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The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters.

The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders.

As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases.

The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

The purpose of this paper is to discuss the flow of Casson nanofluid past a nonlinear permeable stretching sheet in the presence of thermal radiation, chemical reaction, viscous dissipation, heat source, and magnetohydrodynamics.

Appropriate transformations are used to convert the boundary layer equations into nonlinear ODEs which are then solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique.

Solution of this systems is obtained for velocity, temperature, and concentration profiles. Graphical illustrations are added to discuss the effect of evolving parameters against above-mentioned distributions. Tabular values of local skin friction factor, local Nusselt number, and local Sherwood number are also added and studied accordingly.

A good agreement of the present results has been observed by comparing with the existing literature results. It is noted that skin friction coefficient, Nusselt number, and Sherwood number decrease with Casson parameter and increase with suction parameter.

The purpose of this paper is to examine the flow, heat transfer and entropy generation characteristics for an inclined channel of two immiscible micropolar fluids.

The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. The flow is assumed to be governed by Eringen’s micropolar fluid flow equation. The resulting governing equations are then solved using the homotopy analysis method.

The following findings are concluded: first, the entropy generation rate is more near the plates in both the zones as compared to that of the interface. This indicates that the friction due to surface on the fluids increases entropy generation rate. Second, the entropy generation rate is more near the plate in Zone I than that of Zone II. This may be due to the fact that the fluid in Zone I is more viscous. This indicates the more the viscosity of the fluid is, the more the entropy generation. Third, Bejan number is the maximum at the interface of the fluids. This indicates that the amount of exergy (available energy) is maximum and irreversibility is minimized at the interface between the fluids. Fourth, as micropolarity increases, entropy generation rate near the plates decreases and irreversibility decreases. This indicates an important industrial application for micropolar fluids to use them as a good lubricant.

The problem is original as no work has been reported on entropy generation in an inclined channel with two immiscible micropolar fluids.

This paper aims to investigate the entropy generation due to magnetohydrodynamic natural convection flow and heat transfer in a porous enclosure filled with Cu-water nanofluid in the presence of viscous dissipation effect. The left and right walls of the cavity are thermally insulated. There are heated and cold parts, and these are placed on the bottom and top wall, respectively, whereas the remaining parts are thermally insulated.

The finite volume method is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published woks is presented and is found to be in an excellent agreement.

The minimization of entropy generation and local heat transfer according to different values of the governing parameters are presented in details. It is found that the presence of magnetic field has negative effects on the local entropy generation because of heat transfer and the local total entropy generation. Also, the increase in the heated part length leads to a decrease in the local Nusselt number.

This problem is original, as it has not been considered previously.

The purpose of this paper is to address the combined effects of thermal radiation and chemical reaction on steady MHD mixed convective heat and mass transfer flow past a vertical surface under the influence of Joule and viscous dissipation.

The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique.

With the help of graphs, the effects of the various important parameters entering into the problem on the dimensionless velocity, dimensionless temperature and dimensionless concentration fields within the boundary layer are discussed. The authors noticed that the velocity increases with an increase in the porosity parameter. An increase in the Prandtl number Pr, decreases the velocity and the temperature field. An increase in the radiation parameter, decreases the velocity and the temperature field. Also the effects of the pertinent parameters on the skin-friction coefficient and rates of heat and mass transfer in terms of the Nusselt and Sherwood numbers are presented numerically in tabular form.

To the best of the authors’ knowledge, recent this work has not been finished by any other researchers.

The purpose of this paper is to address the impact of gravity induced stretching flow of second grade liquid subject to thermal radiation. The flow is generated by the stretching of an impermeable cylinder. Stagnation point flow is considered. Convective type boundary conditions are applied on temperature and concentration. The present investigation further includes the aspects of magnetohydrodynamics, Joule heating, chemical reaction and viscous dissipation and heat generation/absorption.

The ordinary differential expressions are formed using suitable similarity transformations from the governing partial differential expressions. The subsequent nonlinear ordinary differential expressions are solved analytically using homotopy concept to report the consequences of different dimensionless physical parameters in graphical and tabular forms.

The results witnessed that increasing values of curvature parameter corresponds to higher temperature and concentration. Besides this, the impacts of destructive and constructive chemical processes on the concentration distribution are noted opposite.

No such analysis has yet been reported.

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

The purpose of this study is to present a comprehensive hydrothermal analysis on an inclined mini-channel using numerical and experimental techniques. The fin array acts as heat source within the channel, and a wavy wall located at the top of the channel is heat sink. The side walls are insulated with curved profiles. Also, the channel is inclined with four known inclination angles. To solve the governing equations, the dual-multi-relaxation-time lattice Boltzmann method with D2Q9 and D2Q5 lattice models for flow and temperature fields is used, respectively. Also, the channel is filled with SiO2-glycol nanofluid.

Identifying the behavior of a thermal component during natural convective flow is a challenging topic due to its complexities. This paper focuses on analyzing the thermal and hydrodynamic aspects of a narrow channel equipping with fin array.

Two correlations are proposed considering temperature and volume fraction ranges for thermal conductivity and dynamic viscosity according to measured experimental data which are used in the numerical phase. Finally, the structure of flow, temperature distribution of fluid, local thermal and viscous dissipations, volume-averaged entropy production, Bejan number and heat transfer rate are extracted by numerical simulations. The results show that the average Nusselt number enhances about 57% (maximum enhancement percentage) when volume fraction increases from 1% to 3% at Ra = 10⁶ and θ = 90°. In addition, the value of entropy generation is maximum at φ = 1%, Ra = 10⁶ and φ = 90°. Also, the maximum enhancement of entropy generation in range of Ra = 103 to 106 is about 4 times at φ = 1% and θ = 90°.

The originality of the present study is combining a modern numerical method (i.e. dual/multi-relaxation-time LBM) with experimental observation on characteristics of SiO₂-glycol nanofluid to study the thermal and hydrodynamic properties of the studied mini-channel.

A direct numerical simulation with turbulent transport of a scalar quantity has been carried out to grasp and understand a laminarization phenomena caused by a pipe rotation. In this study, the Reynolds number, which is based on a bulk velocity and a pipe diameter, was set to be constant; Re_b=5283, and the rotating ratios of a wall velocity to a bulk velocity were set to be 0.5, 1.0, 2.0 and 3.0. A uniform heat‐flux was applied to the wall as a thermal boundary condition. Prandtl number of the working fluid was assumed to be 0.71. The number of computational grids used in this study was 256×128×128 in the z‐, r‐ and ϕ‐ directions, respectively. The turbulent quantities such as the mean flow, temperature fluctuations, turbulent stresses and pressure distribution and the turbulent statistics were obtained. Moreover, the Reynolds stress and the scalar flux budgets were also obtained for each rotating ratio. The turbulent drag decreases with the rotating ratio increase. The reason of this drag reduction can be considered that the additional rotational production terms appear in the azimuthal turbulence component. The contributions of convection and production terms to the radial scalar flux budget and also to the balance with temperature‐pressure gradient term are significant. The dissipation and viscous diffusion terms are negligible in higher rotating ratio.

Physical properties of a viscous fluid, e.g. viscosity and thermal conductivity change with temperature and in most of the studies concerned with natural convection, generally, the simultaneous effect of temperature dependent viscosity, thermal conductivity have been neglected. Hence, the purpose of this paper is to investigate the simultaneous effects of varying viscosity and thermal conductivity on free convection flow of a viscous incompressible electrically conducting fluid and heat transfer along an isothermal vertical non‐conducting plate in the presence of exponentially varying internal heat‐generation and uniform transverse magnetic field.

The governing equations of motion and energy are transformed into ordinary differential equations using similarity transformation. The resulting boundary valued, coupled and non‐linear differential equations are converted into system of linear differential equations and solved using Runge‐Kutta fourth order technique along with shooting method.

It was found that: fluid velocity decreases with the increase in magnetic parameter or Prandtl number; fluid temperature increases with the increase in magnetic parameter; velocity and temperature profiles increase due to increase in heat generation parameter; varying viscosity and thermal conductivity modifies the flow and heat transfer characteristic; and skin‐friction and heat transfer are affected by simultaneous change in viscosity and thermal conductivity in presence/absence of exponentially varying heat generation.

The present study is applicable to an incompressible viscous fluid flow and heat transfer with linearly varying viscosity and thermal conductivity.

This paper provides useful information on the physical properties of a viscous fluid with regard to viscosity and thermal conductivity change with temperature.