The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation.The governing partial differential equations(PDEs)are converted into ordinary differential equations(ODEs)using the similarity transformation.The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software.It was found that dual solutions exist for the shrinking parameter values up to a certain range.The numerical results obtained are compared,and the comparison showed a good agreement with the existing results in the literature.The governing parameters’effect on the velocity,temperature and nanoparticle fraction fields as well as the skin friction coefficient,the local Nusselt number and the Sherwood number are represented graphically and analyzed.The variation of the velocity,temperature and concentration increase with the increase in the suction and magnetic field parameters.It seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it.

Effects of Greenbelts in Different Variety under Solar Thermal Radiation on Temperature Reduction

[Objective] The aim was to study on effects of greenbelts in different varieties on temperature drop under solar thermal radiation. [Method] In residential regions, effects of temperature reduction by five varieties of greenbelts （megaphanerophyte, dungarunga, shrub, herbaceous plant and bare land） and changing rules with days under the same solar thermal radiation were researched. [Result] Greenbelts＇ temperature changed with intensity of solar thermal radiation, among which greenbelt of megaphanerophyte absorbed, transfered and reflected thermal radiation through crown canopy. Temperature of underlying surface was reduced accordingly, where correlation between underlying surface＇s temperature and solar thermal radiation （R） was 0.156 and the temperature declined by 1.9 ℃. In contrast, correlation of temperature of underlying surface （of lawn） with solar thermal radiation （R） was as high as 0.820, but the temperature only declined by 0.6℃. [Conclusion] The established linear relationship between crown＇s temperature and air temperature actually provides references for temperature measurement of greenbelts at scale.

Dual solutions in boundary layer flow of a moving fluid over a moving permeable surface in presence of prescribed surface temperature and thermal radiation

An analysis of the heat transfer for a boundary layer forced convective flow past a moving permeable flat surface parallel to a moving fluid is presented. Prescribed surface temperature at the boundary is considered, A thermal radiation term in the energy equation is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with the available results for some particular cases of this study. Dual solutions exist when the surface and the fluid move in the opposite directions.

A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization

In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the black body emissive power U will lead to two different definitions of radiation entransy flow and the corresponding principles for thermal radiation optimization. The two definitions of radiation entransy flow and the corresponding optimization prin ciples are compared in this paper. When the total heat flow is given, the optimization objectives of the extremum entransy dissipation principles （EEDPs） developed based on potentials T and U correspond to the minimum equivalent temperature difference and the minimum equivalent blackbody emissive power difference respectively. The physical meaning of the definition based on potential U is clearer than that based on potential T, but the latter one can be used for the coupled heat transfer optimization problem while the former one cannot. The extremum entropy generation principle （EEGP） for thermal radiation is also derived, which includes the minimum entropy generation principle for thermal radiation. When the radiation heat flow is prescribed, the EEGP reveals that the minimum entropy generation leads to the minimum equivalent thermodynamic potential difference, which is not the expected objective in heat transfer. Therefore, the minimum entropy generation is not always appropriate for thermal radiation optimization. Finally, three thermal radiation optimization examples are discussed, and the results show that the difference in optimization objective between the EEDPs and the EEGP leads to the difference between the optimization results. The EEDP based on potential T is more useful in practical application since its optimization objective is usually consistent with the expected one.

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity,and thermal radiation

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.

Numerical Study of High-Temperature Nonequilibrium Flow around Reentry Vehicle Coupled with Thermal Radiation

Accurate aerodynamic heating prediction is of great significance to current manned space flight and deep space exploration missions.The temperature in the shock layer surrounding the reentry vehicle can reach up to 10,000 K and result in remarkable thermochemical nonequilibrium,as well as considerable radiative heat transfer.In general,high-temperature flow simulations coupled with thermal radiation require appropriate numerical schemes and physical models.In this paper,the equations governing hypersonic nonequilibrium flow,based on a three-temperature model combined with a thermal radiation solving approach,are used to investigate the radiation effects in the reentry shock layer.An axisymmetric spherical case shows that coupling the flow-field simulation with radiation has a scarce influence on the convective heating prediction,but has some impact on the radiative heating calculation.In particular,for the Apollo capsule reentry,both the absorption coefficient and incident radiation are remarkable inside the shock layer.The radiative heating maximum reaches nearly 38%of that of the convective heating making a considerable contribution to the total aerodynamic heating.These results indicate that in the hypersonic regime,in order to account for the total heating,it is necessary to simulate the high-temperature thermochemical nonequilibrium flows coupled with thermal radiation.

MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation

This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.

Similarity solutions for the mixed convection flow over a vertical plate with thermal radiation

The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual solutions exist for both cases. Moreover,numerical results show that the heat transfer rate at the surface decreases in the presence of the radiation effect.

Effects of thermal radiation on MHD viscous fluid flow and heat transfer over nonlinear shrinking porous sheet

This paper investigates the effects of thermal radiation on the magnetohy- drodynamic （MHD） flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transfor- mation is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.

Investigation on the thermal radiation properties of antimony doped tin oxide particles

This paper reports the preparation of antimony doped tin oxide crystalline powders by chemical coprecipitation method. The influence of sintering temperature and the sintering retention time on the thermal infrared emissivity is analysed. The thermal infrared reflectivity is measured and the optimum doping concentration is proposed.

Peristaltic flow with convective mass condition and thermal radiation

The primary objective of present investigation is to introduce the novel aspects of convective mass condition and thermal radiation in the peristaltic transport of fluid. Magnetohydrodynamic(MHD) fluid was considered in a symmetric channel. Heat and mass transfer characteristics were analyzed in the presence of Soret and Dufour effects, and the results were presented via two forms of thermal radiation. The temperature, concentration and pressure rise per wavelength were examined. It is observed that the velocity slip and magnetic field parameters have opposite effects on the pressure rise per wavelength. Temperature of fluid is a decreasing function of the radiation parameter. Further, the temperature of fluid decreases by increasing the heat transfer Biot number. It is notified that the heat transfer rate at the wall is a decreasing function of radiation parameter.

Effect of Nonlinear Thermal Radiation on Boundary Layer Flow of Viscous Fluid over Nonlinear Stretching Sheet with Injection/Suction

The present study reveals the effect of nonlinear thermal radiation and magnetic field on a boundary layer flow of a viscous fluid over a nonlinear stretching sheet with suction or an injection. Using suitable similarity transformations, governing partial differential equations were reduced to higher order ordinary differential equations and further these are solved numerically using of Keller-Box method. Effect of flow controlling parameter on velocity, temperature and nanoparticle fluid concentration, local skin friction coefficient, local Nusselt number and local Sherwood numbers are discussed. It is found that the dimensionless velocity decreases and temperature, concentration are increased with the increasing of magnetic parameter. The temperature profile is an increasing function of thermal radiation when it is increasing.

Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

The magnetohydrodynamic(MHD)mixed convection flow past a shrinking vertical sheet with thermal radiation is considered.Besides,the effects of Cu-Al_(2)O_(3) nanoparticles and dust particles are considered.The similarity variables reduce the governing equations to the similarity equations,which are then solved numerically.The outcome shows that,for the shrinking case,the solutions are not unique.The rate of heat transfer and the friction factor enlarge with increasing the values of the copper nanoparticle volume fraction as well as the magnetic parameter.Meanwhile,the assisting flow and the rise of the thermal radiation reduce these quantities.Two solutions are found,and the boundary layer separation is dependent on the mixed convection parameter.

Effects of homogeneous-heterogeneous reactions and thermal radiation on magneto-hydrodynamic Cu-water nanofluid flow over an expanding flat plate with non-uniform heat source

This study presents the effect of non-uniform heat source on the magneto-hydrodynamic flow of nanofluid across an expanding plate with consideration of the homogeneous-heterogeneous reactions and thermal radiation effects.A nanofluid’s dynamic viscosity and effective thermal conductivity are specified with Corcione correlation.According to this correlation,the thermal conductivity is carried out by the Brownian motion.Similarity transformations reduce the governing equations concerned with energy,momentum,and concentration of nanofluid and then numerically solved.The influences of the effective parameters,e.g.,the internal heat source parameters,the volume fraction of nanofluid,the radiation parameter,the homogeneous reaction parameter,the magnetic parameter,the heterogeneous parameter and the Schmidt number are studied on the heat and flow transfer features.Further,regarding the effective parameters of the present work,the correlation for the Nusselt number has been developed.The outcomes illustrate that with the raising of the heterogeneous parameter and the homogeneous reaction parameter,the concentration profile diminishes.In addition,the outcomes point to a reverse relationship between the Nusselt number and the internal heat source parameters.

Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature, and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.

Unsteady flow of a Maxwell hybrid nanofluid past a stretching/shrinking surface with thermal radiation effect

The non-Newtonian fluid model reflects the behavior of the fluid flow in global manufacturing progress and increases product performance.Therefore,the present work strives to analyze the unsteady Maxwell hybrid nanofluid toward a stretching/shrinking surface with thermal radiation effect and heat transfer.The partial derivatives of the multivariable differential equations are transformed into ordinary differential equations in a specified form by applying appropriate transformations.The resulting mathematical model is clarified by utilizing the bvp4c technique.Different control parameters are investigated to see how they affect the outcomes.The results reveal that the skin friction coefficient increases by adding nanoparticles and suction parameters.The inclusion of the Maxwell parameter and thermal radiation effect both show a declining tendency in the local Nusselt number,and as a result,the thermal flow efficacy is reduced.The reduction of the unsteadiness characteristic,on the other hand,considerably promotes the improvement of heat transfer performance.The existence of more than one solution is proven,and this invariably leads to an analysis of solution stability,which validates the first solution viability.