Effects of Magnetohydrodynamics and Heat Transfer in Casson Fluid Through a Channel
Keywords:Casson fluid, MHD, free convection flow, Laplace Transform
AbstractUnsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection ﬂows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article  with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid, time, Prandtl number, Grashof number and magnetic field. Laplace transform method is used to solve the dimensionless equations with associated initial and boundary conditions. Solutions for velocity and temperature profiles are obtained. Skin friction and Nusselt number are also calculated. The obtained analytical results for velocity and temperature are plotted graphically to discuss the influence of dimensionless parameters on profiles. It is observed that fluid velocity increases with increases of Grashof number, Gr and time, t whereas it decreases with increases of Casson parameter, γ, magnetic field parameter, M and Prandtl number, Pr. Besides that, it is found that temperature profiles decrease with high value of Prandtl number, Pr while increases with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and it is found to be in a mutual agreement.
C.S.K Raju, N. Sandeep, V. Sugunamma, M.J Babu and J.V.R Reddy, “Heat and Mass Transfer in Magnetohydrodynamic Casson Fluid Over an Exponentially Permeable Stretching Surface”, Engineering Science and Technology, an International Journal, 19(1): 45–52, 2016.
M. Tamoor, M. Waqas, M.I. Khan, A. Alsaedi and T. Hayat, “Results in Physics Magnetohydrodynamic Flow of Casson Fluid Over A Stretching Cylinder”, Results in Physics, 7: 498–502, 2017.
M. Nawaz, R. Naz and M. Awais, “Magnetohydrodynamic Axisymmetric Flow of Casson Fluid with Variable Thermal Conductivity and Free Stream”, Alexandria Engineering Journal, 57(3): 2043–2050, 2018.
M.F. Javed, M.I. Khan, N.B Khan and R. Muhammad, “Axisymmetric Flow of Casson Fluid by a Swirling Cylinder”, Results in Physics, 9(March):1250– 1255, 2018.
F. Mabood and K. Das, “Outlining the Impact of Melting on MHD Casson Fluid Flow Past A Stretching Sheet in A Porous Medium with Radiation”, Heliyon, 5(e01216):1-17, 2019.
A. Khalid, I. Khan, A. Khan et al., “Unsteady MHD Free Convection Flow of Casson Fluid Past Over an Oscillating Vertical Plate Embedded in A Porous Medium”, Engineering Science and Technology, an International Journal, 18(3): 309–317, 2015.
H.R Kataria and H.R. Patel, “Heat and Mass Transfer in Magnetohydrodynamic (MHD) Casson Fluid Flow Past Over an Oscillating Vertical Plate Embedded in Porous Medium with Ramped Wall Temperature”, Propulsion and Power Research, 7(3): 257–267, 2018.
H.R Kataria and H.R Patel, “Effects of Chemical Reaction and Heat Generation/Absorption on Magnetohydrodynamic (MHD) Casson Fluid Flow Over an Exponentially Accelerated Vertical Plate Embedded in Porous Medium with Ramped Wall Temperature and Ramped Surface Concentration”, Propulsion and Power Research,1-12, 2019.
D. Khan, A. Khan, I. Khan et al., “Effects of Relative Magnetic Field, Chemical Reaction, Heat Generation and Newtonian Heating on Convection Flow of Casson Fluid over a Moving Vertical Plate Embedded in a Porous Medium”, Scientific Reports, 9(1): 1–18, 2019.
T. Paul, B.K Jha and A.K Singh, “Transient Free Convective Flow in A Vertical Channel with Constant Temperature and Constant Heat Flux on Walls”, Heat and Mass Transfer/Waerme- und Stoffuebertragung, 32(1–2): 61–63, 1996.
B.K Jha, “Effects of Applied Magnetic Field on Transient Free-Convective Flow in a Vertical Channel”, Indian Journal of Pure and Applied Mathematics, 29: 441–445, 1998.
M. Narahari, “Natural Convection in Unsteady Couette Flow Between Two Vertical Parallel Plates in the Presence of Constant Heat Flux and Radiation”, Applied Sciences, 73–78, 2008.
N. Marneni, “Transient Free Convection Flow Between Two Long Vertical Parallel Plates with Constant Temperature and Mass Diffusion”, Proceedings of the World Congress on Engineering, 2:1-6, 2008.
M. Narahari and V.R Raghavan, “Natural Convection Flow in Vertical Channel Due to Ramped Wall Temperature at One Boundary”, Proceedings of the ASME 2009 Heat Transfer Summer Conference, 1–8, 2009.
B.K Jha and A.O Ajibade, “Diffusion-Thermo Effects on Free Convective Heat and Mass Transfer Flow in a Vertical Channel with Symmetric Boundary Conditions”, Journal of Heat Transfer, 133(5): 052502, 2011.
G.S Seth, B. Kumbhakar and R. Sharma, “Unsteady Hydromagnetic Natural Convection Flow of a Heat Absorbing Fluid Within A Rotating Vertical Channel in Porous Medium with Hall Effects”, Journal of Applied Fluid Mechanics, 8(4): 767–779, 2015.
I. Khan, M. Saqib and F. Ali, “Application of Time-Fractional Derivatives with Non-Singular Kernel to The Generalized Convective Flow of Casson Fluid in A Microchannel with Constant Walls Temperature”, European Physical Journal: Special Topics, 226(16–18): 3791–3802, 2017.
M. Ahmad Qushairi, J. Lim Yeou, S. Shafie, et al., “Exact Solution for Unsteady Free Convection Flow of Casson Fluid in Vertical Channel”, MATEC Web of Conferences, 189: 01007, 2018.
M. Saqib, F. Ali, I. Khan et al., “Heat And Mass Transfer Phenomena In The Flow Of Casson Fluid Over An Infinite Oscillating Plate In The Presence Of First-Order Chemical Reaction And Slip Effect”, Neural Computing and Applications, 30(7): 2159–2172, 2018.
M. Das, R. Mahato and R. Nandkeolyar, “Newtonian Heating Effect On Unsteady Hydromagnetic Casson Fluid Flow Past A Flat Plate With Heat And Mass Transfer”, Alexandria Engineering Journal, 54(4):871–879, 2015.