# Forced convection performance of a MEPCM suspension through an iso-flux heated circular tube: an experimental study

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## Abstract

The paper examines experimentally forced convection performance of a microencapsulated phase change material (MEPCM) suspension through an iso-flux heated circular tube. Forced convection experiments have been undertaken using the pure water or MEPCM suspensions as the working fluid. The heat transfer performance of the MEPCM suspension was gauged in terms of local/average heat transfer coefficients and temperature control effectiveness along the tube wall compared with that obtained for the pure water.

## Keywords

Nusselt Number Wall Temperature Phase Change Material Heat Transfer Enhancement Local Heat Transfer## List of symbols

*c*_{p}Specific heat, (J kg

^{−1}K^{−1})*c*_{p,eff}Effective specific heat, (J kg

^{−1}K^{−1})- \( c_{p,\,mf}^{*} \)
Specific heat ratio, \( c_{p,\,m} /c_{p,\,f} \)

- \( d_{i}^{ + } \)
Inner diameter of tube, (m)

- \( d_{o}^{ + } \)
Outer diameter of tube, (m)

- \( d_{p}^{ + } \)
diameter of MEPCM particle, (m)

*f*Darcy friction factor, \( - \Updelta p(d_{i}^{ + } /l^{ + } )/(\rho_{f} u_{b}^{ + 2} /2) \)

*h*Heat transfer coefficient, (W m

^{−2}K^{−1})*h*_{ls}Latent heat of fusion, (J kg

^{−1})- I
Electric current, (A)

*k*Thermal conductivity, (W m

^{−1}K^{−1})- \( l_{d}^{ + } \)
Length of downstream section, (m)

- \( l_{h}^{ + } \)
Length of heated section, (m)

- \( l_{u}^{ + } \)
Length of upstream section, (m)

*Nu*Nusselt number

- Δ
*p* Pressure drop, (Pa)

*Pe*_{f}Peclet number based on base fluid properties, \( u_{b}^{ + } d_{i}^{ + } /\alpha_{f} \)

*Pe*_{m}Peclet number on suspension properties, \( u_{b}^{ + } d_{i}^{ + } /\alpha_{m} \)

*Q*Volumetric flow rate, (cm

^{3}min^{−1})*q*Heat input, (W)

- \( q^{\prime \prime } \)
Heat flux, (W m

^{−2})- \( r^{ + } \)
Radial coordinate, (m)

- \( r_{i}^{ + } \)
Inner radius of tube, (m)

- \( r_{o}^{ + } \)
Outer radius of tube, (m)

*Re*_{f}Reynolds number based on base fluid properties, \( \rho_{f} u_{b}^{ + } d_{i}^{ + } /\mu_{f} \)

- \( Sb_{in,\,m}^{*} \)
Inlet subcooling factor based on suspension properties, (

*T*_{ M }−*T*_{ in })/Δ*T*_{ ref,m }- \( Ste_{m}^{*} \)
Modified Stefan number based on suspension properties, \( c_{p,\,m} \Updelta T_{ref,\,m} /h_{ls} \)

- \( t_{w}^{ + } \)
Tube wall thickness, (m)

*T*Temperature, (K)

*T*_{M}Melting temperature of phase change material

*T*_{mean}Mean temperature, (K)

- \( \Updelta T_{ref,\,f} \)
Reference temperature difference, (K), \( q_{i}^{\prime \prime } r_{i}^{ + } /k_{f} \)

- \( \Updelta T_{ref,\,m} \)
Reference temperature difference, (K), \( q_{i}^{\prime \prime } r_{i}^{ + } /k_{m} \)

- \( u_{b}^{ + } \)
Bulk fluid velocity, (m s

^{−1})*V*Electric voltage, (Volt)

*x*^{+}Axial coordinates, (m)

## Greek symbols

- α
Thermal diffusivity, (m

^{2}s^{−1})- ε
_{h} Local heat transfer effectiveness,

*h*_{ m }*/h*_{ f }- \( \varepsilon_{{\bar{h}}} \)
Average heat transfer effectiveness, \( \bar{h}_{m} /\bar{h}_{f} \)

- \( \varepsilon_{{\theta_{w} }} \)
Effectiveness of wall temperature suppression

- θ
Dimensionless temperature, \( (T - T_{in} )/\Updelta T_{ref,\,f} \)

- μ
Dynamic viscosity, (kg m

^{−1}s^{−1})- ρ
Density, (kg m

^{−3})- ϕ
Volume fraction

- ω
Mass fraction

## Subscripts

*b*Bulk quantities

*d*Downstream

*eff*Effective quantities

*f*Base fluid

*h*Heated section

*i*Inner surface of tube

*in*Inlet

*m*Suspension

*o*Outer surface of tube

*out*Outlet

*p*MEPCM particle

*pcm*Phase change material

*u*Upstream

*w*Tube wall

## Superscripts

- +
Dimensional quantities

## Notes

### Acknowledgments

The present study was supported by National Science Council (NSC) of ROC in Taiwan under Project Nos. NSC94-2212-E006-101 and NSC95-2212-E006-233.

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