
-
Solid-to-fluid ratio
- w:
-
Wall
- u:
-
Velocity
- US:
-
Unsteady
- 0, m:
-
Mean value
- *:
-
Dimensional variable
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Forooghi, P., Abkar, M. & Saffar-Avval, M. Steady and Unsteady Heat Transfer in a Channel Partially Filled with Porous Media Under Thermal Non-Equilibrium Condition. Transp Porous Med 86, 177–198 (2011). https://doi.org/10.1007/s11242-010-9615-7
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DOI: https://doi.org/10.1007/s11242-010-9615-7