Mixed convective flow of an Oldroyd-B nanofluid impinging over an unsteady bidirectional stretching surface with the sig
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Mixed convective flow of an Oldroyd‑B nanofluid impinging over an unsteady bidirectional stretching surface with the significances of double stratification and chemical reaction Iftikhar Ahmad1 · Iqra Khurshid1 · Muhammad Faisal1 · Tariq Javed2 · Zaheer Abbas3 Received: 15 March 2020 / Accepted: 26 August 2020 © Springer Nature Switzerland AG 2020
Abstract The numerous applications of non-Newtonian nanofluids in engineering, geothermal and industrial processes motivated us to formulate a comprehensive model for unsteady 3D flow of an Oldroyd-B nanomaterial. Brownian motion and thermophoresis characteristics are also accommodated through a Buongiorno nanofluid model. Moreover, assessments of thermal stratification, chemical reaction, solutal stratification, mixed convection, and prescribed heat source are also elucidated in the combinations of momentum, energy, and concentration equations. The transformed system of ODEs is tackled by homotopy analysis method. A comparison benchmark for limited cases is also constructed to confirm the correctness of whole parametric exploration. It is scrutinized through present communication that intensifying values of Prandtl factor, unsteady factor, heat distribution indices, thermal stratification constraint, mixed convective parameter, and Deborah number for time retardation diminish the temperature of the nanomaterial. Also, escalating amounts of Lewis number, chemically reactive species, Brownian motion parameter, and solutal stratification constraint reduce the concentration profile. Keywords Chemical reaction · HAM solution · Mixed convection · Oldroyd-B nanofluid · Prescribed heat distribution · Solutal stratification · Thermal stratification · Unsteady bidirectional stretching List of symbols a, b, c Rates of stretching (s−1 ) C Nanoparticle concentration (–) Cw Nanoparticle concentration at the wall (–) C∞ Surrounding nanoparticles concentration (–) C∞,0 Positive constant (–) cf Operative heat ability of base liquid (m2 s−2 K−1 ) cp Heat capability of nanoparticles (m2 s−2 K−1 ) DB Brownian diffusion coefficient (m2 s−1 ) DT Thermophoresis influence (m2 s−1 ) Gr Grashof number (–) f , g Dimensionless velocities (–) ge Gravitational acceleration (m s−2 ) k Thermal conductivity (W m−1 K−1 )
Kr Reaction rate of species (s−1 ) Le Lewis factor (–) N Buoyancy factor (–) Nb Brownian movement constraint (–) Nt Thermophoresis constraint (–) Nux Local Nusselt number (–) Pr Prandtl factor (–) Rex Local Reynolds number (–) r, s Temperature controlled indices (–) S Unsteady stretching constraint (–) Shx Local Sherwood number (–) T Temperature of the liquid (K) Tw Wall temperature (K) T∞ Far away temperature field (K)
* Muhammad Faisal, [email protected] | 1Department of Mathematics, Azad Jammu & Kashmir University, Muzaffarabad 13100, Pakistan. 2Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan. 3Department of Mathematics, Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan. SN App
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