Simultaneous Effects of Thermal Radiation and Chemical Reaction on Hydromagnetic Pulsatile Flow of a Casson Fluid in a Porous Space
Abstract
In the present study, the hydromagnetic pulsating flow of Casson fluid between two parallel plates in a porous space, thermal radiation and chemical reaction are investigated. The analytical solutions for flow variables are obtained by using a perturbation technique. The effects of pertinent parameters on velocity, temperature, concentration, Nusselt number and Sherwood number distributions are studied in detail.Keywords:
Casson fluid, porous space, chemical reaction, Soret number, Hartmann numberReferences
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2. Hameed M., Nadeem S., Unsteady MHD flow of a non-Newtonian fluid on a porous plate, Journal of Mathematical Analysis and Applications, 325(1): 724–733, 2007.
3. Nadeem S., Ul-Haq R., Akbar N.S., Khan Z.H., MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet, Alexandria Engineering Journal, 52(4): 577–582, 2013.
4. Misra J.C., Shit G.C., Chandra S., Kundu P.K., Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow, Journal of Engineering Mathematics, 69(1): 91–100, 2011.
5. Rosca A.V., Pop I., Flow and heat transfer of Powell-Eyring fluid over a shrinking surface in a parallel free stream, International Journal of Heat and Mass Transfer, 71: 321–327, 2014.
6. Wenchang T., Wenxiao P., Mingyu X., A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates, International Journal of Non-Linear Mechanics, 38(5): 645–650, 2003.
7. Khan U., Ahmed N., Khan S.I., Bano S., Mohyud-Din S.T., Unsteady squeezing flow of a Casson fluid between parallel plates, World Journal of Modelling and Simulation, 10(4): 308–319, 2014.
8. Attia H.A., Sayed-Ahmed M.E., Transient MHD Couette flow of a Casson fluid between parallel plates with heat transfer, Italian Journal of Pure and Applied Mathematics, 27−2010: 19−38, 2010, http://ijpam.uniud.it/online_issue/201027/02-Attia2.pdf.
9. Chiu-On Ng, Combined pressure-driven and electroosmotic flow of Casson fluid through a slit microchannel, Journal of Non-Newtonian Fluid Mechanics, 198: 1–9, 2013.
10. Hayat T., Farooq M., Iqbal Z., Stretched flow of Casson fluid with variable thermal conductivity, Walailak Journal of Science and Technology, 10(2): 181–190, 2013.
11. Nadeem S., Haq R., Lee C., MHD flow of a Casson fluid over an exponentially shrinking sheet, Scientia Iranica B, 19(6): 1550–1553, 2012.
12. Srinivas S., Malathy T., Sachdev P.L., On pulsatile hydromagnetic flow of an Oldroyd fluid with heat transfer, Engineering Transactions, 55(1): 79–94, 2007.
13. Malathy T., Srinivas S., Pulsating flow of hydromagnetic fluid between permeable beds, International Communications in Heat and Mass Transfer, 35(5): 681–688, 2008.
14. Wang C.Y., Pulsatile flow in a porous channel, Journal of Applied Mechanics, 38(2): 553–555, 1971.
15. Radhakrishnamacharya G., Maiti M.K., Heat transfer to pulsatile flow in a porous channel, International Journal of Heat and Mass Transfer, 20(2): 171–173, 1977.
16. Siddiqui S.U., Gupta R.S., Verma N.K., Mishra S., Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis, Applied Mathematics and Computations, 210: 1–10, 2009.
17. Shit G.C., Roy M., Pulsatile flow and heat transfer of magneto-micropolar fluid through a stenosed artery under the influence of body acceleration, Journal of Mechanics in Medicine and Biology, 11(3): 643–661, 2011.
18. Shawky H.M., Pulsatile flow with heat transfer of dusty magnetohydrodynamic Ree-Eyring fluid through channel, Heat and Mass Transfer, 45(10): 1261–1269, 2009.
19. Brewster M.Q., Thermal radiative transfer and properties, Wiley, New York, 1992.
20. T. Hayat, R. Sajjad, Z. Abbas, M. Sajjad, A.A. Hendi, Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium, International Journal of Heat and Mass Transfer, 54(4): 854–862, 2011.
21. Srinivas S., Shukla A.K., Ramamohan T.R., Reddy A.S., Influence of thermal radiation on unsteady flow over an expanding or contracting cylinder with thermal-diffusion and diffusion-thermo effects, Journal of Aerospace Engineering, 28(5): 04014134–10, 2015.
22. Pal D., Vajravelu K., Mandal G., Convective-radiation effects on stagnation point flow of nanofluids over a stretching/shrinking surface with viscous dissipation, Journal of Mechanics, 30(3): 289–297, 2014.
23. Mustafa M., Mushtaq A., Hayat T., Alsaedi A., Radiation effects in three-dimensional flow over a bi-directional exponentially stretching sheet, Journal of the Taiwan Institute of Chemical Engineers, 47: 43–49, 2015.
24. Hossain M.A., Alim M.A., Rees D.A.S., The effect of radiation on free convection from a porous vertical plate, International Journal of Heat and Mass Transfer, 42(1): 181–191, 1999.
25. Raptis A., Perdikis C., Takhar H.S., Effect of thermal radiation on MHD flow, Applied Mathematics and Computation, 153(3): 645–649, 2004.
26. Mukhopadhyay S., Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing, Chinese Physics B, 22(11): 114702–7, 2013.
27. Makanda G., Shaw S., Sibanda P., Effects of radiation on MHD free convection of a Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation, Boundary Value Problems, 2015, https://doi.org/10.1186/s13661-015-0333-5.
28. Muthuraj R., Srinivas S., A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel, International Communications in Heat and Mass Transfer, 37(9): 1255–1260, 2010.
29. Bridges C., Rajagopal K.R., Pulsatile flow of a chemically-reacting nonlinear fluid, Computers & Mathematics with Applications, 52(6–7): 1131–1144, 2006.
30. Hayat T., Abbas Z., Channel flow of a Maxwell fluid with chemical reaction, Zeitschrift fur Angewandte Mathematik und Physik, 59(1): 124–144, 2008.
31. Hayat T., Mustafa M., Asghar S., Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction, Nonlinear Analysis: Real World Applications, 11(4): 3186–3197, 2010.
32. Vajravelu K., Prasad K.V., Prasanna Rao N.S., Diffusion of a chemically reactive species of a power-law fluid past a stretching surface, Computers & Mathematics with Applications, 62(1): 93–108, 2011.
33. Das U.N., Deka R.K., Soundalgekar V.M., Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction, Forschung im Ingenieurwesen, 60(10): 284–287, 1994.
34. Nabil E.T.M., Elsaka A.G., Radwan A.E., Magdy A.M.E., Effects of chemical reaction and heat radiation on the MHD flow of vicoelastic fluid through a porous medium over a horizontal stretching flat plate, Journal of American Science, 6(9): 126–136, 2010.
35. Shehzad S.A., Hayat T., Qasim M., Asghar S., Effects of mass transfer on MHD flow of Casson fluid with chemical reaction and suction, Brazilian Journal of Chemical Engineering, 30(1): 187–195, 2013.
36. Srinivas S., Malathy T., Reddy A.S., A note on thermal-diffusion and chemical reaction effects on MHD pulsating flow in a porous channel with slip and convective boundary conditions, Journal of King Saud University– Engineering Sciences, 28(2): 213–221, 2016.
2. Hameed M., Nadeem S., Unsteady MHD flow of a non-Newtonian fluid on a porous plate, Journal of Mathematical Analysis and Applications, 325(1): 724–733, 2007.
3. Nadeem S., Ul-Haq R., Akbar N.S., Khan Z.H., MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet, Alexandria Engineering Journal, 52(4): 577–582, 2013.
4. Misra J.C., Shit G.C., Chandra S., Kundu P.K., Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow, Journal of Engineering Mathematics, 69(1): 91–100, 2011.
5. Rosca A.V., Pop I., Flow and heat transfer of Powell-Eyring fluid over a shrinking surface in a parallel free stream, International Journal of Heat and Mass Transfer, 71: 321–327, 2014.
6. Wenchang T., Wenxiao P., Mingyu X., A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates, International Journal of Non-Linear Mechanics, 38(5): 645–650, 2003.
7. Khan U., Ahmed N., Khan S.I., Bano S., Mohyud-Din S.T., Unsteady squeezing flow of a Casson fluid between parallel plates, World Journal of Modelling and Simulation, 10(4): 308–319, 2014.
8. Attia H.A., Sayed-Ahmed M.E., Transient MHD Couette flow of a Casson fluid between parallel plates with heat transfer, Italian Journal of Pure and Applied Mathematics, 27−2010: 19−38, 2010, http://ijpam.uniud.it/online_issue/201027/02-Attia2.pdf.
9. Chiu-On Ng, Combined pressure-driven and electroosmotic flow of Casson fluid through a slit microchannel, Journal of Non-Newtonian Fluid Mechanics, 198: 1–9, 2013.
10. Hayat T., Farooq M., Iqbal Z., Stretched flow of Casson fluid with variable thermal conductivity, Walailak Journal of Science and Technology, 10(2): 181–190, 2013.
11. Nadeem S., Haq R., Lee C., MHD flow of a Casson fluid over an exponentially shrinking sheet, Scientia Iranica B, 19(6): 1550–1553, 2012.
12. Srinivas S., Malathy T., Sachdev P.L., On pulsatile hydromagnetic flow of an Oldroyd fluid with heat transfer, Engineering Transactions, 55(1): 79–94, 2007.
13. Malathy T., Srinivas S., Pulsating flow of hydromagnetic fluid between permeable beds, International Communications in Heat and Mass Transfer, 35(5): 681–688, 2008.
14. Wang C.Y., Pulsatile flow in a porous channel, Journal of Applied Mechanics, 38(2): 553–555, 1971.
15. Radhakrishnamacharya G., Maiti M.K., Heat transfer to pulsatile flow in a porous channel, International Journal of Heat and Mass Transfer, 20(2): 171–173, 1977.
16. Siddiqui S.U., Gupta R.S., Verma N.K., Mishra S., Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis, Applied Mathematics and Computations, 210: 1–10, 2009.
17. Shit G.C., Roy M., Pulsatile flow and heat transfer of magneto-micropolar fluid through a stenosed artery under the influence of body acceleration, Journal of Mechanics in Medicine and Biology, 11(3): 643–661, 2011.
18. Shawky H.M., Pulsatile flow with heat transfer of dusty magnetohydrodynamic Ree-Eyring fluid through channel, Heat and Mass Transfer, 45(10): 1261–1269, 2009.
19. Brewster M.Q., Thermal radiative transfer and properties, Wiley, New York, 1992.
20. T. Hayat, R. Sajjad, Z. Abbas, M. Sajjad, A.A. Hendi, Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium, International Journal of Heat and Mass Transfer, 54(4): 854–862, 2011.
21. Srinivas S., Shukla A.K., Ramamohan T.R., Reddy A.S., Influence of thermal radiation on unsteady flow over an expanding or contracting cylinder with thermal-diffusion and diffusion-thermo effects, Journal of Aerospace Engineering, 28(5): 04014134–10, 2015.
22. Pal D., Vajravelu K., Mandal G., Convective-radiation effects on stagnation point flow of nanofluids over a stretching/shrinking surface with viscous dissipation, Journal of Mechanics, 30(3): 289–297, 2014.
23. Mustafa M., Mushtaq A., Hayat T., Alsaedi A., Radiation effects in three-dimensional flow over a bi-directional exponentially stretching sheet, Journal of the Taiwan Institute of Chemical Engineers, 47: 43–49, 2015.
24. Hossain M.A., Alim M.A., Rees D.A.S., The effect of radiation on free convection from a porous vertical plate, International Journal of Heat and Mass Transfer, 42(1): 181–191, 1999.
25. Raptis A., Perdikis C., Takhar H.S., Effect of thermal radiation on MHD flow, Applied Mathematics and Computation, 153(3): 645–649, 2004.
26. Mukhopadhyay S., Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing, Chinese Physics B, 22(11): 114702–7, 2013.
27. Makanda G., Shaw S., Sibanda P., Effects of radiation on MHD free convection of a Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation, Boundary Value Problems, 2015, https://doi.org/10.1186/s13661-015-0333-5.
28. Muthuraj R., Srinivas S., A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel, International Communications in Heat and Mass Transfer, 37(9): 1255–1260, 2010.
29. Bridges C., Rajagopal K.R., Pulsatile flow of a chemically-reacting nonlinear fluid, Computers & Mathematics with Applications, 52(6–7): 1131–1144, 2006.
30. Hayat T., Abbas Z., Channel flow of a Maxwell fluid with chemical reaction, Zeitschrift fur Angewandte Mathematik und Physik, 59(1): 124–144, 2008.
31. Hayat T., Mustafa M., Asghar S., Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction, Nonlinear Analysis: Real World Applications, 11(4): 3186–3197, 2010.
32. Vajravelu K., Prasad K.V., Prasanna Rao N.S., Diffusion of a chemically reactive species of a power-law fluid past a stretching surface, Computers & Mathematics with Applications, 62(1): 93–108, 2011.
33. Das U.N., Deka R.K., Soundalgekar V.M., Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction, Forschung im Ingenieurwesen, 60(10): 284–287, 1994.
34. Nabil E.T.M., Elsaka A.G., Radwan A.E., Magdy A.M.E., Effects of chemical reaction and heat radiation on the MHD flow of vicoelastic fluid through a porous medium over a horizontal stretching flat plate, Journal of American Science, 6(9): 126–136, 2010.
35. Shehzad S.A., Hayat T., Qasim M., Asghar S., Effects of mass transfer on MHD flow of Casson fluid with chemical reaction and suction, Brazilian Journal of Chemical Engineering, 30(1): 187–195, 2013.
36. Srinivas S., Malathy T., Reddy A.S., A note on thermal-diffusion and chemical reaction effects on MHD pulsating flow in a porous channel with slip and convective boundary conditions, Journal of King Saud University– Engineering Sciences, 28(2): 213–221, 2016.
