Velocity Slip and Entropy Generation Phenomena in Thermal Transport Through Metallic Porous Channel

Mustafa Turkyilmazoglu

doi:10.1515/jnet-2019-0097

Article

Velocity Slip and Entropy Generation Phenomena in Thermal Transport Through Metallic Porous Channel

Mustafa Turkyilmazoglu

Published/Copyright: March 7, 2020

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From the journal Journal of Non-Equilibrium Thermodynamics Volume 45 Issue 3

Abstract

Momentum and thermal transport through open-celled metallic foams filled in a channel of small height is studied in the present technical brief. Fully developed momentum and thermal layers via the Brinkman–Darcy model enable us to obtain closed-form solutions regarding the fluid velocity and temperature distributions of metal and fluid, all depending upon a factor related to the wall slip velocity. A comparative study on the pertinent physical parameters helps us conclude that the wall slip cools the porous channel, enhancing the rate of heat transfer. In addition to this, increasing pore density leads to an effective reduction in the entropy generation number, followed by further reduction with the nonzero slip velocity, except the near-wall regions.

Keywords: metallic porous channel; forced convection; wall slippage; pressure drop; Momentum transfer; thermal transport; entropy generation

Appendix A Physical parameters and fluid properties

The physical parameters, in line with the experimental and theoretical research papers, such as [2], [3], [5], and [7], satisfy the empirical formulas

dp=25410−4ω,df=11810−21−ϵ3π1−Expϵ−1410−2−1dpK=7310−5(1−ϵ)−22410−3dfdp−11110−2dp2,asf=3πdf1−Expϵ−1410−2/59100dp2,e=33910−3,λ=22−58e32−2ϵπ3−42e−e,RA=4λ2e2+πλ(1−e)ks+4−2e2−πλ(1−e)kf,RB=(e−2λ)2(e−2λ)e2ks+2e−4λ−(e−2λ)e2kf,RC=2−2e22πλ21−22eks+22−2e−πλ21−22ekf,RD=2ee2ks+4−e2kf,ke=12(RA+RB+RC+RD),kse=ke|kf=0,kfe=ke|ks=0,d=1−Expϵ−1410−2df,Red=ρfumdμf,Pr=μfCpkf,hsf=7610−2Red4/10Pr37/100kf/d,1≤Red≤40,5210−2Red5/10Pr37/100kf/d,40≤Red≤103,2610−2Red6/10Pr37/100kf/d,103≤Red≤2105

The fluid properties are also

ρf=120510−3,μf=18110−7,kf=25910−4,Cp=1005.

Appendix B Dummy variables

θ1=−3Cs61+L2s2+3Cs41+L−1+Ls2t2+(1+C)2D2−6+s2+L6+Ls4(s−t)(s+t),θ2=3(1+2C)(−1+L)s2+C−3L2s4+CL2s6−−3+6L−3L2s2+C−6+s2+L6+Ls4t2,θ3=s2−DL2+C1+L2−D+s2+L2D+CD−Cs2t2,θ4=−6Cs4t3+D215(1+C)2−24CLs2+4(1+C)2Ls4(s−t)t(s+t),θ5=Ds29+C3(8+5C)−24Ls2+4(1+C)Ls4(s−t)t(s+t),θ6=cosh(s)sinh(s)θ4−θ5−6Ls6D+CD+Ct2tanh(t),θ7=θ6+scosh(s)2tθ1−(1+C)Ds2θ2+3s4θ3tanh(t),θ8=−(1+C)2D29−s2+L6+Ls4(s−t)(s+t),θ9=3Cs4L2s4+(1+L)t2−s21+L2t2,θ10=CL2s6−3(2+3C+2(1+C)L)t2−s4C+3L2+CL2t2,θ11=(1+C)Ds2s2C9+6L+t2+32+L+L2t2+θ10,θ12=s23DL2+C1+3L2D−s2−3L2D+CD−Cs2t2+θ3cosh(2s),θ13=1+C2D2−1+C2Ds2+Cs4(s−t)t(s+t),θ14=t(θ11+θ8+θ9)+tθ1−(1+C)Ds2θ2sinh(s)2.

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Received: 2019-12-05

Revised: 2020-01-07

Accepted: 2020-02-24

Published Online: 2020-03-07

Published in Print: 2020-07-26

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https://doi.org/10.1515/jnet-2019-0097

Keywords for this article

metallic porous channel; forced convection; wall slippage; pressure drop; Momentum transfer; thermal transport; entropy generation