The endeavor of this study is to explore the nature of dual solutions (steady and unsteady) for the Casson fluid flow with the simultaneous consequences of both thermal and mass transmissions. The flow passes above an absorbent elongating sheet in the existence of a constant magnetic field. The supported leading equations are remodeled into a set of solvable forms with the assist of suitable similarity variables and hence deciphered utilizing the “MATLAB routine bvp4c scheme.” Due to the sudden changes in the surface with time, the temperature and flow behavior over the sheet also change, and hence dual‐type flow solutions exist. Stability scrutiny is implemented to examine the less (more) stable and visually achievable solutions. From this study, we have achieved many interesting facts, among them, we can use magnetic and Casson fluid parameters to control the motion of the fluid and to enlarge of thermal transmission of the fluid. This flow model has many important applications in different physical fields, such as engineering sciences, medical sciences, and different industrial processes. One of the most important results, which has been achieved from this investigation, is that the Prandtl number enriches the heat transfer rate of the fluid at the surface during the time‐independent case under the suction environment. Also, the chemical reaction parameter helps to enhance the mass accumulation rate of the fluid in both cases.
An unsteady two dimensional free convective flow of viscoelastic fluid past a flat surface with heat and mass transfer has been investigated. The surface is oscillating with about a mean velocity U 0. Oscillating temperature and concentration about T ∞ and C ∞ respectively have been considered at the surface. The visco-elastic fluid flow is characterized by Oldroyd-B fluid model having two rheological parameters: relaxation time and retardation time. In the governing fluid flow, a magnetic field of uniform strength B 0 has been applied along the transverse direction to the surface. Governing equations of motion are solved analytically by using perturbation scheme. Analytical expressions for velocity profiles, shearing stress at the surface, temperature and concentration fields are obtained. Results are discussed graphically for various combinations of flow parameters involved in the solution. A special emphasis is given on the effects of relaxation and retardation times.
Free convective binary mixture flow of visco-elastic fluid through a porous channel in presence of Hall effects, radiation and first order chemical reaction has been considered. A magnetic field of uniform strength has been applied along the transverse direction to the channel. The visco-elastic fluid flow is governed by Oldroyd fluid-B model. Two important rheological parameters involved in the constitutive equation are relaxation parameter and retardation parameter. In the mixture, one of the components is assumed to be rarer lighter. The temperature and concentration of the fluid at one surface is assumed to be constant but temperature and concentration of the fluid at the second surface are assumed to be oscillating about a constant temperature and concentration respectively. The governing equations of momentum, temperature and concentration are solved analytically by using separation of variable technique. Results are discussed graphically for various values of flow parameters involved in the solution.
An unsteady visco-elastic fluid flow through an annulus with heat and mass transfer has been studied. The visco-elastic fluid is characterized by Oldroyd fluid constitutive model consisting of rheological parameters namely relaxation time (λ1) and retardation time (λ2). The annulus is bounded by two infinite co-axial circular cylinders of radius c and d respectively. Fluid flow in the annular region is governed by periodic pressure gradient. A magnetic field of uniform strength B0 has been applied perpendicular to the axis of annulus. The governing partial differential equations from conservation laws of momentum, energy and concentration principles are converted into the ordinary differential equations and these equations are solved analytically using modified Bessel functions of first kind Iυ(z) and second kind Kυ(z).
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