This numerical study was devoted to examining the occurrence of non-unique solutions in boundary layer flow due to deformable surfaces (cylinder and flat plate) with the imposition of prescribed surface heat flux. The hybrid Al2O3-Cu/water nanofluid was formulated using the single phase model with respective correlations of hybrid nanofluids. The governing model was simplified by adopting a similarity transformation. The transformed differential equations were then numerically computed using the efficient bvp4c solver with the ranges of the control parameters 0.5%≤ϕ1,ϕ2≤1.5% (Al2O3 and Cu volumetric concentration), 0≤K≤0.2 (curvature parameter), 2.6<S≤3.2 (suction parameter) and −2.5<λ≤0.5 (stretching/shrinking parameter). Dual steady solutions are presentable for both a cylinder (K>0) and a flat plate (K=0) with the inclusion of only the suction (transpiration) parameter. The real and stable solutions were mathematically validated through the stability analysis. The Al2O3-Cu/water nanofluid with ϕ1=0.5% (alumina) and ϕ2=1.5% (copper) has the highest skin friction coefficient and heat transfer rate, followed by the hybrid nanofluids with volumetric concentrations (ϕ1=1%,ϕ2=1%) and (ϕ1=1.5%,ϕ2=0.5%), respectively. Surprisingly, the flat plate surface abates the separation of boundary layer while it enhances the heat transfer process.
The flow of fluids over the boundaries of a rotating disc has many practical uses, including boundary-layer control and separation. Therefore, the aim of this study is to discuss the impact of unsteady magnetohydrodynamics (MHD) hybrid ferrofluid flow over a stretching/shrinking rotating disk. The time-dependent mathematical model is transformed into a set of ordinary differential equations (ODE’s) by using similarity variables. The bvp4c method in the MATLAB platform is utilised in order to solve the present model. Since the occurrence of more than one solution is presentable, an analysis of solution stabilities is conducted. Both solutions were surprisingly found to be stable. Meanwhile, the skin friction coefficient, heat transfer rate—in cooperation with velocity—and temperature profile distributions are examined for the progressing parameters. The findings reveal that the unsteadiness parameter causes the boundary layer thickness of the velocity and temperature distribution profile to decrease. A higher value of magnetic and mass flux parameter lowers the skin friction coefficient. In contrast, the addition of the unsteadiness parameter yields a supportive effect on the heat transfer rate. An increment of the magnetic parameter up to 30% reduces the skin friction coefficient by 15.98% and enhances the heat transfer rate approximately up to 1.88%, significantly. In contrast, the heat transfer is rapidly enhanced by improving the mass flux parameter by almost 20%.
This paper delves into the problem of mixed convection boundary layer flow from a horizontal circular cylinder filled in a Jeffrey fluid with viscous dissipation effect. Both cases of cooled and heated cylinders are discussed. The governing equations which have been converted into a dimensionless form using the appropriate non-dimensional variables are solved numerically through the Keller-box method. A comparative study is performed and authentication of the present results with documented outcomes from formerly published works is excellently achieved. Tabular and graphical representations of the numerical results are executed for the specified distributions, considering the mixed convection parameter, Jeffrey fluid parameters and the Prandtl and Eckert numbers. Interestingly, boundary layer separation for mixed convection parameter happens for some positive (assisting flow) and negative (opposing flow) values. Strong assisting flow means the cylinder is heated, which causes the delay in boundary layer separation, whereas strong opposing flow means the cylinder is cooled, which conveys the separation point close to the lower stagnation point. Contradictory behaviours of both Jeffrey fluid parameters are observed over the velocity and temperature profiles together with the skin friction coefficient and Nusselt number. The increase of the Prandtl number leads to the decrement of the temperature profile, while the increase of the Eckert number results in the slight increment of the skin friction coefficient and decrement of the Nusselt number. Both velocity and temperature profiles of Eckert number show no effects at the lower stagnation point of the cylinder.
The purpose of this study was to examine the effect of viscous dissipation on mixed convection flow of viscoelastic nanofluid past a horizontal circular cylinder. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as a nanoparticle with the Prandtl number Pr = 6.2. The transformed boundary layer equations for momentum and temperature subject to the appropriate boundary conditions are solved numerically by using Keller-box method. The influenced of the dimensionless parameters such as Eckert number, mixed convection parameter, nanoparticles volume fraction and viscoelastic parameter on the flow and heat transfer characteristics is analyzed in detail and presented graphically. The results come out with the velocity profiles are increased while the temperature profiles are decreased by increasing the values of nanoparticles volume fraction and viscoelastic parameter, respectively. The graph shows that, increasing Eckert number the skin friction is also increases. The values of skin friction are increased by increasing mixed convection parameter, but the values of Nusselt number produce an opposite behavior. The present study has many applications especially in heat exchangers technology and oceanography. Therefore, in future, it is hoping to study the viscoelastic nanofluid flow past a different geometric such as sphere and cylindrical cone.
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