ψ - v Computation of steady-state conjugate heat transfer in backward-facing step flow

In this paper, we study steady-state conjugate heat transfer over a backward-facing step flow using a combination of a compact finite difference scheme for the $\psi$-$v$ form of the Navier–Stokes equations and a higher-order compact scheme for the temperature equations on nonuniform grids. We investigate the effect of Reynolds number ($200\le Re\le 800$), conductivity ratio ($1\le k\le 1000$), Prandtl number ($0.1\le Pr\le 15$), and slab thickness ($h\le b\le 6h$) on the heat transfer characteristics. Isotherms remain clustered near the reattachment point in the fluid, while the temperature in the solid decreases vertically, with the minima at the reattachment point. Heat transfer rate (HTR) increases with Re, the maximum at the reattachment point. The HTR increases with $k$ till $k=100$ after, which it becomes invariant as $k\to \infty$. Isotherms at the inlet become more disorderly with increasing Pr, and progressively clustered near the interface, indicating an increase in HTR, while the temperature in the solid region decreases with Pr. Increasing b decreases the HTR. In addition to obtaining an excellent match with results previously reported in the literature, we offer more comprehensive and previously unreported insights on flow physics.     

Boundary layer flow and stability analysis of forced convection over a diverging channel with variable properties of fluids

The objective of the current study is to investigate the forced convection laminar boundary layer flow over a flat plate in a diverging channel with variable viscosity. The physical governing equations are converted to nondimensional partial differential equations (PDEs) using similarity transformation. The coupled PDEs with boundary constrains are solved numerically using quasilinearization technique. Computational results are given in terms of flow parameter $ϵ\left(0<ϵ<1\right)$, suction or injection A, and viscous dissipation parameter Ec. Stability analysis was conducted and the solutions were found to be stable for real values of $\gamma$. We found that variable Prandtl number with quasilinearization technique method gives smoothness of solution compared to fixed Prandtl number. This is shown graphically for different fluids in Section 5. Also, the significant effect of the suction/injection parameter $\left(A\right)$ on velocity, temperature profiles, skin friction, and heat transfer is observed.     

Non-Newtonian electromagnetic fluid flow through a slanted parabolic started Riga surface with ramped energy

The present study deals with the implications of non-Newtonian fluid via a slanted parabolic started surface with ramped energy. In addition, the characteristics of electrically conducting viscoelastic liquid moving across the Riga surface are investigated systematically, emphasized within the time-dependent concentration and temperature variations. The mathematical model is made possible by enforcing momentum and heat conservation principles in the format of partial differential equations (PDEs). Heat considerations are emphasized with respect to radiant heat influx. Similarity characteristics are leveraged to convert PDEs to ordinary differential equations. The Laplace transform method is used to find the exact solutions for the obtained differential configuration. The effect of flow on associated patterns is depicted graphically and with tables. Furthermore, fluctuation in relevant engineering parameters such as wall shear stress, temperature, and mass variability on the surface is measured. The range of parameters selected is as follows: $\psi [0.1-1]$, $Pr[0.71-10]$, $Sc[0.16-2.01]$, $Gr=Gc[5-20]$, $E[1-5]$, and $R[2-10]$. The analytical and numerical solutions are validated and in good agreement. It is worth reporting that the improved Hartmann number and thermal radiation values boost velocity dispersion and skin friction. As expected, respectively, energy and mass transfer rates are escalated with large values of Prandtl number and Schmidt number.     

Influence of a curved conical turbulator on heat transfer augmentation in a helical double-pipe heat exchanger

The rate of heat transfer in helical pipes is much more than straight pipes. In the present study, heat transfer and fluid flow in a double-coil heat exchanger with an innovative swirl generator with a curved structure in the inner channel (hot side) are studied, numerically. The proposed turbulator has a curved structure and 12 blades to produce swirl flows. Also, two holes are considered at the semi-conical part of the turbulator. The effects of geometrical parameters of the proposed turbulator including the inner radius of the turbulator and the radius of the turbulator's holes are evaluated. Results indicate that the maximum effectiveness belongs to the case with inner diameter of the turbulator and radius of turbulator' holes equal to 19 and 3.6 mm, respectively, at $\dot{m}=0.008\mathrm{k}\mathrm{g}\mathrm{/}\mathrm{s}$. Also, the generated swirl flows by the turbulator has a significant influence on heat transfer augmentation. Furthermore, a high inner radius of the turbulator leads to an increase in heat transfer rate and effectiveness, consequently. As a result, by increasing the inner radius of turbulator by 26.7%, the effectiveness rises by 80% (maximum at $\dot{m}$ = 0.008 kg/s). Increasing the radius of turbulator's hole by 133.34% leads to an growth in effectiveness of about 50% (maximum at $\dot{m}$ = 0.058 kg/s).     

A mathematical simulation of unsteady MHD Casson nanofluid flow subject to the influence of chemical reaction over a stretching surface: Buongiorno's model

In this study, unsteady boundary layer flow with Casson nanofluid within the sight of chemical reaction toward a stretching sheet has been analyzed mathematically. The fundamental motivation behind the present examination is to research the influence of different fluid parameters, in particular, Casson fluid $\beta (0.2\le \beta \le 0.4)$, thermophoresis $Nt(0.5\le Nt\le 1.5)$, magnetohydrodynamic $M(3.0\le M\le 5.0)$, Brownian movement $Nb(0.5\le Nb\le 2.0)$, Prandtl numberty, unsteadiness parameter $A(0.10\le A\le 0.25)$, chemical reaction parameter $\gamma (0.1\le \gamma \le 0.8)$, and Schmidt number $Sc(1.0\le Sc\le 3.0)$ on nanoparticle concentration, temperature, and velocity distribution. The shooting procedure has been adopted to solve transformed equations with the assistance of Runge–Kutta Fehlberg technique. The impact of different controlling fluid parameters on flow, heat, and mass transportation are depicted in tabular form and are shown graphically. Additionally, values of skin friction coefficient, Nusselt number, and Sherwood number are depicted via tables. Present consequences of the investigation for Nusselt number are related with existing results in writing by taking $Nb=0$ and $Nt=0$ where results are finding by utilization of MATLAB programming. Findings of current research help in controlling the rate of heat and mass aspects to make the desired quality of final product aiding manufacturing companies and industrial areas.