Heat transfer enhancement in permeable tubes subjected to transverse suction flow is investigated in this work. Both momentum and energy equations are solved analytically and numerically. Both solutions based on negligible entry regions are well matched. Two different suction velocity distributions are considered. A parametric study including the influence of the average suction velocity and the suction velocity profile is conducted for various Peclet numbers. It is found that enhancement of heat transfer over that in impermeable tubes is only possible with large Peclet numbers. This enhancement increases as suction velocities towards the tube outlet increase and as those towards the tube inlet decrease simultaneously. The identified enhancement mechanisms are expanding the entry regions, increasing the transverse advection, and increasing the downstream excess temperatures under same transverse advection. The average suction velocity that produces maximum enhancement increases as the Peclet number increases until it reaches asymptotically its uppermost value at large Peclet numbers. The maximum reported enhancement ratios for the exponential and linear suction velocity distributions are 17.62-fold and 14.67-fold above those for impermeable tubes, respectively. This work demonstrates that significant heat transfer enhancement is attainable when the suction flow inside the permeable tubes is distributed properly.

The study of fluid flow and heat transfer inside permeable tubes or channels exposed to surface suction is important to many industrial applications. These applications include transpiration cooling where channel surfaces are cooled by passing cooled fluid through the pores of these surfaces, controlling boundary layers over surfaces of airplane wings or turbine blades by injection or suction of fluid at theses surfaces, lubrication of permeable bearings, fluid filtration processes, cooling of combustion chambers exhaust ports, and cooling of porous walled reactors [

Bergles [

Among initial works that analyzed the problem of fluid flow and heat transfer inside permeable tubes or channels with surface suction are the works of Kinney [

Promoting flow close to the energy exchanging boundary usually results in heat transfer enhancement [

In the next sections, flow and heat transfer inside a preamble tube subjected to internal suction flow are modelled and analyzed. The surface suction velocity is considered to have either linear or exponential profile distributions. Both momentum and thermal energy transfer equations are solved using various analytical and numerical methods. Different heat transfer enhancement indicators are computed. Both analytical and numerical computations of these indicators are validated under an applicable constraint and using early studies. An extensive parametric study has been conducted in order to identify and explore the influence of average suction velocity, suction velocity profile, and Peclet number on the heat transfer enhancement indicators.

Consider a tube of length

(a) 3D view of the tube with suction passages embedded on its material volume, (b) cross section of the tube, and (c) schematic profile of the tube and the coordinates system.

The mass flow rate

The Nusselt number at the tube inner boundary is defined as

For this case, the dimensionless suction velocity denoted by

For this case, the dimensionless suction velocity denoted by

Substituting (

The ideal case of the present problem is constructed when the fluid is subjected to perfect slip condition at the solid boundary. For this ideal case, the conservation of mass and the continuity equation reveal the following expressions:

Let the heat transfer enhancement indicator

The second performance indicator

For uniform suction case, the mean velocity inside the tube can be found using (

Effects of

Effects of

Effects of

Equations (

The results of the present work are shown in Figures

Effects of

Effects of

Effects of

Effects of

Effects of

Effects of

Effects of

Effects of

Effects of

Effects of

As suction velocity

The Nusselt number for perfect fluid slip at the solid boundary (

Figure

When

For large

Figure

For the upper

For large

Figure

Flow and heat transfer in permeable tubes subjected to transverse suction flow were analyzed in this work. The continuity, momentum, and energy equations of the internal fluid were solved analytically and numerically. The numerical and the analytical results based on negligible combined entry regions were well matched. Two different suction velocity distributions were considered. They are the linear and exponential distributions. The influence of the average suction velocity, the suction velocity profile, and the Peclet number on the heat transfer enhancement indicators was studied. It was found that heat transfer enhancement over that in impermeable tubes is only attainable if large Peclet numbers are encountered. This enhancement is further increased as suction velocities towards the tube outlet increase and as those towards the tube inlet decrease simultaneously. The enhancement mechanisms were identified and they are expanding the entry regions, increasing the transverse advection, and increasing the downstream excess temperatures under same transverse advection. The maximum reported enhancement ratios in this work are 17.62-fold and 14.67-fold above those for impermeable tubes for the exponential and linear suction velocity distributions, respectively. The average suction velocity that maximizes the heat transfer enhancement indicator increases as the Peclet number increases until it reaches asymptotically its uppermost value at large Peclet numbers. Finally, this work reveals that significant heat transfer enhancement is attainable when the suction flow inside the permeable tube is managed properly.

Aspect ratio (

Controlling parameter for suction flow with linear profile; (

Controlling parameter for suction flow with exponential profile; (

Fluid specific heat (J/kgK)

Tube inner diameter (m)

Convection heat transfer coefficient (W/m^{2}K)

Fluid thermal conductivity (W/m·K)

Tube length (m)

Mass flow rate at given section; (

Mass flow rate at inlet section; (kg/s)

Nusselt number (

Reference Peclet number (

Fluid Prandtl number

(Inlet, outlet) fluid pressures (N/m^{2})

Dimensionless fluid pressure (N/m^{2})

Constant heat flux applied at the tube inner boundary (W/m^{2})

Reference Reynolds number (

(Dimensional, dimensionless) radial distance (

Fluid temperature field (K)

Inlet fluid temperature (K)

Fluid mean bulk temperature field (K)

Tube inner boundary temperature (K)

(Dimensional, dimensionless) axial velocity field (

Axial velocity field under perfect slip condition (m/s)

Dimensionless axial velocity field under perfect slip condition (

Reference axial velocity; (

(Dimensional, dimensionless) transverse velocity (

(Dimensional, dimensionless) local suction velocity (m/s)

(Dimensional, dimensionless) average suction velocity (m/s)

Dimensional and dimensionless axial distances (

Second heat transfer enhancement indicator; (

First heat transfer enhancement indicator; (

Fluid dynamic viscosity (Ns/m^{2})

Dimensionless temperature field; (

Dimensionless temperature field under perfect slip condition; (

Dimensionless mean bulk temperature; (

Tube dimensionless inner boundary temperature; (

Fluid density (kg/m^{3}).

Average value of the quantity

Fully developed value of the quantity

Quantity under perfect slip flow at the solid boundary.

The author declares that there is no conflict of interests regarding the publication of this paper.

This paper was funded by the Deanship of Scientific research (DSR), King Abdulaziz University, Jeddah. The author, therefore, acknowledges with thanks DSR technical and financial support.