Heat and Mass Transfer in a Viscous Nanofluid Containing a Gyrotactic Micro-Organism Over a Stretching Cylinder
Abstract
:1. Introduction
2. Governing Equations
3. Spectral Relaxation Method and Comparison
- By using the velocity equation can transformed in terms of .
- Supposing that are familiar since past iterations (symbolized by ) form an iteration scheme for by supposing that only linear terms in are to be calculated at the present iteration level (indicated by ) and all dissimilar expressions are supposed to be familiar from the past iteration. Further, nonlinear terms in are calculated at the past iteration.
4. Discussions
5. Conclusions
- enhance the temperature field ;
- decreases the velocity profile ;
- reduce the temperature field ;
- The wall thickness of the motile microorganism is a declining function of ;
- The density of the motile microorganism is an enhancing function of ;
- regulate the concentration profile;
- The concentration field increases with the rise of and decreases with the increase of .
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Radius of the cylinder | |
Magnetic field of strength | |
Concentration | |
Skin friction coefficient | |
Concentration at the surface | |
Concentration in the free stream | |
Specific heat at constant pressure | |
Brownian diffusion coefficient | |
Diffusivity of the microorganism | |
Thermophoresis coefficient | |
Eckert number | |
Bioconvection Lewis number | |
Lewis number | |
Characteristic length. | |
Magnetic field parameter | |
Brownian motion parameter | |
Thermophoresis parameter | |
Density number of the motile microorganism | |
Local Nusselt number | |
Density of the motile microorganism | |
Constant motile microorganism | |
Peclet number | |
Prandtl number | |
Surface motile microorganism flux. | |
Surface mass flux | |
Surface heat flux | |
Reynolds number | |
Local Sherwood number | |
Indicates the temperature | |
Constant temperature | |
Velocity parts along directions | |
Constant | |
Axial route having velocity | |
Constant maximum cell swimming speed | |
Velocity parts along directions | |
Greek letters | |
Bioconvection parameter | |
Electrical conductivity | |
Thermal diffusivity | |
Effective heat capacitance | |
Kinematic viscosity | |
Curvature parameter | |
Surface shear stress |
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Pr | Present Study | Khan and Pop [34] | Wang [35] | Elbashbeshy et al. [39] |
---|---|---|---|---|
0.2 | 0.16911012 | 0.1691 | 0.1697 | 0.1690886 |
0.7 | 0.45391616 | 0.4539 | 0.4539 | 0.4539161 |
2 | 0.91135768 | 0.9114 | 0.9114 | 0.9113577 |
7 | 1.89540305 | 1.8954 | 1.8954 | 1.8954033 |
20 | 3.35390414 | 3.3539 | 3.3539 | 3.3539042 |
70 | 6.46218077 | 6.4622 | 6.4622 | 6.4621996 |
0.5 1 2 3 | 1 | 5 | 0.3 | 0.5 | 0.2 | 5 | 0.2 | 0.2 | 0.01 | 1.62649308 1.82111645 2.17941349 2.51241569 | 2.42810268 2.67528648 3.03778670 3.23014786 | 0.85568261 0.81591240 0.79123180 0.83834565 | 0.77721513 0.91919885 1.17739872 1.43491309 |
1 | 0 1 2 | 0.71 | 0.5 | 0.5 | 0.1 | 5 | 0.5 | 0.2 | 0.2 | 1.35577051 2.82111645 2.15890400 | 1.08610352 0.71283719 0.32331590 | 1.71241497 1.63058296 1.59635412 | 1.34116551 1.28080156 1.25335316 |
1 | 1 | 0.71 1 5 7 | 0.5 | 0.5 | 0.2 | 5 | 0.5 | 0.2 | 0.1 | 1.82111645 1.82111645 1.82111645 1.82111645 | 0.99942787 1.08600254 1.12591585 0.87986583 | 1.39642364 1.37153874 1.40748237 1.51248713 | 1.12678471 1.13654847 1.52920649 1.77773396 |
1 | 1 | 0.71 | 0.3 0.5 0.7 | 0.5 | 0.1 | 5 | 0.5 | 0.2 | 0.2 | 1.82111645 1.82111645 1.82111645 | 0.71283719 0.71283719 0.71283719 | 1.63058296 1.63058296 1.63058296 | 1.19404622 1.28080156 1.35483099 |
0.5 | 1 | 0.71 | 0.5 | 0.25 0.5 1.2 | 0.2 | 5 | 0.5 | 0.2 | 0.1 | 1.62649308 1.62649308 1.62649308 | 0.40047131 0.62834887 1.18153356 | 1.39670138 1.43755939 1.47036457 | 0.97004499 0.98733892 0.99954647 |
0.5 | 1 | 0.71 | 0.3 | 0.5 | 0.2 0.5 1.2 | 5 | 0.5 | 0.2 | 0.1 | 1.62649308 1.62649308 1.62649308 | 0.81885213 0.72661881 0.55314537 | 1.37025917 1.07378725 0.63142889 | 0.87739871 0.73600200 0.49242417 |
1 | 1 | 0.71 | 0.5 | 0.5 | 0.1 | 1 1.5 2 5 | 0.5 | 0.2 | 0.2 | 1.82111645 1.82111645 1.82111645 1.82111645 | 0.71283719 0.71283719 0.71283719 0.71283719 | 0.67841111 0.81415772 0.94753387 1.63058296 | 0.64189010 0.73312212 0.81755282 1.19404622 |
1 | 1 | 5 | 0.5 | 0.5 | 0.1 | 5 | 0.5 0.6 0.7 | 0.2 | 0.1 | 1.82111645 1.82111645 1.82111645 | 1.67403063 1.67403063 1.67403063 | 1.47926112 1.47926112 1.47926112 | 1.55544165 1.63930009 1.7210218 |
1 | 1 | 0.71 | 0.5 | 0.5 | 0.1 | 5 | 0.5 | 0.2 0.4 0.6 | 0.2 | 1.82111645 1.82111645 1.82111645 | 1.04300428 1.04300428 1.04300428 | 1.56883842 1.56883842 1.56883842 | 1.23920758 1.49489645 1.69489645 |
1 | 1 | 6.17 | 0.5 | 0.5 | 0.2 | 5 | 0.5 | 0.2 | 0.01 0.1 0.2 | 1.82111645 1.82111645 1.82111645 | 2.80350693 0.99256106 0.53315880 | 0.77232258 1.46526840 1.64145133 | 1.19996973 1.67326495 1.79135562 |
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Ferdows, M.; Reddy, M.G.; Alzahrani, F.; Sun, S. Heat and Mass Transfer in a Viscous Nanofluid Containing a Gyrotactic Micro-Organism Over a Stretching Cylinder. Symmetry 2019, 11, 1131. https://doi.org/10.3390/sym11091131
Ferdows M, Reddy MG, Alzahrani F, Sun S. Heat and Mass Transfer in a Viscous Nanofluid Containing a Gyrotactic Micro-Organism Over a Stretching Cylinder. Symmetry. 2019; 11(9):1131. https://doi.org/10.3390/sym11091131
Chicago/Turabian StyleFerdows, Mohammad, M. Gnaneswara Reddy, Faris Alzahrani, and Shuyu Sun. 2019. "Heat and Mass Transfer in a Viscous Nanofluid Containing a Gyrotactic Micro-Organism Over a Stretching Cylinder" Symmetry 11, no. 9: 1131. https://doi.org/10.3390/sym11091131