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Friction and forced convective heat transfer in a sintered porous channel with obstacle blocks

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Abstract

This work experimentally studies the flow characteristics and forced convective heat transfer in a sintered porous channel that filled with sintered copper beads of three average diameters ( \(\overline{{d}} = 0.704,\) 0.830, and 1.163 mm). The pressure drop and the local temperature measurements can be applied to figure out the distributions of the friction coefficient and the heat transfer coefficient. Three sintered porous channels differ in the arrangement of obstacle blocks. Model A has no obstacle. Models B and C have five obstacle blocks facing down and up, respectively, in a sintered porous channel. The range of experimental parameters, porosity, heat flux, and effect of forced convection are 0.370 ≤ ɛ ≤ 0.385, q=0.228, 0.872, 1.862 W/cm2, and 200 ≤ Re d ≤ 800. The permeability and inertia coefficient of each of the three sintered porous channels are analyzed. The results for Model A agree with those obtained by previous investigations in C f distribution. The heat transfer of Model C exceeds that of Model A by approximately 20%. Finally, a series of empirical correlation equations were obtained for practical applications and engineering problems.

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Abbreviations

C f :

friction factor, \(\left(\frac{\Delta {P}}{{L}}\right)\frac{{\overline{{d}} }}{\rho U^{2}}\frac{\varepsilon ^{3} }{(1 - { \varepsilon)}}\)

C n :

heat loss coefficient

D e :

hydraulic diameter for sintered porous channel, m

d :

copper bead diameter, mm

F :

inertia coefficient constant

H :

channel height, m

h :

local heat transfer coefficient, q/(T w − T b), W/m2 K or height of obstacle block, mm

I :

electric current, A

K :

permeability, ɛ 3 d 2/[150(1 − ɛ)2 ], m2

k e :

effective thermal conductivity, W/m K

L :

length of test section, m

N :

number of copper bead

Nu :

Nusselt number, \(\overline{h} {D}_{\rm e}/{k}_{\rm e} \)

n :

number of obstacle blocks

P w :

perimeter of the test section, m

Pr :

Prandtl number

Q :

power input, W

q :

wall heat flux per unit area, W/m2

Re d :

particle Reynolds number, \( \rho \overline{U}d/\mu \)

T :

temperature, °C

u :

volume average velocity, \(\frac{1}{v}\int\limits_{v} U{\rm d}v,\) m/s

V :

voltage, V

v :

volume, m3

X :

axial local position

ℓ:

length of obstacle block, mm

ɛ:

porosity

μ:

viscosity, kg/m s

ν:

kinematic viscosity, m2/s

ρ:

density, kg/m3

ϕ:

amendment porosity, \(\phi = 1 - \frac{{nwh}}{{\ell }}\)

\(\bar{\,} \) :

average value

b:

bulk temperature

F:

fluid

in:

measured position at inlet

loc:

local

loss:

heat loss

out:

measured position at exit

w:

quantity based on the wall

∞:

ambient

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Acknowledgements

The authors would like to thank the National Science Council of Taiwan, Republic of China, for financially supporting this research under Contract No. NSC 92-2622-E-270-003-CC3.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Chiekuo Technology University, No. 1, Chieh Shou N Road, Changhua, 500, Taiwan, ROC

    Sheng-Chung Tzeng & Yen-Chan Wang

  2. Department of Computer Application Engineering, Lanyang Institute of Technology, Ilan, 261, Taiwan, ROC

    Wei-Ping Ma

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  1. Sheng-Chung Tzeng
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Correspondence to Sheng-Chung Tzeng.

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Tzeng, SC., Ma, WP. & Wang, YC. Friction and forced convective heat transfer in a sintered porous channel with obstacle blocks. Heat Mass Transfer 43, 687–697 (2007). https://doi.org/10.1007/s00231-006-0149-z

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