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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 (dcyl = 6 mm and lcyl = 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.

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Abbreviations

A :

Heat transfer area for heat exchanger (mm2)

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 (mm3)

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)

PBHE :

Packed Bed Heat Exchanger

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Acknowledgements

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

Author information

Author notes

  1. Surfarazhussain S. Halkarni

    Present address: Department of Mechanical Engineering, School of Engineering & Applied Sciences, SRM University Amaravati, Guntur, Andhra Pradesh, 522502, India

Authors and Affiliations

  1. Fluid Mechanics and Fluid Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400 076, India

    Surfarazhussain S. Halkarni, Arunkumar Sridharan & S. V. Prabhu

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  1. Surfarazhussain S. Halkarni
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  3. S. V. Prabhu
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Correspondence to S. V. Prabhu.

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Appendices

*Appendix 1

Relations used to calculate for the case of constant pumping power analogy are:

Average performance ratio (Nua/ Nuc) is a factor used to estimate the amount of augmentation in heat transfer (Nua) due to packing in comparison to the case without any packing. It is also popularly known as Constant pumping power analogy. If the value (Nua/ Nuc) is above 1 then it is economically feasible for operation.

Packed bed friction factor: \( {f}_{Eisfeld}=\left(\frac{190}{\left(\frac{R{e}_p}{1-\varepsilon}\right)}{A}_w^2+\frac{A_w}{B_w}\right)\frac{1-\varepsilon }{\varepsilon^3} \)

Comparable friction factor: \( f=2\times \left(\frac{D}{d_p}\right)\times {f}_{Eisfeld} \)

Equivalent Reynolds number (Reo): \( {\operatorname{Re}}_o={\left(\frac{f{\operatorname{Re}}^3}{0.3164}\right)}^{1/2.75} \)

Smooth pipe friction factor (fo): fo = [1.58 ln (Reo) − 3.28]−2

Packed bed Nusselt number to comparable form: \( N{u}_a= Nu\left(\frac{D}{d_p}\right)=\frac{h_w{d}_p}{k_f}\left(\frac{D}{d_p}\right) \)

Nusselt number based on Constant pumping power analogy (Gnieleinski correlation):

$$ N{u}_c=\frac{h_wD}{k_f}=\frac{\frac{f_o}{2}\left({\operatorname{Re}}_o-1000\right)\Pr }{1+\left\{12.7{\left(\frac{f_o}{2}\right)}^{1/2}\left[{\Pr}^{2/3}-1\right]\right\}} $$

Relations used to calculate for the case of same Reynolds number analogy are:

The other comparative basis is the Same Reynolds number analogy (Nua/Nus;f/fs). Under this analogy the enhancement in heat transfer (Average Nusselt number ratio = Nua/ Nus) and ratio of friction factors (f / fs) are compared for tubes with and without packing.

Packed bed friction factor: \( {f}_{Eisfeld}=\left(\frac{190}{\left(\frac{R{e}_p}{1-\varepsilon}\right)}{A}_w^2+\frac{A_w}{B_w}\right)\frac{1-\varepsilon }{\varepsilon^3} \)

Comparable friction factor: \( f=2\times \left(\frac{D}{d_p}\right)\times {f}_{Eisfeld} \)

Smooth pipe friction factor correlation (fs): fs = [1.58 ln (Re) − 3.28]−2

Packed bed Nusselt number to comparable form: \( N{u}_a= Nu\left(\frac{D}{d_p}\right)=\frac{h_w{d}_p}{k_f}\left(\frac{D}{d_p}\right) \)

Nusselt number based on Same Reynolds number analogy (Gnieleinski correlation):

$$ N{u}_s=\frac{h_wD}{k_f}=\frac{\frac{f_s}{2}\left(\operatorname{Re}-1000\right)\Pr }{1+\left\{12.7{\left(\frac{f_s}{2}\right)}^{1/2}\left[{\Pr}^{2/3}-1\right]\right\}} $$

Appendix 2

Heat loss calculations

The heat loss to surroundings from the external walls of test section is possible through natural convection and radiation. The inlet fluid temperature (Tfi), exit fluid temperature (Tfo), outer wall temperature of test sect ion (Two), surrounding ambient air temperature (Tamb) and mass flow rate of flowing fluid are measured. The heat loss by natural convection is calculated assuming value of convective heat transfer coefficient to be 10 (Wm−2 K−1) for surrounding air of the test section as per standardized norm.

$$ {Q}_{convection}=h\kern0.36em \left(\pi {D}_o{L}_h\right)\kern0.24em \left({T}_{wo}-{T}_{amb}\right) $$

For the case of lowest flow rate

\( \overset{.}{m} \) = 19.8 gs−1and packing with 6 mm particles; h = 10 Wm−2 K−1, Do = 14 mm, Lh = 500 mm, Outer wall temperature (Two) = 75.84 °C, ambient air temperature surrounding test section (Tamb) = 28.03 °C.

$$ {Q}_{convection}=10\kern0.36em \left(\uppi \times 0.014\times 0.5\right)\kern0.24em \left(75.84\kern0.6em -\kern0.36em 28.03\kern0.36em \right)=10.51\kern0.24em W $$

The heat loss by radiation is calculated using Stefan- Boltzmann law given by:

$$ {\displaystyle \begin{array}{l}{Q}_{radiation}=\sigma \kern0.36em \left({\uppi \mathrm{D}}_{\mathrm{o}}{\mathrm{L}}_{\mathrm{h}}\right)\;\upvarepsilon \kern0.24em \left[{\left({\mathrm{T}}_{\mathrm{wo}}+273\right)}^4-{\left({\mathrm{T}}_{\mathrm{amb}}+273\right)}^4\right]\\ {}\begin{array}{l}{Q}_{radiation}=5.66\times {10}^{-8}\kern0.36em \left(\uppi \times 0.014\times 0.5\right)\;0.88\kern0.24em \left[{\left(75.84+273\right)}^4-{\left(28.03+273\right)}^4\right]\\ {}{Q}_{radiation}=7.22\kern0.24em W\end{array}\end{array}} $$

Hence the total heat loss to the surroundings is:

$$ {\displaystyle \begin{array}{l}{Q}_{loss}={Q}_{convection}+{Q}_{radiation}\\ {}{Q}_{loss}=10.51+7.22=17.7\kern0.24em W\end{array}} $$

Total heat input to system of packed bed is given by:

$$ {\displaystyle \begin{array}{l}{Q}_{total}=\overset{.}{m}\;{C}_{pf}\left({T}_{fo}-{T}_{fi}\right)\\ {}{Q}_{total}=0.0198\times 4181\left(75.84-28.08\right)=3953.75\;W\end{array}} $$

For the case of highest flow rate

\( \overset{.}{m} \) = 44 gs−1 and packing with 6 mm particles; h = 10 Wm−2 K−1, Do = 14 mm, Lh = 500 mm, Outer wall temperature (Two) = 52.43 °C, ambient air temperature surrounding test section (Tamb) = 27.85 °C.

$$ {\displaystyle \begin{array}{l}{Q}_{convection}=10\kern0.36em \left(\uppi \times 0.014\times 0.5\right)\kern0.24em \left(52.43-27.85\right)=5.4\kern0.24em \mathrm{W}\\ {}\begin{array}{l}{Q}_{radiation}=5.66\times {10}^{-8}\kern0.36em \left(\pi \times 0.014\times 0.5\right)\;0.88\kern0.24em \left[{\left(52.43+273\right)}^4-{\left(27.85+273\right)}^4\right]\\ {}{Q}_{radiation}=3.31\kern0.24em W\end{array}\end{array}} $$

Hence the total heat loss to the surroundings is:

$$ {\displaystyle \begin{array}{l}{Q}_{loss}={Q}_{convection}+{Q}_{radiation}\\ {}{Q}_{loss}=5.4+3.31=8.71\kern0.24em W\end{array}} $$

Total heat input to system of packed bed:

$$ {Q}_{total}=0.044\times 4179.3\kern0.24em \left(52.43-27.85\right)=4519.9\kern0.24em W $$

Hence the percentage of heat loss to surroundings is 0.46% and 0.19% and similar approach is followed for all particle size packing and higher flow rate. Table 9 shows the calculations of heat loss to surroundings for all packing sizes and range of highest and lowest flow rates. It is evident that the amount of heat loss occurring with surrounding is less than 1%.

Table 9 Percentage of heat loss from the test section to surroundings in packed bed
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Table 10 Summary of measured variables in present work
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Halkarni, S.S., Sridharan, A. & Prabhu, S.V. 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. Heat Mass Transfer 55, 2305–2328 (2019). https://doi.org/10.1007/s00231-019-02569-2

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