Heat and Mass Transfer

, Volume 55, Issue 3, pp 769–790 | Cite as

Comprehensive analysis of melting and solidification of a phase change material in an annulus

  • Rohit KothariEmail author
  • S. K. Sahu
  • S. I. Kundalwal


A one-dimensional conduction heat transfer model has been proposed to study the melting and solidification of phase change material (PCM) inside an annulus. Here, the phase change process is divided into two main sub-processes such as melting and solidification sub-process. Subsequently, each sub-process is analyzed for various temporal regimes. The temporal regimes include completely solid, partially molten and completely molten for melting sub-process and in reverse order for solidification sub-process. Later on, the solution for temperature distribution for each temporal regime is obtained either by employing Variational formulation or using a method of quasi-steady state. The solution of each temporal regime is united to provide a closed form solution for temperature distribution for the sub-process. Present model exhibits good agreement with the existing experimental data. The results indicate that melt duration can be increased by increasing the thickness of PCM in an annulus. It is also found observed that for any thermal storage unit there exists a particular percentage of TCE-PCM distribution through which maximum melt duration can be achieved.


cs, cl

Solid and liquid specific heat, J/kg-K


Outside heat transfer coefficient, W/m2-K

r1, r2

Inner and outer radii of cylinder, m

ks, kl

Solid and liquid thermal conductivity, W/m-K


Latent heat of PCM, J/kg


Heat flux, W/m2


Temperature, 0C


Ambient temperature, 0C


Initial temperature of PCM, 0C


Melting temperature, 0C

Ts, Tl

Solid and liquid temperature, 0C


Tm − T, 0C


Time, s


Thermal penetration time, s


Time for start of melting, s


Time for complete melting, s


Time for complete solidification


Time for start of solidification


Thermal penetration depth, m

R (t)

Melt interface location, m

Bis, Bil

\( \frac{h{r}_2}{k_s},\frac{h{r}_2}{k_s} \) (Biot number)

Stes, Stel

\( \frac{c_s\varDelta T}{L_p},\frac{c_l\varDelta T}{L_p} \)(Stefan’s number)



Greek symbols

αs, αl

Solid and liquid thermal diffusivity, m2/s


\( \frac{r_1}{r_2} \)


\( \frac{r_2}{R(t)} \)


\( \frac{k_s\varDelta T}{q^{\prime \prime }} \), m


\( \frac{k_l\varDelta T}{q^{\prime \prime }} \), m


Density of PCM, kg/m3







Phase change material



The financial support provided by Department of Science and Technology (DST), India under the project grant DST/TMD/MES/2 k17/65 (G) is gratefully acknowledged. The first author acknowledges the financial support by DST, India under DST-INSPIRE Fellowship program (IF170534).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Discipline of Mechanical EngineeringIndian Institute of Technology IndoreIndoreIndia

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