Steady Flow of Thermo-Viscous Fluid between Infinitely Stretched Porous Parallel Plates-A Perturbation Technique

Authors

  • Pothanna Nalimela Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India
  • Srinivas Joshi Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India
  • Aparna Podila Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India
  • Padmaja Podila Department of Mathematics, Prasad V Potluri Siddhartha Institute of Technology, Vijayawada, AP, India
  • Rajashekar Pemmaraju Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India

DOI:

https://doi.org/10.37934/cfdl.17.1.7889

Keywords:

Suction/Injection Parameter, Strain Thermal Conductivity Coefficient, Thermo-mechanical Stress Coefficient

Abstract

The steady flow of a thermo-viscous incompressible fluid bounded between porous parallel plates is examined in this paper. The governing equations of the flow are coupled in the velocity and temperature field. The solutions of velocity and temperature are obtained using a powerful and most elegant method called perturbation technique. The closed form solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain thermal conductivity coefficient and coefficient of cross viscosity. The variations of velocity and temperature distributions on the flow field have been discussed with the help of illustrations. The effect of various flow parameters on the flow field have been discussed with the help of graphs. The rate of variation of the velocity is observed as far less when compare to the temperature of the fluid. This effect is due to the porosity and suction/injection of the flow passes through the horizontal parallel plates. This study includes the applications in extraction of petrol and oils from porous rocks, chemical reactors, and human cardiovascular system and in several engineering devices such as heat and mass exchanges. The results of the present study will hopefully enable a better understanding of nuclear and clinical applications.

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Author Biographies

Pothanna Nalimela, Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India

pothareddy81@gmail.com

Srinivas Joshi, Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India

srinivas_j@vnrvjiet.in

Aparna Podila, Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India

aparnapodila@gmail.com

Padmaja Podila, Department of Mathematics, Prasad V Potluri Siddhartha Institute of Technology, Vijayawada, AP, India

padmajapodila@gmail.com

Rajashekar Pemmaraju, Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, TS, India

rajoct25@gmail.com

References

Koh, S. L., and A. C. Eringen. "On the foundations of non-linear thermo-viscoelasticity." International Journal of Engineering Science 1, no. 2 (1963): 199-229. https://doi.org/10.1016/0020-7225(63)90034-X. DOI: https://doi.org/10.1016/0020-7225(63)90034-X

Langlois, William E. "Steady flow of a slightly viscoelastic fluid between rotating spheres." Quarterly of Applied Mathematics 21, no. 1 (1963): 61-71. https://doi.org/10.1090/qam/145816. DOI: https://doi.org/10.1090/qam/145816

Rivlin, R. S. "The solution of problems in second order elasticity theory." In Collected Papers of RS Rivlin: Volume I and II, pp. 273-301. New York, NY: Springer New York, 1953. https://doi.org/10.1007/978-1-4612-2416-7_20. DOI: https://doi.org/10.1007/978-1-4612-2416-7_20

Yamamoto, Kyoji, and Zen-ichi Yoshida. "Flow through a porous wall with convective acceleration." Journal of the Physical Society of Japan 37, no. 3 (1974): 774-779. https://doi.org/10.1143/JPSJ.37.774. DOI: https://doi.org/10.1143/JPSJ.37.774

Beavers, Gordon S., and Daniel D. Joseph. "Boundary conditions at a naturally permeable wall." Journal of fluid mechanics 30, no. 1 (1967): 197-207. https://doi.org/10.1017/S0022112067001375. DOI: https://doi.org/10.1017/S0022112067001375

Green, Albert Edward, and Paul Mansour Naghdi. "A dynamical theory of interacting continua." International journal of engineering Science 3, no. 2 (1965): 231-241. https://doi.org/10.1016/0020-7225(65)90046-7. DOI: https://doi.org/10.1016/0020-7225(65)90046-7

Coleman, Bernard D., and Victor J. Mizel. "Existence of caloric equations of state in thermodynamics." The Journal of Chemical Physics 40, no. 4 (1964): 1116-1125. https://doi.org/10.1063/1.1725257 DOI: https://doi.org/10.1063/1.1725257

Kelly, P. D. "Some viscometric flows of incompressible thermoviscous fluids." International Journal of Engineering Science 2, no. 5 (1965): 519-533. https://doi.org/10.1016/0020-7225(65)90007-8. DOI: https://doi.org/10.1016/0020-7225(65)90007-8

Pothanna, N., P. Nageswara Rao, and N. Ch Pattabhi Ramacharyulu. "Flow of slightly thermo-viscous fluid in a porous slab bounded between two permeable parallel plates." Int. J. Adv. Appl. Math. and Mech 2, no. 3 (2015): 1-9. https://doi.org/10.7726/jac.2015.1003.

Pothanna, N., Pattabhi Ramacharyulu N. Ch, and P. Nageswara Rao. "Effect of strain thermal conductivity on slightly thermo-viscous fluid in a porous slab bounded between two parallel plates." Journal of Advanced Computing 4, no. 1 (2015): 37-58. https://doi.org/10.7726/jac.2015.1003. DOI: https://doi.org/10.7726/jac.2015.1003

Rao, P. Nageswara, and N. Ch Pattabhiramacharyulu. "Steady flow of a second-order thermo-viscous fluid over an infinite plate." In Proceedings of the Indian Academy of Sciences-Mathematical Sciences, vol. 88, pp. 157-161. Springer India, 1979. https://doi.org/10.1007/BF02871612. DOI: https://doi.org/10.1007/BF02871612

Aparna, Podila, Podila Padmaja, Nalimela Pothanna, and Josyula Venkata Ramana Murthy. "Uniform Flow of Viscous Fluid Past a Porous Sphere Saturated with Micro Polar Fluid." Biointerface Research in Applied Chemistry 13 (2022): 1-12.https://doi.org/10.33263/BRIAC131.069. DOI: https://doi.org/10.33263/BRIAC131.069

Aparna, P., N. Pothanna, JV Ramana Murthy, and K. Sreelatha. "Flow generated by slow steady rotation of a permeable sphere in a micro-polar fluid." Alexandria Engineering Journal 56, no. 4 (2017): 679-685. https://doi.org/10.1016/j.aej.2017.01.018 DOI: https://doi.org/10.1016/j.aej.2017.01.018

Aparna, P., N. Pothanna, and J. V. Ramana Murthy. "Viscous Fluid Flow Past a Permeable Cylinder." In Numerical Heat Transfer and Fluid Flow: Select Proceedings of NHTFF 2018, pp. 285-293. Springer Singapore, 2019. https://doi.org/10.1007/978-981-13-1903-7_33. DOI: https://doi.org/10.1007/978-981-13-1903-7_33

Aparna, P., N. Pothanna, and J. V. R. Murthy. "Rotary Oscillations of a Permeable Sphere in an Incompressible Couple Stress Fluid." In Advances in Fluid Dynamics: Selected Proceedings of ICAFD 2018, pp. 135-146. Singapore: Springer Singapore, 2020. https://doi.org/10.1007/978-981-15-4308-1_10 DOI: https://doi.org/10.1007/978-981-15-4308-1_10

Padmaja, P., P. Aparna, Rama Subba Reddy Gorla, and N. Pothanna. "Numerical solution of singularly perturbed two parameter problems using exponential splines." International Journal of Applied Mechanics and Engineering 26, no. 2 (2021): 160-172. https://doi.org/10.2478/ijame-2021-0025. DOI: https://doi.org/10.2478/ijame-2021-0025

Pothanna, N., Podila Aparna, and Rama Subba Reddy Gorla. "A numerical study of coupled non-linear equations of thermo-viscous fluid flow in cylindrical geometry." International Journal of Applied Mechanics and Engineering 22, no. 4 (2017): 965-979. https://doi.org/10.1515/ijame-2017-0062. DOI: https://doi.org/10.1515/ijame-2017-0062

Pothanna, N., P. Aparna, G. Sireesha, and P. Padmaja. "Analytical and Numerical Study of Steady Flow of Thermo-Viscous Fluid Between Two Horizontal Parallel Plates in Relative Motion." Communications in Mathematics and Applications 13, no. 5 (2022): 1427. https://doi.org/10.26713/cma.v13i5.2254. DOI: https://doi.org/10.26713/cma.v13i5.2254

Bakar, Shahirah Abu, Norihan Md Arifin, and Ioan Pop. "Stability Analysis on Mixed Convection Nanofluid Flow in a Permeable Porous Medium with Radiation and Internal Heat Generation." Journal of Advanced Research in Micro and Nano Engineering 13, no. 1 (2023): 1-17. https://doi.org/10.37934/armne.13.1.117 DOI: https://doi.org/10.37934/armne.13.1.117

Juwari, Afif Deyan Monlei Wicaksono, Tommy Arbianzah, Rendra Panca Anugraha, and Renanto Handogo. "Simulation of Dispersion and Explosion in Petrol Station using 3D Computational Fluid Dynamics FLACS Software." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 109, no. 2 (2023): 113-135. https://doi.org/10.37934/arfmts.109.2.113135 DOI: https://doi.org/10.37934/arfmts.109.2.113135

Benkara-Mostefa, Karima Heguehoug, and Rahima Benchabi-Lanani. "Heat Transfer and Entropy Generation of Turbulent Flow in Corrugated Channel using Nanofluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 109, no. 2 (2023): 136-150. https://doi.org/10.37934/arfmts.109.2.136150 DOI: https://doi.org/10.37934/arfmts.109.2.136150

Parasa, Naga Lakshmi Devi, and Phani Kumar Meduri. "Oscillatory Flow of Couple Stress Fluid Flow over a Contaminated Fluid Sphere with Slip Condition." CFD Letters 15, no. 8 (2023): 148-165. https://doi.org/10.37934/cfdl.15.8.148165 DOI: https://doi.org/10.37934/cfdl.15.8.148165

Khan, Mair, M. Y. Malik, T. Salahuddin, and Arif Hussian. "Heat and mass transfer of Williamson nanofluid flow yield by an inclined Lorentz force over a nonlinear stretching sheet." Results in Physics 8 (2018): 862-868. https://doi.org/10.1016/j.rinp.2018.01.005 DOI: https://doi.org/10.1016/j.rinp.2018.01.005

Khan, Mair, T. Salahuddin, M. Y. Malik, Anum Tanveer, Arif Hussain, and Ali S. Alqahtani. "3-D axisymmetric Carreau nanofluid flow near the Homann stagnation region along with chemical reaction: application Fourier’s and Fick’s laws." Mathematics and Computers in Simulation 170 (2020): 221-235. https://doi.org/10.1016/j.matcom.2019.10.019 DOI: https://doi.org/10.1016/j.matcom.2019.10.019

Khan, Mair, T. Salahuddin, M. Y. Malik, and Farzana Khan. "Change in internal energy of Carreau fluid flow along with Ohmic heating: a Von Karman application." Physica A: Statistical Mechanics and Its Applications 547 (2020): 123440. https://doi.org/10.1016/j.physa.2019.123440 DOI: https://doi.org/10.1016/j.physa.2019.123440

Chu, Yu-Ming, Faris Alzahrani, Obulesu Mopuri, Charankumar Ganteda, M. Ijaz Khan, Sami Ullah Khan, and Sayed M. Eldin. "Thermal impact of hybrid nanofluid due to inclined oscillatory porous surface with thermo-diffusion features." Case Studies in Thermal Engineering42 (2023): 102695. https://doi.org/10.1016/j.csite.2023.102695 DOI: https://doi.org/10.1016/j.csite.2023.102695

Li, Shuguang, M. Ijaz Khan, Adel Bandar Alruqi, Sami Ullah Khan, Sherzod Shukhratovich Abdullaev, Bandar M. Fadhl, and Basim M. Makhdoum. "Entropy optimized flow of Sutterby nanomaterial subject to porous medium: Buongiorno nanofluid model." Heliyon 9, no. 7 (2023). https://doi.org/10.1016/j.heliyon.2023.e17784 DOI: https://doi.org/10.1016/j.heliyon.2023.e17784

Published

2024-08-31

How to Cite

Nalimela, P., Joshi, S., Podila, A., Podila, P., & Pemmaraju, R. (2024). Steady Flow of Thermo-Viscous Fluid between Infinitely Stretched Porous Parallel Plates-A Perturbation Technique . CFD Letters, 17(1), 78–89. https://doi.org/10.37934/cfdl.17.1.7889

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