Porous Channel Flow Plate in Engineering Applications
Heat transfer and fluid in porous channel flow plate (PCP) has been the subject of great interest for many decades. The reason why it is there for such a long time is that it has been a suitable choice for so many engineering applications. The most conventional applications of PCP include a solar receiver, thermal insulation building materials, energy-storing units, and packed-bed heat exchangers. Apart from the conventional applications, PCP is also an ideal choice for advanced applications in the new fields of micro-scale heat transfer.
Today, we can see the use of microchannels in various equipment and industries, including electronic package cooling, and heating and cooling of various devices. They are suitable for more applications in microchannel fabrication, heat exchangers, and heat sinks, etc.
Porous Channel Flow Plate Impact on Different Engineering Applications
A major difficulty in the prediction of a micron-size device’s gaseous transport is due the assumption of continuum flow in Navier-Stokes equations when the molecules’ mean-free path is similar to the flow domain’s characteristics dimension. Under this environment, the heat transfer and momentum begin to get effects from the gas’s discrete composition of the molecule, and several rarefactions or non-continuum effects likely show up, like temperature jump and velocity slip at a gas-solid interface. The flow rate of fluid, velocity profiles, shear stresses of boundary wall, the rates of heat transfer, Nusselt number, and temperature profiles come under the influence of the non-continuum regime.
However, a specific channel size limit exists with which you can apply the equation with a few modifications on boundary conditions. When the Kn (Knudsen number) is within the range, we call the flow in such a situation as the slip-flow. The Knudsen number (Kn) is the molecular mean-free path ratio to the system’s characteristic length. It also measures the rarefaction degree of the gases met in the flows via narrow passages. Moreover, it measures the continuum model’s validity degree. It is a significant element of porous channel flow plate in several ways.
Continuum Model and Kn Flows
The validity of the continuum model implies very small flows of the Knudsen number. When the Kn increases, we see that the effects of rarefaction become more noticeable. Eventually, the assumption of continuum breaks down. According to so many researchers, a no-slip, well-accepted boundary condition might not be appropriate for nano-scale and microflows. Several mechanisms are available for explaining this phenomenon. Many studies have concluded that Navier-Stokes equations in combination with the velocity-slip yield outcomes for friction factor and pressure drop in contract with trial data for porous channel flow plate flow.
The suitable heat transfer and flow models for specific gas flow issues rely on the Knudsen number range. The grouping of dissimilar regimes of gas flow is as follows:
- Kn < 10-3: for continuum flow
- 10-3 <Kn <10-1: for slip flow
- 10-1 <Kn <10+1: for transition flow
- 10+1 <Kn: for free molecular flow
In the above study, the regime of slip flow 10-3 <Kn < 10-1 is chosen and adjusted to extend the model of Darcy-Brinkman-Forchheimer for the power-law fluid for describing the porous medium flow behavior.
Convection in Noncircular and Circular Microchannels
Convection in the non-circular and circular microchannels has been successfully solved for years. In such studies, the temperature jump and velocity slip effects at the viscous dissipation and wall were considered. Temperature jump and velocity slip came up with opposite heat transfer effects, which was the key consequence. Velocity slip leans towards the increase of Nusselt number, but it experiences reduction due to temperature jump. Viscous heating inclusion increases the number of Nusselt for the needed cooling of fluid and decreasing it to acquire the heating of the fluid.
Laminar-forced Newtonian Fluid Flow Convection
To solve the laminar-forced Newtonian flow of fluid convection in porous channel flow plate microchannels with the porous medium there was a use of analytical and numerical means for years. In such studies, the influence of Knudsen number, Forchheimer number, Reynolds number, and Darcy number on temperature jump and velocity slip was considered at a wall. The primary results suggested an increase in the friction of skin by:
- Decrease of Knudsen number
- Increase in Darcy number
- Decrease in Forchheimer number
On the other hand, heat transfer had different consequences. There was a decrease in heat transfer with the decrease in Forchheimer and Knudsen numbers and there was an increase when there was an increase in the Darcy and Reynolds numbers.
An Important Numerical and Theoretical Analysis
Recently, an investigation took place regarding a numerical and theoretical analysis of forced, fully-developed convection in the porous channel with a porous channel power-law fluid. A closed shape layer of boundary solutions with an integral technique was gained for temperature fields, velocity profiles, and Nusselt number. We can use theoretical solutions for predicting the basic physical phenomena characteristic linked with non-Newtonian fluids’ forced convection in the porous media. Such solutions were useful for use as a standard for more complex numerical solutions. Consequently, we came to know that the power-law index effects, non-Darcy regime, and the behavior of heat transfer within the porous channel flow plate are significant. However, the Darcy number effects were predominant in the regime of Darcy.
According to researchers, there is an increase in Nusselt number in the non-Darcy regime. Likewise, a decrease in pressure drop whenever there is a decrease in the index of power-law. As a result, the combined utilization of the highly absorptive porous with shear retreating liquid appeared as promising like the augmentation technique of heat transfer. However, a small portion of data on relevant literature about the power-law fluids’ heat transfer and flow fluids through the porous microchannels. The study concluded that the forced fluid and heat flow convection of power-law moves through the microchannels with the porous media.
Also, the objective of the recent research is to study the outcomes of Darcy number, inertia parameter, and the Knudsen number on the thermal and hydrodynamic power-law fluid flow behavior between the substantially lengthy microchannels (parallel-plates) with the porous media.
Final Words
The recent numerical solutions for the steady, forced laminar convection flow among parallel-plate microchannels with power-law fluid-saturated and porous medium are conducted. In addition, the results show that in a higher permeability regime, the outcomes of the power-law index and Knudsen number on the heat transfer and flow in porous medium microchannels are substantial. However, if the permeability regime is low, the Darcy number effects become even evident. If the permeability is higher, the number of Nusselt and friction of skin decreases and the power-law index and Knudsen number increases.
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