# Unsteady flow of chemically reactive Oldroyd-B fluid over oscillatory moving surface with thermo-diffusion and heat absorption/generation effects

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## Abstract

This theoretical investigation deals with the magnetohydrodynamic mass and heat transportation of oscillatory Oldroyd-B fluid flow under thermo-diffusion effects. Flow is produced due to periodic motion of sheet. Some interesting effects like heat absorption/generation and chemical reaction are superposed in the energy and mass species equations, respectively. By utilizing apposite variables, independent variables in the model equations are reduced. The set of these equations is solved with help of homotopy analysis method. Reliable results for different physical flow constraints are prepared for the velocity, temperature and concentration profiles. It is noted that the Deborah number in terms of relaxation time resists the motion of fluid particles at various time instants. Both temperature and concentration profiles increase by increasing Deborah number in terms of relaxation time. The presence of Dufour number may enhance the thermal boundary layer effectively. It is also concluded that the species concentration profile is promoted by increasing Hartmann number and Soret number. An excellent accuracy of obtained solution is observed with already reported numerical values as a special case.

## Keywords

Magnetohydrodynamic Oldroyd-B fluid Thermo-diffusion effects Homotopy analysis method## List of symbols

- (
*u*,*v*) Velocity component (m/s)

*ω*Frequency (s

^{−1})*λ*_{1}Relaxation time (t)

*σ*Electrical conductivity (s/m)

*α*Thermal diffusivity of fluid (m

^{2}/s)- \(\nu\)
Kinematic viscosity (m

^{2}/s)*Q*Volumetric rate of heat generation/absorption (KW/m

^{3})*C*Concentration

*k*_{T}Thermal diffusion ratio (W/m)

- (
*β*_{1},*β*_{1}) Material parameters

*Pr*Prandtl number

*Du*Dufour number

*δ*Heat source/sink parameter and

*Re*_{x}Local Reynolds number

*Sh*Local Sherwood number

- \(j_{\text{s}}\)
Surface mass flux (W/m

^{2})*b*Stretching rate (s

^{−1})*λ*_{2}Retardation time (t)

- \(f_{y}\)
Dimensionless velocity

*T*Temperature (K)

*ρ*Fluid density (kg/m

^{3})*T*_{m}Mean fluid temperature (K)

- \(c_{\text{p}}\)
Specific heat (J/KgK)

*D*_{m}Molecular diffusivity (m

^{2}/s)*k*_{a}Reaction rate (s)

^{−1}*M*Hartmann number

*Sc*Schmidt number

*Sr*Soret number

*Kr*Chemical reaction parameter

*Nu*_{x}Local Nusselt number

- \(q_{s}\)
Surface heat flux (W/m

^{2})*S*Ratio of oscillating frequency to stretching rate

## Notes

### Acknowledgement

Authors are thankful to the editor and reviewers for their valuable comments to improve the earlier version of the paper.

### Funding

There are no funders to report for this submission.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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