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Effects of axial temperature gradient on momentum and heat transfer with oscillating pressure and flow

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Abstract

Effects of axial temperature gradient on heat transfer, momentum transfer and energy conversion mechanisms within a closed cylinder-piston apparatus are analyzed. Assuming that the gas density change is small, the first-order and steady second-order solutions of continuity, momentum and energy equations are obtained. The solutions show that there exists a steady circulating flow and the magnitude of the steady axial velocity increases as the axial temperature gradient increases. There exists not only an oscillating component of heat flux between the gas and the wall, but also a steady component whose direction depends on axial temperature gradient. It is shown that heat is pumped from the wall near the piston to the wall near closed-end for negative axial temperature gradient. Heat transfer relation for both oscillating pressure and oscillating flow conditions is proposed.

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Abbreviations

a 0 :

Speed of\( = \sqrt {\gamma RT} \)

C p :

Specific heat for constant pressure

H :

Half the distance between the parallel plates (Fig. 1)

i :

Imaginary unit\( = \sqrt { - 1} \)

k :

Thermal conductivity

L :

Mean distance between the closed end and the piston (Fig. 1)

Ma :

Mach number\( = \omega s/\sqrt {\gamma RT_m } \)

Nu c :

Complex Nusselt number

p :

Pressure

Pr :

Prandtl number=ν/α

q s :

Steady heat flux from the gas to the wall

R :

Gas constant

ℜ:

Real part of a complex variable or number

s :

Amplitude of piston motion

T :

Temperature

T bulk :

Bulk temperature of gas

t :

Time

u :

Velocity component parallel to the wall

v :

Velocity component perpendicular to the wall

x, y :

Cartesian coordinates (Fig. 1)

α:

Thermal diffusivity=k/ρC p

β:

Parameter defined in Eq. (24)

γ:

Specific heat ratio

ζ:

Parameter defined in Eq. (40)

η:

Dimensionless distance from the wall defined in Eq. (29)

λr :

Parameter defined in Eq. (25)

λi :

Parameter defined in Eq. (26)

μ:

Shear viscosity

ν:

Kinematic viscosity=μ/ρ

ρ:

Density

τ:

Period of a cycle

ω:

Angular frequency, Vorticity

0:

Zeroth-order value or variable, mean variable

1:

First-order value or variable

2:

Second-order value or variable

i :

Imaginary part of a complex number or variable

m :

Mean value defined atT m

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  1. Department of Mechanical Engineering, Hong-Ik University, 72-1 Sangsudong, Mapo-ku, 121-791, Seoul, Korea

    Eun Soo Jeong

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Jeong, E.S. Effects of axial temperature gradient on momentum and heat transfer with oscillating pressure and flow. KSME Journal 9, 225–239 (1995). https://doi.org/10.1007/BF02953623

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  • DOI: https://doi.org/10.1007/BF02953623

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