Abstract
This paper theoretically analyzes the heat transfer characteristics associated with electroosmotic flow of blood through a micro-vessel having permeable walls. The analysis is based on the Debye–Hückel approximation for charge distributions and the Navier–Stokes equations are assumed to represent the flow field in a rotating system. The velocity slip condition at the vessel walls is taken into account. The essential features of the rotating electroosmotic flow of blood and associated heat transfer characteristics through a micro-vessel are clearly highlighted by the variation in the non-dimensional flow velocity, volumetric flow rate and non-dimensional temperature profiles. Moreover, the effect of Joule heating parameter and Prandtl number on the thermal transport characteristics are discussed thoroughly. The study reveals that the flow of blood is appreciably influenced by the elctroosmotic parameter as well as rotating Reynolds number.
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Abbreviations
- \((u^{\prime},\,v^{\prime})\) :
-
Velocity components in \(x^{\prime}\) and \(y^{\prime}\) directions recpectively
- \(T^{\prime}\) :
-
Temperature of blood
- \(T_0\) :
-
Lower wall temperature
- \(T_w\) :
-
Upper wall temperature
- \(\Omega\) :
-
Angular velocity in \(y^{\prime}\) direction
- \(v_0\) :
-
Scale of suction/injection velocity
- h :
-
Half-width of micro-vessel
- \(\mu\) :
-
Dynamic viscosity of blood
- \(\nu\) :
-
Kinematic viscosity of blood
- \(\rho\) :
-
Density of blood
- \(\rho _e\) :
-
EDL charge density
- \(\sigma\) :
-
Electrical conductivity
- \(\epsilon\) :
-
Dielectric constant of blood
- \(\lambda _D\) :
-
Debye length
- \(\alpha\) :
-
Ionic energy parameter
- g :
-
Acceleration due to gravity
- \(c_p\) :
-
Specific heat at constant pressure
- k :
-
Electro-osmotic parameter
- S :
-
Suction/injection parameter
- \(\lambda\) :
-
Buoyancy parameter
- Pr :
-
Prandtl number
- \(\gamma 1\) :
-
Joule heating parameter
- \(\beta 1\) :
-
Slip parameter
- Re :
-
Reynolds number
- \(\omega\) :
-
Rotating Reynolds number
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Acknowledgments
The authors wish to convey their sincere thanks to all the esteemed reviewers for their comments and suggestions based upon which the present version of the manuscript has been revised. One of the authors (A. Mondal) is sincerely thankful to UGC, New Delhi, while the other authors are greatly acknowledge to SERB, Department of Science and Technology (DST), New Delhi, for the financial support of this investigation.
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Sinha, A., Mondal, A., Shit, G.C. et al. Effect of heat transfer on rotating electroosmotic flow through a micro-vessel: haemodynamical applications. Heat Mass Transfer 52, 1549–1557 (2016). https://doi.org/10.1007/s00231-015-1673-5
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DOI: https://doi.org/10.1007/s00231-015-1673-5