190
J. Prakash et al.
flow rate. Thereafter, Bandopadhyay et al. (2016) improved the Chakraborty’s model
for thick EDL and unsteady peristaltic flow in the presence of electroosmosis. The
authors explained the effects of EDL thickness and Helmholtz–Smoluchowski (HS)
velocity on pumping characteristics and trapping phenomenon. The pumping mechanism can be smoothly controlled using the electroosmosis mechanism. In this direction, many more mathematical models (Goswami et al. 2016; Shit et al. 2016; Tripathi et al. 2017a, b) have been reported to investigate the effects of non-Newtonian
parameters on the electroosmotically induced peristaltic pumping through capillary/microchannel. Furthermore, the effect of heat transfer analysis to understand
the applications in bioenergy systems and bionanofluid dynamics, some mathematical models (Bhatti et al. 2017; Guo and Qi 2017; Prakash et al. 2018a, b; Ranjit and
Shit 2017; Tripathi et al. 2018) are added in literature to analyze the thermal radiation effects, Joule heating, buoyancy effects, and entropy generation on peristaltic
pumping in presence of electric field.
A depth literature review on the electroosmosis modulated peristaltic pumping
enabled us to identify that there is hardly any modeling method on the pseudoplastic
nanofluids flow in presence of electroosmosis. Motivated from the huge applications
of nanofluid dynamics with electroosmosis and peristaltic pumping mechanisms in
bioenergy systems and biotechnologies, this chapter attempts to give an idea on
the development of a mathematical model to investigate the effects of Joule heating parameter and EDL thickness on flow characteristics, pumping characteristics,
thermal characteristics, and trapping. The flow geometry is considered as a vertical asymmetric microchannel which is assumed to be a complex flow geometry.
Assumptions such as Debye–Hückel linearization, low Reynolds number, and large
wavelength are considered in the model. Numerical simulation of the model is using
MATHEMATICA 9 symbolic software. The numerical results are also validated with
the existing analytical results. The findings of this chapter may be extended to design
the bioinspired-smart micro pumps for bioheat transfer and energy transport systems.
The model may also be further developed as a benchmark to work experimentally in
the field of microfluidics device design and development.
4 Mathematical Formulation of the Problem
4.1 Problem Definition
A two-dimensional peristaltic motion of pseudoplastic nanofluid subject to heat flux
through a microfluidic channel with thickness (d 1 + d 2 ) is considered. The movement
is caused by the flow of the sinusoidal peristaltic motion with constant speed c along
with different amplitudes and phase of the microfluidic asymmetric channel walls.
We prefer a rectangular coordinate system for the microfluidic vessel with x along
the centerline in the direction of wave propagation and y is taken normal to it. The
potential electric field is enforced along the microfluidic asymmetric channel, which
J. Prakash et al.
flow rate. Thereafter, Bandopadhyay et al. (2016) improved the Chakraborty’s model
for thick EDL and unsteady peristaltic flow in the presence of electroosmosis. The
authors explained the effects of EDL thickness and Helmholtz–Smoluchowski (HS)
velocity on pumping characteristics and trapping phenomenon. The pumping mechanism can be smoothly controlled using the electroosmosis mechanism. In this direction, many more mathematical models (Goswami et al. 2016; Shit et al. 2016; Tripathi et al. 2017a, b) have been reported to investigate the effects of non-Newtonian
parameters on the electroosmotically induced peristaltic pumping through capillary/microchannel. Furthermore, the effect of heat transfer analysis to understand
the applications in bioenergy systems and bionanofluid dynamics, some mathematical models (Bhatti et al. 2017; Guo and Qi 2017; Prakash et al. 2018a, b; Ranjit and
Shit 2017; Tripathi et al. 2018) are added in literature to analyze the thermal radiation effects, Joule heating, buoyancy effects, and entropy generation on peristaltic
pumping in presence of electric field.
A depth literature review on the electroosmosis modulated peristaltic pumping
enabled us to identify that there is hardly any modeling method on the pseudoplastic
nanofluids flow in presence of electroosmosis. Motivated from the huge applications
of nanofluid dynamics with electroosmosis and peristaltic pumping mechanisms in
bioenergy systems and biotechnologies, this chapter attempts to give an idea on
the development of a mathematical model to investigate the effects of Joule heating parameter and EDL thickness on flow characteristics, pumping characteristics,
thermal characteristics, and trapping. The flow geometry is considered as a vertical asymmetric microchannel which is assumed to be a complex flow geometry.
Assumptions such as Debye–Hückel linearization, low Reynolds number, and large
wavelength are considered in the model. Numerical simulation of the model is using
MATHEMATICA 9 symbolic software. The numerical results are also validated with
the existing analytical results. The findings of this chapter may be extended to design
the bioinspired-smart micro pumps for bioheat transfer and energy transport systems.
The model may also be further developed as a benchmark to work experimentally in
the field of microfluidics device design and development.
4 Mathematical Formulation of the Problem
4.1 Problem Definition
A two-dimensional peristaltic motion of pseudoplastic nanofluid subject to heat flux
through a microfluidic channel with thickness (d 1 + d 2 ) is considered. The movement
is caused by the flow of the sinusoidal peristaltic motion with constant speed c along
with different amplitudes and phase of the microfluidic asymmetric channel walls.
We prefer a rectangular coordinate system for the microfluidic vessel with x along
the centerline in the direction of wave propagation and y is taken normal to it. The
potential electric field is enforced along the microfluidic asymmetric channel, which