Significance of chemical reaction on MHD near stagnation point flow towards a stretching sheet with radiation
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Significance of chemical reaction on MHD near stagnation point flow towards a stretching sheet with radiation S. Harinath Reddy1 · K. Kumaraswamy Naidu2 · D. Harish Babu2 · P. V. Satya Narayana3 · M. C. Raju4 Received: 31 March 2020 / Accepted: 3 October 2020 © Springer Nature Switzerland AG 2020
Abstract The influence of variable surface temperature and concentration on MHD stagnation point flow towards a stretching sheet plays an important role in wire coating, film blowing, fiber spinning and coating. In this work an attempt has been made to study the ramification of thermal radiation on MHD chemically reacting liquid past a stretching surface with nonlinear temperature and concentration. The nonlinear coupled governing equations are changed into a set of nonlinear ordinary differential equations by adopting similarity transformations. The set of nonlinear equations together with the boundary conditions are solved computationally by employing shooting technique. The influence of various flow field parameters (magnetic parameter, suction/injection parameter, velocity ratio parameter, heat absorption, radiation, chemical reaction parameter, Schmidt number) on momentum, heat measure, diffusion, skin friction coefficient, rate of heat transfer and rate of mass transfer is depicted and discussed in detail. The outcomes disclosed that the fluid temperature accelerates on rising the thermal radiation and reverse trend with heat absorption parameter. Species concentration diminishes on enhancing the chemical reaction parameter. A comparison has been made with the published results as a particular case and found to be in fair agreement. Keywords Power law form of surface temperature and concentration · MHD · Thermal radiation · Chemical reaction List of symbols B0 Uniform magnetic field a, b, c, n Constants cfx Skin-friction coefficient cp Specific heat at constant pressure (J kg−1 K) n C̃ w (x) = C̃ ∞ + cx Concentration of the sheet f ′ Dimensionless velocity k Thermal conductivity of fluid (W m−1 k−1) Kr1 𝛿 2 Kr = 𝜐 Chemical reaction parameter Ks Rosseland absorption coefficient 4𝜎 ∗ T̃ 3 R = K k∞ Radiation parameter s
Nux Nusselt number 𝜎B2 M = a𝜌0 Magnetic parameter
Pr = 𝛼𝜐 Prandtl number qr Radiative heat flux (W m−1) qw Surface heat flux Rex Local Reynolds number Shx Sherwood number T̃ Fluid temperature (K) T̃∞ Temperature far away from the wall (K) T̃w (x) = T̃∞ + cx n Temperature of the sheet ũ , ṽ Velocity components in x-, y-directions, respectively (m s−1) ̃Uw (x) = ax Stretching velocity Ũ ∞ (x) = bx Free stream velocity Ṽ w (x) = −(a𝜐)0.5 S Mass flux velocity S S > 0 suction and S 0)-direction. The coordinate system and physical model of the problem are depicted in Fig. 1. Based on aforesaid physical assumptions, the governing flow equations and corresponding conditions are represented by [30].
𝜕 ũ 𝜕 ṽ + =0 𝜕x 𝜕y
ũ
ũ
Research Article
| https://doi.org/10.1007/s42452-020-03621-1
(1)
∗
The radiative heat flux qr is defined as qr = − 43 𝜎K
s
𝜕 T̃ ∗ 𝜕y
4
by uti
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