Heat transfer analysis of mixed convection flow in a vertical microchannel with electrokinetic effect
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(2020) 11:29
ORIGINAL PAPER
Heat transfer analysis of mixed convection flow in a vertical microchannel with electrokinetic effect Michael O. Oni1
· Basant K. Jha1
Received: 6 February 2020 / Accepted: 24 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this article, the transient/steady mixed convective flow formation inside a vertical microchannel subjected to uneven wall zeta potentials in the presence of an electric body force is carried out theoretically. Employing the Navier–Stokes, Poisson–Boltzmann and energy equations, the velocity profile, electric potential and temperature distributions respectively governing flow formation and heat transfer in dimensional form are presented. Using appropriate dimensionless parameters, the corresponding dimensionless form of the governing equations are obtained. At the transient state, the Laplace transform technique is utilized while at the steady-state, direct integration as well as undetermined coefficients are employed to obtain solutions to governing equations. To justify solutions obtained, the steady state solution is found and compared with the implicit finite difference method at large time; this comparison gives an excellent agreement. Graphical simulations show that the skin-friction could have incurred an error of up to 19% if the buoyancy term in the momentum equation had been neglected. In addition, it is established that for a large electric double layer, the interval of no reverse flow at the microchannel walls is significantly extended. Keywords Electrokinetics · Streaming potential · Vertical microchannel · Mixed convection · Transient state Mathematics Subject Classification 76W05
List of symbols C0
B
Concentration of ions in bulk fluid
Michael O. Oni [email protected] Basant K. Jha [email protected]
1
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria 0123456789().: V,-vol
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GEM - International Journal on Geomathematics
Ex Ex F g Gr
Dimensional streaming potential Dimensionless streaming potential Faraday’s constant Acceleration due to gravity Grash of number Gr Mixed convection parameter Re G 3 Dimensionless parameter H Spacing between the microchannel p Dimensional pressure P Dimensionless pressure Universal gas constant R Re Reynolds number Dimensional time t t Dimensionless time T Dimensional temperature T 0 Ambient fluid temperature T 1 Temperature at the wall y 0 T 2 Temperature at the wall y H Tˆ Absolute temperature u Axial velocity u 0 Dimensional mean velocity U Dimensionless axial velocity z Valence number of ions in the solution x, y Axial and transverse coordinates respectively X Dimensionless axial coordinate Y Dimensionless transverse coordinate
Greek letters α α β δ δ ε ξ 1, ξ 2 ξ *1 , ξ *2 ξt φ κ λD ψ ψ
Dimensional velocity slip-length Dimensionless velocity slip-length Thermal expansion coefficient Dimensional temperature jump-length Dimensionless temperature jump-length Fluid permittivity Dimensional zeta-potential Dimen
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