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Research Papers: Conduction

# Analysis of Microheat Pipes With Axial Conduction in the Solid Wall

[+] Author and Article Information
Yew Mun Hung1

Faculty of Engineering and Technology, Multimedia University, 75450 Melaka, Malaysiahung.yew.mun@eng.monash.edu.my

Kek-Kiong Tio

Faculty of Engineering and Technology, Multimedia University, 75450 Melaka, Malaysiakktio@mmu.edu.my

1

Present address: School of Engineering, Monash University, 46150 Bandar Sunway, Malaysia.

J. Heat Transfer 132(7), 071301 (Apr 22, 2010) (11 pages) doi:10.1115/1.4000947 History: Received November 14, 2008; Revised December 11, 2009; Published April 22, 2010; Online April 22, 2010

## Abstract

A one-dimensional, steady-state model of a triangular microheat pipe (MHP) is developed, with the main purpose of investigating the thermal effects of the solid wall on the heat transport capacity of an MHP. The energy equation of the solid wall is solved analytically to obtain the axial temperature distribution, the average of which over the entire length of the MHP is simply its operating temperature. Next, the liquid phase is coupled with the solid wall by a heat transfer coefficient. Then, the continuity, momentum, and energy equations of the liquid and vapor phases are, together with the Young–Laplace equation, solved numerically to yield the heat and fluid flow characteristics of the MHP. The heat transport capacity and the associated optimal charge level of the working fluid are predicted for different operating conditions. Comparison between the models with and without a solid wall reveals that the presence of the solid wall induces a change in the phase change heat transport by the working fluid, besides facilitating axial heat conduction in the solid wall. The analysis also highlights the effects of the thickness and thermal conductivity of the solid wall on its axial temperature distribution. Finally, while the contribution of the thermal effects of the solid wall on the heat transport capacity of the MHP is usually not dominant, it is, nevertheless, not negligible either.

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## Figures

Figure 1

A schematic diagram of an inclined microheat pipe, β being its angle of inclination

Figure 2

Schematic infinitesimal control volumes for the derivation of governing equations. (a) Energy equation for conduction in the solid wall. (b) Momentum equations for liquid and vapor flows. (c) Energy equation for evaporation in the liquid domain.

Figure 3

Heat transport capacity Q̇cap of a copper MHP as a function of the operating temperature Top for different values of contact angle. Experimental data from Ref. 14 are included.

Figure 4

Optimal charge level M̂opt corresponding to the heat transport capacity Q̇cap of Fig. 3, as a function of the operating temperature Top for different values of contact angle

Figure 5

Heat transport capacity Q̇cap of a copper MHP as a function of contact angle θ, the operating temperature Top being a parameter

Figure 6

Relative difference between Q̇cap and Q̇cap∗, δ, as a function of the operating temperature Top of a copper MHP, the solid wall thicknesses ts being a parameter

Figure 7

Fractional errors contributed by axial solid conduction δ̃c and change in phase change heat transport δ̃p for a copper MHP as a function of the operating temperature Top, the solid wall thickness ts being a parameter

Figure 8

Relative difference between Q̇cap and Q̇cap∗, δ, as a function of the operating temperature Top of an MHP with a solid wall thicknesses of ts=0.14 mm and three different solid wall materials: copper, nickel, and monel

Figure 9

Fractional errors contributed by axial solid conduction δ̃c and change in phase change heat transport δ̃p as a function of the solid wall thickness of MHPs of different solid materials. The MHPs are optimally charged for and operated at 60°C.

Figure 10

Absolute rate of axial conduction in the solid wall Q̇c and the absolute rate of heat transport by phase change Q̇p as a function of the solid wall thickness of the MHPs of Fig. 9

Figure 11

Axial solid wall temperature profiles of MHPs of a solid wall thickness of ts=0.14 mm and made of three different materials: copper, nickel, and monel. The MHPs are optimally charged and operated at 60°C.

Figure 12

Axial solid wall temperature profiles of monel MHPs of different values of solid wall thickness, all optimally charged for and operated at 60°C

Figure 13

A map of the relation governing the rate of heat transport Q̇, the operating temperature Top, and the temperatures at the evaporator and condenser ends, T0 and T1, of a copper MHP optimally charged for 60°C. The parallel lines of positive slope are lines of constant heat transport rate; those of negative slope are lines of constant operating temperature.

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