A Mathematical Study on a Steady MHD Flow in Double Stratification Medium
DOI:
https://doi.org/10.37934/cfdl.15.10.3451Keywords:
MHD Boundary layer flow, ; Double stratified medium, Exponential permeability, Ananthaswamy-Sivasankari method (ASM), Modified Homotopy Analysis Method (MHAM)Abstract
The detailed analysis on the flow of MHD fluid in double stratification medium across a stretching sheet with exponential permeability is examined in this research. The approximate analytical solution for the governing equations in steady state is found by using a new approximate analytical method called Ananthaswamy-Sivasankari Method (ASM) and Modified Homotopy Analysis Method (MHAM). The approximate analytical expressions for the dimensionless velocity, dimensionless temperature and dimensionless concentration are derived using these methods. The analytical and numerical results (previous work) are compared and there is a good agreement between our analytical results and numerical works. The impacts of several parameters including porosity, magnetic, suction and heat source parameters are shown in graphical representation. The error table for the physical parameter namely Nusselt number for various values of Prandtl number has been provided. Both ASM and MHAM are very useful to solve some other non-linear boundary value problems especially in MHD fluid flow
References
Sa’adAldin, AbdelLatif, and Naji Qatanani. "Finite element solution of an unsteady MHD flow through porous medium between two parallel flat plates." Journal of Applied Mathematics 2017 (2017). https://doi.org/10.1155/2017/6856470
Acharya, A. K., G. C. Dash, and S. R. Mishra. "Free convective fluctuating MHD flow through porous media past a vertical porous plate with variable temperature and heat source." Physics Research International 2014 (2014). http://dx.doi.org/10.1155/2014/587367
Ali, Mohammad, Md Abdul Alim, and Mohammad Shah Alam. "Heat transfer boundary layer flow past an inclined stretching sheet in the presence of magnetic field." Int. J. Adv. Res. Technol 3, no. 5 (2014): 34-40.
Ananthaswamy, V., C. Sumathi, and M. Subha. "Mathematical Analysis of Variable Viscosity Fluid Flow through a Channel and Homotopy Analysis Method." Int. J. Modern Math. Sci 14, no. 3 (2016): 296-316.
Ananthaswamy, V., M. Subha, and A. Mohamed Fathima. "Approximate Analytical Expressions of Non-Linear Boundary Value problem for a Boundary Layer Flow using the Homotopy Analysis Method." Madridge J Bioinform Syst Biol 1, no. 2 (2019): 34-39. http://dx.doi.org/10.18689/mjbsb-1000107
Barik, R. N., G. C. Dash, and P. K. Rath. "Heat and mass transfer on MHD flow through a porous medium over a stretching surface with heat source." Mathematical Theory and Modeling 2, no. 7 (2012): 49-59.
Chamkha, Ali J., and A. M. Aly. "MHD free convection flow of a nanofluid past a vertical plate in the presence of heat generation or absorption effects." Chemical Engineering Communications 198, no. 3 (2010): 425-441. https://doi.org/10.1080/00986445.2010.520232
Chitra, J., Vembu Ananthaswamy, S. Sivasankari, and Seenith Sivasundaram. "A new approximate analytical method (ASM) for solving non-linear boundary value problem in heat transfer through porous fin." Mathematics in Engineering, Science & Aerospace (MESA) 14, no. 1 (2023).
Choudhary, Mohan Kumar, Santosh Chaudhary, and Ritu Sharma. "Unsteady MHD flow and heat transfer over a stretching permeable surface with suction or injection." Procedia Engineering 127 (2015): 703-710. https://doi.org/10.1016/j.proeng.2015.11.371
Dessie, Hunegnaw, and Naikoti Kishan. "MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink." Ain shams engineering journal 5, no. 3 (2014): 967-977. https://doi.org/10.1016/j.asej.2014.03.008
Goud, B. Shankar, Pudhari Srilatha, P. Bindu, and Y. Hari Krishna. "Radiation effect on MHD boundary layer flow due to an exponentially stretching sheet." Advances in Mathematics: Scientific Journal 9, no. 12 (2020): 10755-10761. https://doi.org/10.37418/amsj.9.12.59
Ibrahim, S. Mohammed. "Heat and mass transfer effects on steady MHD flow over an exponentially stretching surface with viscous dissipation, heat generation and radiation." Journal of Global Research in Mathematical Archives (JGRMA) 1, no. 8 (2013): 67-77.
Ibrahim, S. Mohammed, and K. Suneetha. "Heat source and chemical effects on MHD convection flow embedded in a porous medium with Soret, viscous and Joules dissipation." Ain Shams Engineering Journal 7, no. 2 (2016): 811-818. http://dx.doi.org/10.1016/j.asej.2015.12.008
Liao, Shijun, and Antonio Campo. "Analytic solutions of the temperature distribution in Blasius viscous flow problems." Journal of Fluid Mechanics 453 (2002): 411-425. http://dx.doi.org/10.1017/S0022112001007169
Liao, Shi-Jun. "The proposed homotopy analysis technique for the solution of nonlinear problems." PhD diss., PhD thesis, Shanghai Jiao Tong University, 1992.
Liao, Shi-Jun. "A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate." Journal of Fluid Mechanics 385 (1999): 101-128. http://dx.doi.org/10.1017/S0022112099004292
Liao, Shi-Jun. "An explicit, totally analytic approximate solution for Blasius’ viscous flow problems." International Journal of Non-Linear Mechanics 34, no. 4 (1999): 759-778. https://doi.org/10.1016/S0020-7462(98)00056-0
Liao, Shi-Jun. "An approximate solution technique not depending on small parameters: a special example." International Journal of Non-Linear Mechanics 30, no. 3 (1995): 371-380. https://doi.org/10.1016/0020-7462(94)00054-E
Faudzi, Muhamad Affan Mohd, Ahmad Sukri Abd Aziz, and Zaileha Md Ali. "Heat and mass transfer in magnetohydrodynamics (MHD) flow over an exponentially stretching sheet in a thermally stratified medium." In AIP Conference Proceedings, vol. 1974, no. 1, p. 020007. AIP Publishing LLC, 2018. https://doi.org/10.1063/1.5041538
Mukhopadhyay, Swati. "MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium." Alexandria Engineering Journal 52, no. 3 (2013): 259-265. https://doi.org/10.1016/j.aej.2013.02.003
Mukhopadhyay, Swati, Krishnendu Bhattacharyya, and G. C. Layek. "Mass transfer over an exponentially stretching porous sheet embedded in a stratified medium." Chemical Engineering Communications 201, no. 2 (2014): 272-286. https://doi.org/10.1080/00986445.2013.768236
Nazari, Nur Liyana, Ahmad Sukri Abd Aziz, Vincent Daniel David, and Zaileha Md Ali. "Heat and Mass Transfer of Magnetohydrodynamics (MHD) Boundary Layer Flow using Homotopy Analysis Method." MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics (2018): 189-201. http://dx.doi.org/10.11113/matematika.v34.n3.1150
Ismail, Nur Suhaida Aznidar, Ahmad Sukri Abd Aziz, Mohd Rijal Ilias, and Siti Khuzaimah Soid. "Mhd boundary layer flow in double stratification medium." In Journal of Physics: Conference Series, vol. 1770, no. 1, p. 012045. IOP Publishing, 2021. http://dx.doi.org/10.1088/1742-6596/1770/1/012045.
Reddy, P. Bala Anki. "Magnetohydrodynamic flow of a Casson fluid over an exponentially inclined permeable stretching surface with thermal radiation and chemical reaction." Ain Shams Engineering Journal 7, no. 2 (2016): 593-602. https://doi.org/10.1016/j.asej.2015.12.010
Saidulu, N., and A. Venkata Lakshmi. "Slip effects on MHD flow of Casson fluid over an exponentially stretching sheet in presence of thermal radiation, heat source/sink and chemical reaction." European journal of advances in engineering and technology 3, no. 1 (2016): 47-55.
Zaman, Azmanira Shaharuz, Ahmad Sukri Abd Aziz, and Zaileha Md Ali. "Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction." In Journal of Physics: Conference Series, vol. 890, no. 1, p. 012020. IOP Publishing, 2017. http://dx.doi.org/10.1088/1742-6596/890/1/012020.
Sekhar, K. C. "Boundary layer phenomena of MHD flow and heat and mass transfer over an exponentially stretching sheet embedded in thermally stratified medium." International Journal of Science, Engineering and Technology Research (IJSETR) 3, no. 10 (2014): 2715-2721.
Singh, Khilap, and Manoj Kumar. "The Effect of Chemical Reaction and Double Stratification on MHD Free Convection in a Micropolar Fluid with Heat Generation and Ohmic Heating." Jordan Journal of Mechanical & Industrial Engineering 9, no. 4 (2015).
Sivasankari, S., Vembu Ananthaswamy, and Seenith Sivasundaram. "A new approximate analytical method for solving some non-linear initial value problems in physical sciences." Mathematics in Engineering, Science & Aerospace (MESA) 14, no. 1 (2023).
Swain, I., S. R. Mishra, and H. B. Pattanayak. "Flow over exponentially stretching sheet through porous medium with heat source/sink." Journal of Engineering 2015 (2015). https://doi.org/10.1155/2015/452592.
Yusof, Z. M., A. A. Aziz, S. K. Soid, Z. M. Ali, and S. A. Kechil, (2014). “MHD boundary layer flow due to an exponentially stretching surface embedded in porous medium with radiation effect.” Proceedings of the 10th IMT-GT ICMSA, Kuala Terengganu), 159-169.
Hamrelaine, Salim, Fateh Mebarek-Oudina, and Mohamed Rafik Sari. "Analysis of MHD Jeffery Hamel flow with suction/injection by homotopy analysis method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 58, no. 2 (2019): 173-186.
Mahat, Rahimah, Muhammad Saqib, Imran Ulah, Sharidan Shafie, and Sharena Mohamad Isa. "MHD Mixed Convection of Viscoelastic Nanofluid Flow due to Constant Heat Flux." Journal of Advanced Research in Numerical Heat Transfer 9, no. 1 (2022): 19-25.
Bakar, Fairul Naim Abu, and Siti Khuzaimah Soid. "MHD Stagnation-Point Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Vertical Sheet in a Micropolar Fluid with a Buoyancy Effect." Journal of Advanced Research in Numerical Heat Transfer 8, no. 1 (2022): 50-55.
Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD flow and heat transfer of double stratified micropolar fluid over a vertical permeable shrinking/stretching sheet with chemical reaction and heat source." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 1-14. https://doi.org/10.37934/araset.21.1.114
Dandu, Sridevi, Venkata Ramana Murthy Chitrapu, and Udaya Bhaskara Varma Nadimpalli. "Effects of Hall Current, Diffusion Thermos and Activation Energy on MHD Radiative Casson Nanofluid Flow with Chemical Reaction and Thermal Radiation." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 104, no. 1 (2023): 106-123. https://doi.org/10.37934/arfmts.104.1.106123
