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Research Papers

Role of Heating Location on the Performance of a Natural Convection Driven Melting Process Inside a Square-Shaped Thermal Energy Storage System

[+] Author and Article Information
Ojas Satbhai

Mechanical Engineering,
IIT Kharagpur,
Kharagpur 721302, India
e-mail: satbhaiojas@gmail.com

Subhransu Roy

Mechanical Engineering,
IIT Kharagpur,
Kharagpur 721302, India

Sudipto Ghosh

Metallurgical and Materials Engineering,
IIT Kharagpur,
Kharagpur 721302, India

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received October 25, 2017; final manuscript received June 3, 2018; published online August 20, 2018. Assoc. Editor: Steve Q. Cai.

J. Thermal Sci. Eng. Appl 10(6), 061007 (Aug 20, 2018) (12 pages) Paper No: TSEA-17-1410; doi: 10.1115/1.4040655 History: Received October 25, 2017; Revised June 03, 2018

In this work, numerical experiments were performed to compare the heat transfer and thermodynamic performance of melting process inside the square-shaped thermal energy storage system with three different heating configurations: an isothermal heating from left side-wall or bottom-wall or top-wall and with three adiabatic walls. The hot wall is maintained at a temperature higher than the melting temperature of the phase change material (PCM), while all other walls are perfectly insulated. The transient numerical simulations were performed for melting Gallium (a low Prandtl number Pr = 0.0216, low Stefan number, Ste = 0.014, PCM with high latent heat to density ratio) at moderate Rayleigh number (Ra ≊ 105). The transient numerical simulations consist of solving coupled continuity, momentum, and energy equation in the unstructured formulation using the PISO algorithm. In this work, the fixed grid, a source-based enthalpy-porosity approach has been adopted. The heat transfer performance of the melting process was analyzed by studying the time evolution of global fluid fraction, Nusselt number at the hot wall, and volume-averaged normalized flow-kinetic-energy. The thermodynamic performance was analyzed by calculating the local volumetric entropy generation rates and absolute entropy generation considering both irreversibilities due to the finite temperature gradient and viscous dissipation. The bottom-heating configuration yielded the maximum Nusselt number but has a slightly higher total change in entropy generation compared to other heating configurations.

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Figures

Grahic Jump Location
Fig. 2

Time evolution of Nusselt number at the hot wall for Ra = 7.15 × 104 and Ra = 7.15 × 107. The continuous line shows the present numerical results, and the square symbols show the calculated results from the correlation proposed by Gobin and Bernard [38].

Grahic Jump Location
Fig. 1

Schematic diagram of a energy storage device for melting the phase change material inside a square cavity. ((a)–(c)) show three different simulated cases with three adiabatic walls and isothermal heating from side-wall, bottom-wall and top-wall, respectively. The solid line depicts the position of solid–liquid interface at different instants. The hot and cold plumes are shown by the upward and downward pointing arrows, respectively. (a) Hot plate located at the side-wall, (b) hot plate located at the bottom-wall, and (c) hot plate located at the top-wall.

Grahic Jump Location
Fig. 3

The contour plots of nondimensional temperature overlapped with the velocity vectors for case-LH, case-BH, and case-TH are shown in the first, second, and third row, respectively, at different nondimensional time-steps (3≤Fo≤15). The scale bar shows the nondimensional temperature θ=(T−Tm)/(Th−Tm). Note that the solid black line in all the subfigures denotes the solid–liquid interface. (k) Fo = 3, (l) Fo = 6, (m) Fo = 9, (n) Fo = 12, and (o) Fo = 15.

Grahic Jump Location
Fig. 4

The contour plots of the magnitude of the nondimensional velocity overlaid with the streamlines for case-LH, case-BH, and case-TH are shown in the first, second and third row, respectively, at different nondimensional time-steps (3≤Fo≤15). The scale bar shows the magnitude of velocity normalized by the diffusion speed (u0 = αth/h, where αth is the thermal diffusivity). Note that the solid black line in all the subfigures denotes the solid–liquid interface. (f) Fo = 3, (g) Fo = 6, (h) Fo = 9, (i) Fo = 12, and (j) Fo = 15.

Grahic Jump Location
Fig. 5

Melting dynamics inside the square box heated for case-LH (left-side heated cavity), case-BH (bottom-side heated cavity), case-TH (top-side heated cavity) in the left, middle, and right position, respectively. (a) Time evolution of the interface position and (b) variation of nondimensional temperature (θ = (T − Tm)/(Th − Tm)) along the center-line of the box normal to the hot-wall at different dimensionless time (Fo).

Grahic Jump Location
Fig. 6

Variation of nondimensional velocity in x and y direction (Ux=ux/Uo, Uy=uy/Uo) along the midline of cavity (normal to the heating wall) at different dimensionless time (Fo), where uo is the conduction speed. (a) For left-side heated cavity (case-LH) and (b) for bottom heated cavity (case-BH).

Grahic Jump Location
Fig. 7

Evolution of global system properties during the transient melting process for case-LH (left-side heated cavity), case-BH (bottom-side heated cavity), and case-TH (top-side heated cavity). (a) Growth of global fluid fraction during the transient melting, (b) time evolution of Nusselt number at hot wall Nuh. The inset shows the Nuh versus Fo in linear scale and the main figure shows the respective variation on logarithmic scale, (c) time evolution of the total energy content in TH solid phase Qs, and (d) time evolution of the total energy content in the liquid phase Ql.

Grahic Jump Location
Fig. 8

Plot of volume averaged squared velocities Ux2 versus t, Uy2 versus t UT2 versus t and normalized with the speed of thermal diffusion (U0=αth/h), where Ux2(t)=(1/V)∮V(ux/Uo)2dV, Uy2(t)=(1/V)∮V(uy/Uo)2dV and normalized total kinetic energy UT2(t)=Ux2(t)+Uy2(t). (a) Side heated (case-LH) and (b) bottom heated (case-BH).

Grahic Jump Location
Fig. 9

Volume averaged Bejan number versus dimensionless time Fo

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Fig. 10

Rate of entropy generation per unit time and volume Sgen‴ (in W/m3/K) versus the dimensionless time Fo for the three cases: left-side heating (LH), bottom heating (BH), and top heating (TH). (a) Sgen‴ versus the dimensionless time Fo and (b) Sgen‴ versus time t in seconds.

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