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Analysis of transient temperature response under micro jet impinging using nitrogen (N2)

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Abstract

We studied the transient local surface temperature response that occurs when jet impinging of nitrogen gas is applied to the surface to which a pulsating heat flux is applied. After manufacturing a micro jet impinging device, which was composed of three parts—a silicon wafer, a vinyl sticker, and a Pyrex wafer—nitrogen gas was used as working fluid and the velocity was 344.8 m/s, corresponding jet Reynolds was 1467. And the amplitudes of heat fluxes varied from 5.67 to 16.17 W/cm2, the frequency also varied from 0.1 to 1000 Hz, then temperature response of RTDs was acquired. For example, when a heat flux, 8.5 W/cm2, was applied with a frequency of 0.1 Hz, the highest and lowest temperatures of RTD located on the center of the heater and under indirect jets were 30.2 °C and 20.7 °C. From the acquired results, the time constant of the device was estimated between 17 ms and 32 ms, and this result shows the conjugated mode of conduction and convection of heat transfer. To understand the dominant heat transfer, we decoupled the conduction mode and the convective heat transfer mode through analytical calculations and confirmed that the time constants were 11 µs and 128 ms, respectively. In addition, the heat transfer coefficient was inversely calculated through numerical calculation by simulating the RTD manufactured in the device, and through this, it was confirmed that the dimensionless time constant was related to the Nu number and the correlation was developed as τ/t = 3.51Nu−1.067 for f ≤ 1 Hz.

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Abbreviations

d :

Diameter of the jet’s outlet

E :

Energy in control volume (J/kg)

f :

Frequency, Hz

h :

Enthalpy, J/kg

k :

Thermal conductivity in Eq.(5), W/m·K

k :

Specific heat ratio in Eqs. (1) and (2), cp/cv

L :

Distance from the stagnation point to fully developed

l :

Distance from the stagnation point

m :

Mass, kg

ṁ :

Mass flow rate, kg/s

Nu :

Nusselt number

P :

Pressure, Pa

Pr :

Prandtl number

Q :

Heat, J

q″ :

Heat flux, W/cm2

R :

Gas constant, J/(kg·K)

Re :

Reynolds number

T :

Temperature, K

t :

Time, s

V :

Volume, m3

v :

Velocity, m/s

α :

Thermal diffusivity, m2/s

c p :

Specific heat for constant pressure, J/kg·K

c v :

Specific heat for constant volume, J/kg·K

δ :

Boundary layer thickness, m

ΔP :

Pressure drop, Pa

ΔT :

Temperature difference, K

ρ :

Density, kg/m3

τ :

Time constant, s

v :

Kinematic viscosity, m2/s

bi :

Boundary inlet

bo :

Boundary outlet

conv :

Convection

H :

Highest

i :

Inlet of jet

L :

Lowest

m :

Mean

max-min:

Between maximum and minimum

o :

Outlet of jet

st :

Stagnation

T :

Zthermal

∞ :

Ambient

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Acknowledgment

This work was supported by the Hongik University new faculty research support fund.

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Authors and Affiliations

  1. Department of Mechanical and System Design Engineering, Hongik University, 94 Wausan-ro, Mapo-gu, Seoul, 04066, Korea

    Jeong-Heon Shin

  2. Department of Mechanical and Design Engineering, Hongik University, 2639 Sejong-ro, Jochiwon-eup, Sejong, 30016, Korea

    Jaehyun Kim

Authors
  1. Jeong-Heon Shin
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  2. Jaehyun Kim
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Correspondence to Jeong-Heon Shin.

Additional information

Jeong-Heon Shin is currently an Assistant Professor at the Department of Mechanical and System Design Engineering, Hongik University. He received his Ph.D. in Mechanical Engineering from University of Texas, Austin. His research interest fields are heat and fluid flow in nano, micro channels included in the manufactured heat exchangers and reactors.

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Shin, JH., Kim, J. Analysis of transient temperature response under micro jet impinging using nitrogen (N2). J Mech Sci Technol 35, 3713–3722 (2021). https://doi.org/10.1007/s12206-021-0740-8

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  • DOI: https://doi.org/10.1007/s12206-021-0740-8

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