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This paper is dedicated to the comparison of discrete velocity models (DVM) used for the simulation of heat transfer and fluid flows in the lattice Boltzmann method (LBM). In this study, the discrete velocity models of D2Q9 and D2Q8 in which particle velocity vectors are eight are used in simulating four benchmark problems. An enhancement in the stability of the single relaxation time (SRT) model for problems is facilitated by solving the continuous Boltzmann equation, and its application in efficiently addressing conductive heat transfer/fluid flow benchmark problems is expanded by utilizing the finite difference methods paired with the lattice Boltzmann method (FDLBM). To generalize the paper’s conclusion more accurately, the LBM with two-relaxation time (TRT-LBM) is included in all comparisons. A D2Q5 scheme is also considered to understand how it would address heat transfer problems compared to the ones presented. Moreover, an improvement in the accuracy of the FDLBM for some cases is assisted through the integration of the finite differentiation mechanism with the Runge–Kutta method. A series of unsteady and steady problems were numerically solved to validate the introduced methods. The outcomes affirmed that the proposed FDLBM algorithm procures more stable and robust results compared to those derived from the DVMs of SRT-LBM devoid of filtering techniques. Notably, the FDLBM method achieves this increased accuracy without introducing additional complexity to the SRT model by resorting to nonuniform grids. The decision to exclude more complex methods stems from their requirement for refined computational grids. To ascertain the numerical stability and accuracy of the devised algorithm, a comparative analysis was performed with analytical results or other numerical methods. The simulations underscored the efficacy of the current method, showcasing commendable harmony with analytical solutions and other numerical strategies. [ABSTRACT FROM AUTHOR]

Motile cilia are hair-like, tiny structures that originate in different types of biological processes. Yeleswarapu fluid model is approximated as non-Newtonian mucus, which is viscous and slippery fluid with key roles in lubrication, protection, and particle trapping in the respiratory and digestive systems. The properties of Yeleswarapu fluid with heat transfer in ciliated channels are investigated in this study. The fluid flow is characterized as laminar (low Reynold number) and incompressible (constant density) in a two-dimensional complex wavy channel generated via metachronal waves of cilia. A static frame of reference is first transformed into a dynamic frame of reference. Afterward, the system of governing equations is transformed into a non-dimensional form by using scaling factors. The half-width of the channel is substantially smaller than the wavelength of metachronal waves. Hence, the constitutive equations are simplified by the long wavelength hypothesis. The perturbation approach is employed to solve the simplified system of differential equations. This research investigates how different boundary walls and rheology affect fluid flow. Additionally, graphs of the streamlines, velocity field, temperature, heat transfer coefficient, and pressure rise are included. [ABSTRACT FROM AUTHOR]

The study offers a thorough evaluation of the complex fluid dynamics and heat transfer phenomena in Williamson viscoelastic fluid flow, taking into account thermal radiations and variable thermal conductivity. The paper extends its analysis to include heat transfer effects, which are critical in several engineering and industrial applications, and digs into the complexity of non-Newtonian fluid behavior, with a special focus on thermal radiation, heat production, diffusion and viscous dissipation. The study makes use of mathematical models and numerical method RK4 to clarify the nonlinear interactions between convection and diffusion processes in this viscoelastic fluid. The energy and concentration equations are simulated in the presence of the modified Fourier and Fick laws. Moreover, the predicted heat flow is based on the Cattaneo–Christov theory. This research also sheds light on the interaction between rheological properties and thermal characteristics, providing important new knowledge to the broader field of fluid dynamics and heat transfer. [ABSTRACT FROM AUTHOR]

This work gives an insight into the viscous effects of a viscoelastic fluid on the flow and heat transfer when it is put to flow between two nonparallel plates via some source/sink. Modeling of the problem is presented in detail with focus on the viscous dissipation effect. Afterwards, the problem is solved numerically by Keller Box method and bvp4c routine using MATLAB. The comparative analysis of the two techniques has been drawn on the basis of numerical values of Nusselt number. Alongside this, a comprehensive detail of the impact of pertinent parameters on the flow and temperature profiles have been given. The numerical results give an insight about the fluid characteristics like velocity, temperature, heat transfer and skin friction with variations in pertinent physical parameters. [ABSTRACT FROM AUTHOR]

This research offers an analysis of the mixed convective transient boundary film Casson fluid stream and thermal distribution through a vertical sheet. Viscous dissipation and the Soret effect are introduced to support the flow in stimulating heat capacity. Unlike typical investigations, the present flow-formulated model is done to capture an induced magnetic field. The Boussinesq approximation is used to describe the nonlinear formulated partial derivatives governing the heat transfer fluid that is non-dimensionalized using suitable dimensionless quantities. The transformed partial derivative model is numerically solved via the spectral Chebyshev technique and the results of shear stress, current density, Nusselt number, and mass gradient are tabulated. The role of numerous terms on dimensionless flow rate, induced velocity, and heat transfer with species distribution is discussed in a very effective way. Velocity and temperature of liquid decline as boosting the material parameter. Enhancing values G r , G r m favor the flow momentum and oppose the temperature profile. [ABSTRACT FROM AUTHOR]

The Casson viscous gas fluid flow with mass transpiration and radiation is demonstrated in this paper. A similarity transformation is utilized to interpret the representing construction of nonlinear PDEs by nonlinear ODEs. Then, using an exact analysis of the momentum equation, we constructed the dual solutions to the flow problem. This solution domain aids in the solution of the energy equation under the incomplete gamma function condition. The effect of radiation can also be seen in the heat equation. Physical parameters of interest, such as Brinkman number, porous media, thermal radiation number, induced slip, suction/injection and shear stress, are examined and graphically depicted. The gas slip velocity is used to simulate the slip flow model of the overall mass transfer on the moving sheet. Models of first- and second-order slip are introduced to induce the total mass transfer on the moving sheet. Additionally, the suction that causes the slip velocity rather than surface movement is investigated. The neighboring gases are forced to flow in the opposite direction of sheet movement by the mass suction-induced slip. As a result, the slip-induced suction and sheet movement cause the solution space to increase. The closed-form exact solutions are achieved for both the stretching and shrinking sheet cases. For stretched sheet instances, there is never a uniform solution. However, depending on the values of the Casson and wall mass transfer parameters, the solution in the case of the shrinking sheet may or may not exist, and if it does, it may or may not be unique or may have a dual nature. The research also demonstrates that stronger mass suction is required for a consistent flow of Casson fluid. The impacts of inverse Darcy number, induced slip parameter, Casson fluid and suction/injection on the flow and heat transfer properties of the fluid are examined under the influence of radiation, and the solution of each profile is shown in the form of figures along with the outcomes of the interface velocity and heat transfer rate at the surface. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than 1 0 0 % has been observed in f Re , whereas maximum decrease in dilatant fluid is around 3 0 % , when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k. [ABSTRACT FROM AUTHOR]

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software's algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor. [ABSTRACT FROM AUTHOR]

In recent years, physics-informed neural networks (PINNs) have come to the foreground in many disciplines as a new way to solve partial differential equations. Compared with traditional discrete methods and data-driven surrogate models, PINNs can learn the solutions of partial differential equations without relying on tedious mesh generation and simulation data. In this paper, an original neural network structure PINN-FFHT based on PINNs is devised to solve the fluid flow and heat transfer problems. PINN-FFHT can simultaneously predict the flow field and take into consideration the influence of flow on the temperature field to solve the energy equation. A flexible and friendly boundary condition (BC) enforcement method and a dynamic strategy that can adaptively balance the loss term of velocity and that of temperature are proposed for training PINN-FFHT, serving to accelerate the convergence and improve the accuracy of predicted results. Three cases are predicted to validate the capabilities of the network, including the laminar flow with the Dirichlet BCs in heat transfer, respectively, under the Cartesian and the cylindrical coordinate systems, and the thermally fully developed flow with the Neumann BCs in heat transfer. Results show that PINN-FFHT is faster in convergence speed and higher in accuracy than traditional PINN methods. [ABSTRACT FROM AUTHOR]

With the help of commercial software, we have discussed the novel numerical simulations for a two-dimensional rectangular cavity with two square rotating obstacles, Fig. 1, that has fixed dimensions from the reference point (0, 0) placed in it, and we have interpreted a detailed convection analysis for fluid flow that highlights the physical, mathematical and numerical aspects of this system. The square obstacles having an anti-clockwise rotation are heated to a certain temperature, respectively, where the behavior of the fluid distribution depends upon the values of Reynolds number. We have conducted this research by fixing Reynolds number at four different positions like Reynolds 10, 30, 50 and 80. The prime effects of Reynolds number and Prandtl number are highlighted for convection analysis. Finally, we have analyzed the results of velocity, pressure, vorticity and temperature from the viewpoint of numerical simulations. Heat transfer has a huge dependence on the Reynolds number and Prandtl number. [ABSTRACT FROM AUTHOR]

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement. [ABSTRACT FROM AUTHOR]

A numerical solution for steady-state, incompressible, laminar Casson fluid flow and heat transfer in the combined region of a boundary layer is presented for the case of mixed convection and slip velocity. Before introducing the present technique of non-Newtonian Casson model, reviewing the literature has been carefully performed, an improved technique for this model is studied, which has not been previously reported. The presented analysis involves the harness of a magnetic field, viscous dissipation, internal heat generation/absorption and the slip velocity. Finite difference method (FDM) has been used to get an accurate and complete numerical solution. In this novel study, it is proved by means of a finite difference technique, that the velocity and the thermal field may be influenced with the presence of mixed convection phenomenon. The results show that both the fluid velocity and temperature may be predicted from the values of the controlling parameters. Finally, the graphical output reveals that the fluid velocity is diminished by strengthening both the Hartman number and the Casson parameter while the reverse characteristics are observed for the Grashof number. [ABSTRACT FROM AUTHOR]

The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The nondimensional conservation equations for mass, momentum and energy are solved using a Crank–Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter, the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems. [ABSTRACT FROM AUTHOR]