Cooling capacity of magnetic nanofluid in presence of magnetic field based on first and second laws of thermodynamics analysis

ABSTRACT

In this numerical study, the cooling capacity of water/Cu magnetic nanofluids in a horizontal duct exposed to a magnetic field has been investigated. Both the first and second laws of thermodynamics analysis are conducted. All simulations have been performed for the volume fraction of 5%, Reynolds number (Re) of 100, and the Hartmann numbers (Ha) of 0, 20, 50, and 80. Temperature, velocity profiles, Nusselt number (Nu), Lorentz force (F), and thermal, frictional, and magnetic irreversibility have been studied by changing Ha. The received results indicate that as the Ha increases, the hydrodynamic boundary layer thickness decreases, while the length of the hydrodynamic entrance length increases. In addition, as the Ha increases in the range of 0 to 80, the local Nu number increases by about 7.5%, and the local wall temperature drops to 2.7%. The second law of thermodynamic analysis showed that as the Ha increases, the frictional irreversibility augments, while the thermal irreversibility decreases. Finally, the order of thermal irreversibility is larger than that of frictional and magnetic irreversibility.

KEYWORDS:

• Magnetic nanofluid
• magnetic field
• numerical investigation
• first and second laws of thermodynamics
• heat transfer

List of Symbols

$\mathrm{B}$	=	$\mathrm{M}\mathrm{a}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{T}\right]$
${\mathrm{C}}_{\mathrm{p}}$	=	$\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{J}/\mathrm{k}\mathrm{g}\mathrm{K}\right]$
$\mathrm{D}$	=	$\mathrm{D}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{l}\left[\mathrm{m}\right]$
${\mathrm{D}}_{\mathrm{e}}$	=	$\mathrm{H}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{u}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\left[\mathrm{m}\right]$
$\mathrm{E}$	=	$\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{V}/\mathrm{m}\right]$
$\mathrm{F}$	=	$\mathrm{L}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{z}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}\left[\mathrm{N}\right]$
$\mathrm{H}$	=	$\mathrm{m}\mathrm{a}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}\left[\mathrm{A}/\mathrm{m}\right]$
$\mathrm{J}$	=	$\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{A}/{\mathrm{m}}^2\right]$
$\mathrm{k}$	=	$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{W}/\mathrm{m}\mathrm{K}\right]$
${\mathrm{L}}_{\mathrm{h}}$	=	$\mathrm{H}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{y}\mathrm{n}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\left[\mathrm{m}\right]$
$\mathrm{P}$	=	$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\left[\mathrm{P}\mathrm{a}\right]$
q„	=	$\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}\left[\mathrm{W}/{\mathrm{m}}^2\mathrm{K}\right]$
$\mathrm{r}$	=	$\mathrm{R}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}[\mathrm{m}]$
${\dot{\mathrm{S}}}_{\mathrm{g}\mathrm{e}\mathrm{n}}^{{ }^{\prime \prime \prime }}$	=	$\mathrm{E}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}[\mathrm{W}/{\mathrm{m}}^3\mathrm{K}]$
$\mathrm{T}$	=	$\mathrm{T}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\left[\mathrm{K}\right]$
$\mathrm{u}$	=	$\mathrm{V}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{m}/\mathrm{s}\right]$

Greek symbols
$\mu$	=	Dynamic Viscosity [kg m ∙ s]
${\mu }_{\mathrm{r}}$	=	$\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{a}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{t}$
$\rho$	=	$\mathrm{D}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{k}\mathrm{g}/{\mathrm{m}}^3\right]$
$\sigma$	=	$\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}\left[1/\mathrm{\Omega }\mathrm{m}\right]$
$\phi$	=	$\mathrm{V}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$

Declaration of competing interest

None.

Additional information

Notes on contributors

Maryam Dinarvand

Maryam Dinarvand obtained her BSc degree in Chemical Engineering from Jundi Shapur University of Technology in 2009 and her Master from Amirkabir University of Technology (Tehran Polytechnic) in 2012.  She is PhD student in Semnan University since 2016. Her research interest is in Computation Fluid Dynamics (CFD) modeling, nanofluid, and heat transfer.

Mahdieh Abolhasani

Mahdieh Abolhasani received her BSC degree in Chemical Engineering from Sharif University of Technology in 2004 and her Master and PhD degrees in Chemical Engineering from Razi University in 2007 and 2013, respectively. She is Assistant Professor at the Faculty of Chemical, Petroleum and Gas Engineering in Semnan University, Iran, since 2013. Dr. Abolhasani's research interest is in process intensification, rotating packed bed reactors, carbon dioxide capture, Computation Fluid Dynamics (CFD) Modeling, and heat transfer. She has over 40 technical publications, including 12 international refereed journal papers and has 179 citations since 2009.

Faramarz Hormozi

Faramarz Hormozi received his BSc and MSc degrees in Chemical Engineering from University of Tehran in 1992 and 1995, respectively, and his PhD degree in Chemical Engineering from Amirkabir University of Technology (Tehran Polytechnic) in 2001. Now, he is Professor at the Faculty of Chemical, Petroleum and Gas Engineering in Semnan University, Iran. Prof. Hormozi's research interest is in Transport Phenomena (Heat transfer), Computation Fluid Dynamics (CFD) Modeling, nanofluid rheology and heat transfer, boiling heat transfer, hydrogen production and purification. He has over 96 international refereed journal papers, and has over 3160 citations since 2001.

Zohreh Bahrami

Zohreh Bahrami obtained her BS degree in Pure Chemistry from Alzahra University in 2004 and her MS degree in Inorganic Chemistry from Kharazmi University in 2007 and her PhD degree in Inorganic Nanomaterials from University of Tehran in 2014. She is Assistant Professor at the Faculty of Nanotechnology in Semnan University, Iran, since 2014. Dr. Bahrami's research interests include synthesis of nanomaterials, magnetic nanostructures,  nanocarriers and drug delivery, nanocatalyst, and nanofluids. She has over 30 publications, including 15 international refereed journal papers and has 231 citations since 2007.