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A numerical analysis of transpiration cooling as an air cooling mechanism

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Abstract

The present study is focused on investigation of heat transfer from a porous plate by cooling of air with transpiration cooling. Effects of Reynolds number of hot gas stream, inlet temperature of air and mass flow rate of water on local wall temperature and cooling effectiveness of porous flat plate and efficiency of the system inside a rectangular channel with air as a hot gas stream and water as a coolant were investigated numerically. Increasing Reynolds number causes an increase on surface temperature and a decrease on cooling effectiveness of porous plate and efficiency of the system. Increasing of air inlet temperature does not cause a significant increase on cooling efficiency of the system. An increase of water flow rate causes a decrease on surface temperature and an increase on effectiveness of porous plate and cooling efficiency of the system. Numerical results prepared by RNG k-ε turbulence model have a good approximation and show a similar flow characteristic with experimental results.

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Abbreviations

A:

Surface area of porous plate, m2

B m :

Mass transfer driving force, \( {B}_m=\frac{m_{ev}-{m}_s}{m_s-1} \)

B h :

Heat transfer blowing parameter, \( {B}_h=\frac{{\overset{\cdot }{m}}_{ev}. Cp}{hc^{\ast }} \)

F:

Blowing ratio, \( F=\frac{q_c.{V}_c}{q_{air.{V}_{air}}} \)

Cp :

Specific heat of air, kj/kg.°C

Dh :

Hydraulic diameter of the Channel, mm

H:

Channel Height, mm

h c :

Convective heat transfer coefficient for surface of porous plate, \( {h}_c={h_c}^{\ast }.\frac{B_h}{\exp \left({B}_h\right)-1} \)

hc ∗ :

Heat transfer coefficient with zero-mas-transfer, hc∗ = ρ. Vair. Cp. St∗

h airout :

Outlet enthalpy of air, W.m−2.°C -1

h airin :

Inlet enthalpy of air, W.m−2.°C -1

h surface :

Enthalpy of water at surface, W.m−2.°C -1

h waterin :

Inlet enthalpy of water, W.m−2.°C -1

h waterout :

Outlet enthalpy of water, W.m−2.°C -1

h fg :

Latent heat of water, W.m−2.°C -1

k:

Conduction coefficient, W.m−1.°C -1

keff :

Conduction coefficient of porous medium, W.m−1.°C -1

\( {\overset{\cdot }{m}}_{air} \) :

Mass flow rate of air, kg/s

\( {\overset{\cdot }{m}}_{ev} \) :

Mass flow rate of evaporated water, kg/s

ms :

Mass fraction of water vapor at surface

\( {\overset{\cdot }{m}}_{water} \) :

Mass flow rate of water, kg/s

q ″ :

Heat flux, W.m−2

p:

Pressure, Pa

Pr:

Prandtl number, \( \Pr =\frac{Cp.\mu }{k} \)

Sc:

Schmidt number, \( Sc=\frac{\mu }{\rho .D} \)

St ∗ :

Stanton number with zero porosity, St∗ = 0.0296(Re)−0.2(Pr)−2/3

St ∗ mass :

Mass transfer St number, St∗mass = 0.0296(Re)−0.2(Sc)−2/3

Re:

Reynolds number, Re = Vair. Dh/ν

T:

Surface temperature of porous plate, °C

T’:

Eddy temperature, °C

Tavg :

Mean film temperature, °C

Tsurface :

Average surface temperature of porous plate, °C

Tairin :

Inlet temperature of air, °C

Tairout :

Outlet temperature of air, °C

U:

Fluid velocity, m.s−1

u’:

Fluctuating component of fluid velocity, m.s−1

Vair :

Air velocity, m.s−1

ε :

(Porosity)

g ∗ mass :

Zero mass transfer limit conductance, g∗mass = ρ. Vair. St∗mass

g mass :

Mass transfer conductance, \( {g}_{mass}={g^{\ast}}_{mass}.\frac{\ln \left(1+{B}_m\right)}{B_m} \)

μ :

Dynamic viscosity, kg.m−1.s−1

ν :

Kinematic viscosity, m2.s−1

ρ:

Density, kg.m−3

η :

Cooling effectiveness of porous plate, \( \eta =\frac{T_{surface}-{T}_{airin}}{T_{water}-{T}_{airin}} \)

η sys :

Cooling efficiency of the system, \( {\eta}_{sys}=\frac{T_{airin}-{T}_{airout}}{T_{airin}-{T}_{surface}} \)

Exp.:

Experimental

Eff.:

Effective

In:

Inlet

Num.:

Numerical

Out:

Outlet

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Acknowledgements

The financial support of this study by the Scientific Research Council of Turkey (TUBITAK), with the program of postdoctoral scholarship (2219) and University of California Los Angeles Post Doctorate Program (UCLA/USA) at Boiling Heat Transfer Laboratory is gratefully acknowledged.

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  1. Department of Mechanical Engineering, Adana Science and Technology University, Yeşiloba Yerleşkesi Yeşiloba Mah, Öğretmenler Bulvarı 46278 Sokak No:3, 01180, Seyhan, Adana, Turkey

    Mustafa Kilic

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Kilic, M. A numerical analysis of transpiration cooling as an air cooling mechanism. Heat Mass Transfer 54, 3647–3662 (2018). https://doi.org/10.1007/s00231-018-2391-6

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