Abstract In this article, the flow of ternary nanofluid is analysed past a stretching sheet subjected to Thomson and Troian slip condition along with the temperature jump. The ternary nanofluid is formed by suspending three different types of nanoparticles namely $$\text{TiO}_{2}, \text{Cu}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>TiO</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mtext>Cu</mml:mtext> </mml:mrow> </mml:math> and $$\text{Ag}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>Ag</mml:mtext> </mml:math> into water which acts as a base fluid and leads to the motion of nanoparticles. The high thermal conductivity and chemical stability of silver was the main cause for its suspension as the third nanoparticle into the hybrid nanofluid $$\text{Cu-TiO}_{2}/\text{H}_{2} \text{O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>Cu-TiO</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:math> . Thus, forming the ternary nanofluid $$\text{Ag-Cu-TiO}_{2}/\text{H}_{2} \text{O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>Ag-Cu-TiO</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:math> . The sheet is assumed to be vertically stretching where the gravitational force will have its impact in the form of free convection. Furthermore, the presence of radiation and heat source/sink is assumed so that the energy equation thus formed will be similar to most of the real life applications. The assumption mentioned here leads to the mathematical model framed using partial differential equations (PDE) which are further transformed to ordinary differential equations (ODE) using suitable similarity transformations. Thus, obtained system of equations is solved by incorporating the RKF-45 numerical technique. The results indicated that the increase in the suspension of silver nanoparticles enhanced the temperature and due to density, the velocity of the flow is reduced. The slip in the velocity decreased the flow speed while the temperature of the nanofluid was observed to be increasing. 

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Analysis of the Thomson and Troian velocity slip for the flow of ternary nanofluid past a stretching sheet

This study is an attempt to explore two-dimensional magneto-hydrodynamic Casson fluid flow with heat generation or absorption, chemical reaction, and viscous dissipation under the effect of thermal radiation. Prescribed surface temperature (PST) and prescribed heat flux (PHF) cases have been taken into account to investigate the problem. The constitutive relations for Casson fluid incorporated with suitable boundary layer approximation theory have been utilized to achieve the flow model equations. The obtained highly non-linear partial differential equations cannot be solved analytically, so we transform them into first-order differential equations, then tackle them with the boundary value problem (BVP-4c) technique in Matlab. Radiation increment decreases primary and secondary velocity profiles abruptly in both cases. Heat generation and absorption augmentation decrease the thermal and momentum boundaries for both studied cases. The skin coefficient for PHF cases has decreased 80% when compared with PST cases. The increment in Casson parameter has enhanced the Nusselt number by 75% for the PST case, whereas the decline in Nusselt number has doubled for the PHF case with the increase in magnetic field. It is concluded that, with the increment in Casson fluid, magnetic, radiation, and permeability parameter the Nusselt number has significantly increased for the PST case. However, for these parameters, an abrupt decline in Nusselt number has been observed for the PHF case. Results reported in this study for shear stress and Sherwood number are in complete agreement with already published previous work.

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Insight into the Significance of Viscous Dissipation and Heat Generation/Absorption in Magneto-Hydrodynamic Radiative Casson Fluid Flow With First-Order Chemical Reaction

The current analysis concentrated on the consequence of Casson dissipative fluid and spanwise consinusoidally fluctuation temperature on unsteady magnetohydrodynamics free convective flow past a moving hot vertical permeable plate with heat generation, radiation absorption, and chemical reaction. It has imperative practical applications in plentiful fields like physiological processes, biomedical science, food processing, pharmaceutical, chemical material processing engineering, manufacturing systems, and so on. The governing partial differential equations are evaluated analytically by employing a multiple regular perturbation method. The influence of assortment physical estimators on fluid velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number was illustrated quantitatively through graphs. Eventually, it was revealed that velocity, concentration, and Sherwood number declined with the progressive values of the chemical reaction parameter. Velocity and temperature were enhanced with incremental values of Prandtl number, while the contradictory impact occurred in Nusselt number and skin friction. Meanwhile, velocity and skin friction lessened with the incremental values of the magnetic parameter and Casson fluid parameter.

Significance of Casson dissipative fluid and spanwise cosinusoidally fluctuating temperature on unsteady MHD free convective flow past a hot vertical permeable plate with radiation absorption and chemical reaction

The premixed combustion of a lean hydrogen–air mixture is analyzed in this study to examine various properties and flame stabilization. A two‐dimensional (2D) analysis of a microscale combustor is performed with various shapes of bluff bodies (e.g., circular and triangular). Nine bluff bodies are placed at the entrance of the microscale combustor and solved with 2D governing equations. The analysis is performed with the three velocities of 10, 20, and 30 m/s, but the equivalence ratio is fixed in all cases. The various characteristics of the microscale combustor are studied such as the temperature of the wall, difference in peak temperature, the mean velocity at the outlet, and temperature of the exhaust gases. Flame stabilization depends on various factors such as bluff body shape and size, and the velocity of the fuel–air mixture at the inlet and recirculation zone. In comparison to all bluff body cases, we observe that the wall blade bluff body is the most efficient (low exhaust gas temperature, large recirculation zone, low mean velocity at the outlet of the microcombustor, and high wall temperature) compared with all eight other bluff body cases. Combustion efficiency is directly proportional to the wall temperature, meaning that the microcombustor with wall blade bluff bodies is more efficient with a stabilized flame. The simulation results are compared with published data on an L/D ratio of 15.

Optimization of flame stabilization methods in the premixed microcombustion of hydrogen–air mixture

Convective heat transfer and mhd flow through semi-porous cylindrical filters embedded in an impermeable region

Effects of chemical reaction, Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

In the present study, the influence of numerical analysis involves the transfer of heat for moving fin under convection and radiation with fluid properties depending on internal heat generation is considered. The temperature field for the fin is derived based on the defined geometry. This is transformed into a linear model as per the boundary conditions. The dimensionless analysis is performed, and the equations obtained are solved by Runge–Kutta Fehlberg fourth‐order method coupled with the shooting method. The effects of the relative parameters are studied and depicted graphically. Finally, the computational observation indicates that there is an enhancement of temperature variation under the influence of thermal conductivity gradient, heat generation, and opposite behavior results. In understanding the thermal characteristics of various effects, it was seen that thermo geometric film, radiation conduction, and Peclet number were very useful for many industrial applications. To validate the numerical scheme, a comparative study has been done with an earlier result on a few nondimensional parameters and was found in good agreement.

Numerical study of moving fin with thermal properties

This study compares the dynamics of dissipative water–alumina–zinc oxide–iron (II, III) oxide ternary hybrid nanofluid (THNF) and water–alumina–zinc oxide binary hybrid nanofluid flows across an inclined surface when quadratic thermal radiation and chemical reaction are important. This report presents the governing equations for the transportation of both dynamics using the thermo‐physical properties of water (base fluid), alumina nanoparticles, zinc oxide nanoparticles and iron (II, III) oxide nanoparticles. To analyse heat transmission phenomena, the Cattaneo–Christov heat flux model was added into the energy equation. With proper similarity transformations, flow‐driven equations are transformed into nonlinear ordinary differential equations and then solved using the bvp4c solver. Slope of linear regression (SLR) is used to determine the rate at which physical parameters increase or decrease as a result of the influence of relevant factors. It is noticed that, when volume percent of nanoparticles (ϕ1) takes input in the range 0≤ϕ1≤0.3$0 \le {\phi _1} \le 0.3$ , skin friction coefficient decreases at a rate of 16.548 (in case of THNF) and 14.2018 (in case of binary hybrid nanofluid) per unit value of volume percent of nanoparticles. It is detected that when radiation parameter (Rd)$( {{R_d}} )$ increases, Nusselt number decreases. The decrement rates are observed as 2.9451 (in case of THNF) and 1.15337 (in case of binary hybrid nanofluid) when radiation parameter takes input in the range 0≤Rd≤0.3$0 \le {R_d} \le 0.3$ . Furthermore, it is noticed that, when chemical reaction parameter (Kr)$( {{K_r}} )$ increases, Sherwood number increases. The increment rates are observed as 0.1259 (in case of THNF) and 1.1263 (in case of binary hybrid nanofluid) when chemical reaction parameter takes input in the range 0≤Kr≤0.3$0 \le {K_r} \le 0.3$ . There was also good agreement in a validation study between the current and previous results.

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al2O3 + ZnO + Fe3O4) by a quadratically radiated tended elongating surface

In this article, we analytically investigated the effects of fluctuating free stream and suction velocities on unsteady mixed convective flow over a vertical permeable plate in the occurrence of an unvarying porous medium with a thin environment, time-dependent suction, and viscous dissipation. The governing equations of the physical phenomena give rise to a bunch of extremely non-linear coupled PDE's involving various non-dimensional parameters. An analytical solution has been obtained through the plots for distinct chief physical parameters like Grashof number, the amplitude of the fluctuating suction velocity parameter, amplitude of fluctuating free stream velocity parameter, Prandtl number, permeability parameter, solutal Grashof number, and Eckert number, which are involved in the solution. Also, a comparison has been made with published results in the absence of some non-dimensional parameters for a particular case and found in good agreement. The study results that the fluctuating free stream velocity increases the velocity, temperature increases, and a reverse tendency is observed in the Eckert number.

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Suresh Babu Ramakrishna

Papers

Effects of chemical reaction, Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

Numerical study of moving fin with thermal properties

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al2O3 + ZnO + Fe3O4) by a quadratically radiated tended elongating surface

Unsteady Double Diffusive Mixed Convective Flow Over a Vertical Permeable Plate in a Porous Medium