# Local wall heat transfer coefficient measurement in a packed bed of cylinders using infrared (IR) thermography technique and application of random packing of cylindrical particles inside concentric tube heat exchangers with water as working medium

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## Abstract

Heat transfer enhancement is challenging area in which different techniques are utilized to dissipate the generated heat during operation. Packed beds are devices which enhance heat transport while being compact and are used in several applications such as energy storage, heat exchange devices, catalysis, food processing etc. In the present study, the behavior of wall heat transfer coefficient with randomized packing of equal aspect ratio cylinders is investigated. In this work, the local wall heat transfer coefficient is calculated from local wall temperature data obtained using infrared (IR) thermography in packed beds with randomized packing of cylinders under steady state conditions with water as the working fluid. The randomized packing of cylinders is done inside a concentric tube heat exchanger and the heat transfer enhancement is studied. Experiments are conducted for bed to equivalent particle diameter ratio 2 using random packing of mono-dispersed glass cylinders (*d*_{cyl} = 6 mm and *l*_{cyl} = 6 mm). The local wall temperatures are measured using an infrared (IR) camera while the fluid flow takes place through the packed beds. In literature, it is found that wall region contribution to heat transfer is above 90%. The comparison of enhancement in heat transfer for both packing of spheres and cylinders inside concentric tube heat exchangers is done and it is observed that the random sphere packing is superior to cylinder packing.

## Keywords

Wall heat transfer coefficient Void fraction Packed bed of cylinders packed bed of spheres Infrared (IR) thermography## Nomenclature

## Symbol

*A*Heat transfer area for heat exchanger (

*mm*^{2})*C*_{pf}Specific heat capacity of fluid (

*Jkg*^{−1}*K*^{−1})*D*Bed diameter or Inner diameter of tube (

*mm*)*D*_{i}Inner diameter of annular side pipe (

*mm*)*D*_{a}Annulus diameter (

*mm*)*d*_{eq.p}Equivalent particle diameter (

*mm*)*d*_{h}Annulus hydraulic diameter (

*mm*)*d*_{p}Particle diameter (

*mm*)*d*_{cyl}Diameter of cylinder (

*mm*)*f*Comparable friction factor (

*dimensionless*)*f*_{s}Friction factor for open smooth pipe (

*dimensionless*)*l*_{cyl}Length of cylinder (

*mm*)*h*_{w}Wall heat transfer coefficient (

*W m*^{−2}*K*^{−1})*h*_{i}Inner side wall heat transfer coefficient (Tube side) (

*W m*^{−2}*K*^{−1})*h*_{o}Outer side wall heat transfer coefficient (Annular side) (

*W m*^{−2}*K*^{−1})*k*_{f}Thermal conductivity of fluid (

*W m*^{−1}*K*^{−1})*k*_{pipe}Thermal conductivity of tube wall (

*W m*^{−1}*K*^{−1})*k*_{s}Thermal conductivity of solid (

*W m*^{−1}*K*^{−1})*L*Length of packed bed (

*mm*)*L*_{h}Heating length (

*mm*)*ṁ*Mass flow rate (

*kg s*^{−1})*ṁ*_{h}Mass flow rate of hot fluid (

*kg s*^{−1})*ṁ*_{c}Mass flow rate of cold fluid (

*kg s*^{−1})*Nu*_{a}Nusselt number with augmentation (

*dimensionless*)*Nu*_{c}Nusselt number for the case of constant pumping power (

*dimensionless*)*Nu*_{s}Nusselt number for the case of same Reynolds number (Gnieleinski’s correlation) (

*dimensionless*)*Nu*_{w}Nusselt number at wall based on particle diameter, \( \frac{h_w{d}_p}{k_f} \) (

*dimensionless*)*Nu*_{i}Nusselt number on inner side (heat exchangers) (

*dimensionless*)*Nu*_{o}Nusselt number on outer side (heat exchangers) (

*dimensionless*)*Nu*_{h}Nusselt number based on hydraulic diameter for annular side packing (

*dimensionless*)- \( {q}_w^{{\prime\prime} } \)
Heat flux (

*W m*^{−2})- \( {\overset{.}{q}}_w \)
Heat generation per unit volume (

*W m*^{−3})*Re*Reynolds number based on bed diameter, \( \frac{\rho\;U\;D}{\mu } \) (

*dimensionless*)*Re*_{p}Reynolds number based on particle diameter, \( \frac{\rho\;U\;{d}_p}{\mu } \) (

*dimensionless*)*Re*_{a}Reynolds number based on annulus diameter, \( \frac{\rho\;{V}_c\;{D}_a}{\mu } \) (

*dimensionless*)*Re*_{h}Reynolds number based on hydraulic diameter, \( \frac{\rho\;{V}_c\;{d}_e}{\mu } \) (

*dimensionless*)*Re*_{o}Equivalent Reynolds number (defined in Appendix 1) (

*dimensionless*)*S*_{B}Particle surface area per unit volume of packed bed (

*m*^{−1})*T*_{amb}Ambient fluid temperature (surrounding air of test section) (°C)

*T*_{bf}Bulk fluid temperature (°C)

*T*_{fi}Inlet fluid temperature (upstream test section) (°C)

*T*_{fo}Exit fluid temperature (downstream test section) (°C)

*T*_{m}Mixing cup fluid temperature (measuring tank) (°C)

*T*_{wo}Outer wall temperature (test section) (°C)

*T*_{wi}Inner wall temperature (test section) (°C)

*T*_{hi}Inlet fluid temperature in hot line (PBHE) (°C)

*T*_{ho}Exit fluid temperature in hot line (PBHE) (°C)

*T*_{ci}Inlet fluid temperature in cold line (PBHE) (°C)

*T*_{co}Exit fluid temperature in cold line (PBHE) (°C)

*∆T*_{lm}Logarithmic mean temperature difference (PBHE) (°C)

*U*Superficial velocity (based on bed cross-sectional area) (

*m s*^{−1})*U*_{pbhe}Overall heat transfer coefficient for packed bed heat exchanger (PBHE) (

*W m*^{−2}*K*^{−1}*)**V*_{h}Hot fluid velocity (PBHE) (

*m s*^{−1})*V*_{c}Cold fluid velocity (PBHE) (

*m s*^{−1})*V*_{void}Interstitial volume of packed bed (

*mm*^{3})

## Greek symbols

*ε*Void fraction (mean) (

*dimensionless*)*ε*_{paint}Emissivity of paint used for infrared thermography (

*dimensionless*)*ε*_{t}Void fraction (mean) tube side (

*dimensionless*)*ε*_{a}Void fraction (mean) annular side (

*dimensionless*)*μ*Dynamic Viscosity (

*Pa. s*)*ρ*Density (

*kg m*^{−3})

## Abbreviation

*PBHE*Packed Bed Heat Exchanger

## Notes

### Acknowledgements

Authors would like to thank Mr. Rahul Shirsat for his assistance in building the experimental setup.

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