**ABSTRACT**

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite difference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are examined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and current density for various emerging parameters magnetic force parameter, ξ, mixed convection parameter, λ, magnetic Prandtl number, γ, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position α = π/4 and 2π/3. It is further noticed that a fluid velocity increases sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physically in good agreement.

**KEYWORDS**

PAPER SUBMITTED: 2020-04-10

PAPER REVISED: 2020-05-17

PAPER ACCEPTED: 2020-05-25

PUBLISHED ONLINE: 2020-10-25

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Supplement 1**, PAGES [S13 - S23]

- Eshghy, S., et al., The Effect of Longitudinal Oscillations on Free Convection from Vertical Surfaces, Journal Appl. Mech., 32 (1965), 1, pp. 183-191
- Kelleher, M. D., Yang, K. T., Heat Transfer Response of Laminar Free-Convection Boundary-Layers Along a Vertical Heated Plate to Surface-Temperature Oscillations, Z. Angew. Math. Phys., 19 (1968), 1, pp. 31-44
- Chawla, S. S., Magnetohydrodynamic Oscillatory Flow Past a Semi-Infinite Flat Plate, Int. J. Non-Linear Mech., 6 (1971), 1, pp. 117-134
- Pedley, T. J., The 2-D Boundary-Layers in a Free Stream Which Oscillates without Reversing, Journal Fluid Mech., 55 (1972), 2, pp. 359-383
- Mahuri, P. K., Gupta, A. S., Free Convection Boundary-Layer on a Flat Plate Due to Small Fluctuations in Surface Temperature, Joural Appl. Math. Mech., 59 (1979), 2, pp. 117-121
- Verma, A. R., An Asymptotic Analysis of Free Convection Boundary-Layer on a Horizontal Flat Plate Due to Small Fluctuations in Surface Temperature, Int. J. Eng. Sci., 21 (1983), 1, pp. 35-43
- Mei, R., et al., Unsteady Drag on a Sphere at Finite Reynolds Number with Small Fluctuations in the Free-Stream Velocity, Journal Fluid Mech., 233 (1991), 1, pp. 613-631
- Eckerle, W. A., Awad, J. K., Effects of Free Stream Velocity on 3-D Separated Flow Region in Front of a Cylinder, Journal Fluid Eng., 113 (1991), 1, pp. 37-44
- Mei, R., Adrian, R. J., Flow Past a Sphere with an Oscillation in the Free-Stream Velocity and Unsteady Drag at Finite Reynolds Number, Journal Fluid Mech., 237 (1992), 1, pp. 323-341
- Klausner, J. F., Unsteady Force on a Bubble at Finite Reynolds Number with Small Fluctuations in the Free-Stream Velocity, Phys. Fluids A, 4 (1992), 1, pp. 63-70
- Hossain, M. A., et al., Influence of Fluctuating Surface Temperature and Concentration on Natural-Convection Flow from a Vertical Flat Plate, Z. Angew. Math. Mech., 81 (2001), 10, pp. 699-709
- Wang, C. Y., Flow Due to a Stretching Boundary with Partial Slip - An Exact Solution of the Navier-Stokes Equations, Chem. Eng. Sci., 57 (2002), 1, pp. 3745-3747
- Fan, S., Barber, J. R., Solution of Periodic Heating Problems by the Transfer Matrix Method, Int. J. Heat. Mass. Trans., 45 (2002), 5, pp. 155-1158
- Andersson, H. I., Slip Flow Past a Stretching Surface, Acta. Mech.,158 (2002), 1, pp. 121-125
- Cossali, G. E., Periodic Heat Transfer by Forced Laminar Boundary-Layer Flow over a Semi-Infinite Flat Plate, Int. J. Heat. Mass., Trans., 48 (2005), 23-24, pp. 4846-4853
- Martin M. J., Boyd, I. D., Momentum and Heat Transfer in a Laminar Boundary-Layer with Slip Flow, Journal Thermophysics. Heat. Trans., 20 (2006), 4, pp.710-719
- Ariel, P. D., et al., The Flow of an Elastico-Viscous Fluid Past a Stretching Sheet with Partial Slip, Acta Mech., 187 (2006), 1, pp. 29-35
- Ackerberg, R. C., Phillips, J. H., The Unsteady Laminar Boundary-Layer on a Semi-Infinite Flat Plate Due to Small Fluctuations in the Magnitude of the Free-Stream Velocity, Journal Fluid. Mech., 51 (2006), 1, pp. 137-157
- Ariel, P. D., The 2-D Stagnation Point Flow of an Elastico-Viscous Fluid with Partial Slip, Z. Angew. Math. Mech., 88 (2008), 4, pp. 320-324
- Berg, S., et al., Two-Phase Flow in Porous Media with Slip Boundary Condition, Transp. Porous. Med., 74 (2008), 1, pp. 275-292
- Fang, T., et al., Slip MHD Viscous Flow over a Stretching Sheet - An Exact Solution, Commun. Non-Linear. Sci. Numer. Simulat., 14 (2009), 1, pp. 3731-3737
- Abbas, Z., et al., Slip Effects and Heat Transfer Analysis in a Viscous Fluid over an Oscillatory Stretching Surface, Int. J. Num. Methods, Fluids, 59 (2009), 1, pp. 443-458
- Martin, M. J., Boyd, I. D., Falkner-Skan Flow over a Wedge with Slip Boundary Conditions, Journal Thermophysics. Heat. Trans., 24 (2010), 2, pp. 263-270
- Mukhopadhyay, S., The MHD Boundary-Layer Slip-Flow Along a Stretching Cylinder, Ain. Shams. Eng. J., 4 (2012), 1, pp. 317-324
- Roy, N. C., Hossain, M. A., Unsteady Laminar Mixed Convection Boundary-Layer Flow Near a Vertical Wedge Due to Oscillations in the Free-Stream and Surface Temperature, Int. J. Appl. Mech. Eng., 21 (2016), 1, pp. 169-186
- Hirschhorn, J., et al., Magnetohydrodynamic Boundary-Layer Slip Flow and Heat Transfer of Power Law Fluid over a Flat Plate, Journal Appl. Fluid. Mech., 9 (2016), 1, pp. 11-17
- Kamrujjaman, M., et al., Mixed Convection Flow Along a Horizontal Circular Cylinder with Small Amplitude Oscillation in Surface Temperature and Free Stream, Mech. Eng. Research., 6 (2016), 2, pp. 34-47
- Ashraf, M., et al., Effects of Temperature Dependent Viscosity and Thermal Conductivity on Mixed Convection Flow Along a Magnetized Vertical Surface, Int. J. Numerical. Methods. Heat. Fluid. Flow, 26 (2016), 5, pp. 1580-1592
- Ashraf, M., et al., Periodic Momentum and Thermal Boundary-Layer Mixed Convection Flow around the Surface of Sphere in the Presence of Viscous Dissipation, Canadian. J. Phys., 95 (2017), 10, pp. 976-986
- Ashraf, M., et al., Numerical Prediction of Natural-Convection Flow in the Presence of Weak Magnetic Prandtl Number and Strong Magnetic Field with Algebraic Decay in Mainstream Velocity, Advan. Appl. Math. Mech., 9 (2017), 2, pp. 349-361
- Tiainen, J., et al., Effects of Free Stream Velocity Definition on Boundary-Layer Thickness and Losses in Centrifugal Compressor, Radial. Turbomachinery. Aerodynamics, 2C (2017), 1, pp. 26-30
- Garg, P., et al., Free-Convective Unsteady MHD Flow in Slip-Flow Regime Past a Vertical Plate with a Convective Surface Boundary Condition, Journal Info. Math. Sci., 10 (2018), 1-2, pp. 261-270
- Ashraf, M., Fatima, A., Numerical Simulation of the Effect of Transient Shear Stress and Rate of Heat Transfer Around Different Position of Sphere in the Presence of Viscous Dissipation, Journal of Heat Transfer, 140 (2018), 6, pp. 1-1
- Ashraf, M., Ullah, Z., Effects of Variable Density on Oscillatory Flow around a Non-Conducting Horizontal Circular Cylinder, AIP Advances, 10 (2020), 1, 015020
- Kilicman, A., et al., Analytic Approximate Solutions for Fluid-Flow in the Presence of Heat and Mass Transfer, Thermal Science, 22 (2018), Suppl. 1, pp. S259-S264
- Inc, M,. et.al., N-Wave and Other Solutions to the B-Type Kadomtsev-Petviashvili Equation, Thermal Science, 23 (2019), Suppl. 6, pp. S2027 - S2035
- Hashemi, M. S., et al, On Fractional KdV-Burgers and Potential KdV Equations, Existence and Uniqueness Results, Thermal Science, 23 (2019), Suppl. 6, pp. S2107-S2117