Symmetry analysis of MHD Casson fluid flow for heat and mass transfer near a stagnation point over a linearly stretching sheet with variable viscosity and thermal conductivity

In this article, the impacts of variable viscosity and thermal conductivity on magnetohydrodynamic, heat transfer, and mass transfer flow of a Casson fluid are analyzed on a linearly stretching sheet inserted in a permeable medium along with heat source/sink and viscous dissipation. To reduce the ascendant partial differential equations into ordinary differential equations, Lie group transformation is utilized. Further, the fourth-order Runge–Kutta strategy is utilized to solve the ordinary differential equations numerically. The numerical results obtained for various parameters by employing coding in MATLAB programming are investigated and considered through graphical representation and tables. We anatomize the impacts of distinctive parameters on velocity, temperature, and concentration distributions.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet

The influence of temperature-dependent fluid properties on the hydro-magnetic flow and heat transfer over a stretching surface is studied. The stretching velocity and the transverse magnetic field are assumed to vary as a power of the distance from the origin. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. Using the similarity transformation, the governing coupled non-linear partial differential equations are transformed into coupled non-linear ordinary differential equations and are solved numerically by the Keller–Box method. The governing equations of the problem show that the flow and heat transfer characteristics depend on five parameters, namely the stretching parameter, viscosity parameter, magnetic parameter, variable thermal conductivity parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, skin friction, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are discussed.     

Single-phase pressure drop and heat transfer characteristics of turbulent liquid nitrogen flow in micro-tubes

Experiments have been conducted to investigate the single-phase pressure drop and heat transfer characteristics of liquid nitrogen in four micro-tubes with the diameters of 1.931, 1.042, 0.834 and 0.531 mm. The friction factors are compared with the conventional correlations over a Reynolds number range of 10,000–90,000. The effect of the variable thermal properties of liquid nitrogen, i.e., viscosity and thermal conductivity, on the flow and local heat transfer in the micro-tubes is clarified. The average Nusselt numbers are determined and compared with the correlations for the conventional channels and micro-channels, respectively. It is found that large roughness of the micro-tube causes high friction factor, and the modified Colebrook correlation can well predict the experimental friction factors by using the measured surface roughness. With the increase of liquid nitrogen temperature, the pressure drop decreases as a result of the lower viscosity. Opposite to water, the local heat transfer coefficient of liquid nitrogen flow in the micro-tube drops by 12.5% along the tube. The experimental data show that the average Nusselt numbers for the micro-tubes are higher than those predicted by the correlations for the conventional channels. Taking into account the effect of surface roughness of the micro-tubes on the heat transfer, the modified Gnielinski correlation enables to predict the experimental Nusselt numbers with a mean absolute error (MAE) of 6.4%.     

The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating

A numerical study of heat transfer from boundary layer flow driven by a continuous moving porous plate is proposed. The flow with electrically fluid due to the plate in the presence of a transverse magnetic field and Ohmic heating was molded as a steady, viscous, and incompressible. Both viscosity and thermal conductivity were variable and considered only a function of temperature. Similar analysis with Chebyshev finite difference method (ChFD) was developed to solve the governing equations for momentum and energy and determine the skin-friction coefficient and heat transfer rate. As the magnetic parameter and variable viscosity parameter increase, the fluid temperature and skin-friction coefficient increase and the fluid velocity and heat transfer rate decrease. The fluid temperature increases and heat transfer rate decreases with an increasing Eckert number and thermal conductivity parameter. The skin-friction coefficient and heat transfer rate increase, whereas the fluid velocity and temperature decrease as the wall suction velocity increase.     

Uncertainties in physical property effects on viscous flow and heat transfer over a nonlinearly stretching sheet with nanofluids

The purpose of this paper is to investigate a numerical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet utilizing nanofluid. The governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are considered in our problem. Furthermore, four different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. The variations of dimensionless surface temperature, dimensionless surface temperature gradient as well as the flow and heat transfer characteristics with the governing parameters are graphed and tabulated. Comparison with published results for pure fluid flow is presented and it is found to be in excellent agreement.     

The heat transfer and fluid flow of a partially heated microchannel heat sink

Numerical modeling of the conjugate heat transfer in microchannel heat sink is presented. As the most of the cooling applications deals with the partial heated sections, the influence of the heating position on the thermal and hydrodynamic behavior is analyzed. The laminar fluid flow regime and the water as a working fluid are considered. It is observed that partial heating together with variable viscosity has a strong influence on thermal and hydrodynamic characteristics of the micro-heat sink.     

Analysis of heat transfer characteristics of double-layered microchannel heat sink

Numerical analysis is performed to examine the heat transfer characteristics of a double-layered microchannel heat sink. The three-dimensional governing equations are solved by the finite volume method. The effects of substrate materials, coolants, and geometric parameters such as channel number, channel width ratio, channel aspect ratio, substrate thickness, and pumping power on the temperature distribution, pressure drop, and thermal resistance are discussed. Predictions show that the heat transfer performance of the heat sink is improved for a system with substrate materials having a higher thermal conductivity ratio. A coolant with high thermal conductivity and low dynamic viscosity also enhances the heat transfer performance. The pressure drop decreases with the channel aspect ratio and channel width ratio. Further, the thermal resistance of the microchannel heat sink can be minimized by optimizing the geometric parameters. Finally, the results show that for the same geometric dimensions, the thermal performance of the double-layered microchannel heat sink is better than that of the single-layered one, by an average of 6.3%.     

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

The bivariate spectral quasilinearization method (BSQLM) on overlapping grids is presented and applied in the analysis of unsteady magnetohydrodynamic mixed convection flow of Eyring‐Powell fluid over an oscillatory stretching sheet embedded in a non‐Darcy porous medium with nonlinear radiative heat flux and variable thermophysical properties. The fluid properties, namely the fluid viscosity, thermal conductivity, and mass diffusivity, are assumed to vary with temperature. It is assumed that the first‐order chemical reaction with heat generation/absorption takes place in the flow. The flow domain is subject to uniform transverse magnetic field perpendicular to the stretching surface. The transformed flow equations are solved numerically using BSQLM on overlapping grids. The convergence properties and accuracy of the method are assessed. The proposed method is computationally efficient, and it gives stable and highly accurate results after few iterations and using few grid points in each subinterval. The improved accuracy rests upon the use of the overlapping grid, which produces sparse coefficient matrices that are easy to invert and have small condition numbers. The effects of physical parameters on the flow fields, local skin friction, the Nusselt number, and the Sherwood number are exhibited through graphs and tables. Amongst other findings, we found that the amplitude of the fluid flow along with flow characteristics may efficiently improve through the utilization of variable fluid viscosity. Heat and mass transportation processes enhance with the inclusion of nonlinear radiative heat flux, temperature‐dependent thermal conductivity, and mass diffusion coefficient, whereas they diminish with the increase in the local inertia coefficient. The current flow analysis can be useful in various engineering applications including paper production, polymer solution, glass blowing, extrusion of thermal system manufacturing process, and heat transportation enhancement.     

Multislip and Soret–Dufour influence on nonlinear convection flow of MHD dissipative Casson fluid over a slendering stretching sheet with generalized heat flux phenomenon

In the present investigation, Soret–Dufour and multislip's impact on magnetohydrodynamics (MHD) Casson fluid flow encompassing variable thermophysical features in the nonlinear convection process is analyzed. It is believed that to any effective heat and mass transfer enhancement, the relaxation of such fluid and material time along with the thermo-physical features, are well estimated. In this model, a magnetic field of nonuniform strength is applied perpendicular to the slendering sheet with variable thickness, and nonlinear convection flow is considered in this generalized heat flux examination. An appropriate similarity variable is implemented on the governing equations embedding the variable viscosity, thermal conductivity, and generalized Fourier's law to drive ordinary differential equations. Galerkin weighted residual approach is utilized to calculate the flow field among other flow characteristics. The novel flow features are discussed therein. Modified Fourier and multislip's parameters are seen to have downsized the velocity and temperature field greatly. Thermal and solutal buoyancy effects are more pronounced in nonlinear form compared to the linear model. Dufour number influences both velocity and energy fields positively but negates the concentration field, while the Soret number gives an opposing characterization.     

Thermally radiative slip flow of viscous fluid through a microfluidic vessel having sinusoidal walls with variable viscosity

This article explores the influence of variable viscosity on the peristaltic movement of viscous fluid through a tapered microfluidic vessel having sinusoidal walls. The aspect of slip velocity has been considered on the channel walls. Furthermore, the heat transfer phenomenon is explored under the effectiveness of thermal radiation and viscous dissipation. The nonlinearity of the problem is scrutinized by the lubrication approximation hypothesis. Analytic outcomes have been acquired for liquid velocity, temperature, pressure rise, and streamlines. The impact of dissimilar physical parameters influencing the liquid flow features is revealed and deliberated through graphs. The study revealed that the velocity at the central region diminishes with increasing values of the velocity slip parameter. The number of boluses in the streamlines pattern is enhanced by enhancing the viscosity parameter. The current model has been used in bio-engineering processes, industrial fluid mechanics, thermal processing, and cooling systems.     

Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source

In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters.     

Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime

We have measured the pressure drop and convective heat transfer coefficient of water-based Al₂O₃ nanofluids flowing through a uniformly heated circular tube in the fully developed laminar flow regime. The experimental results show that the data for nanofluid friction factor show a good agreement with analytical predictions from the Darcy’s equation for single-phase flow. However, the convective heat transfer coefficient of the nanofluids increases by up to 8% at a concentration of 0.3 vol% compared with that of pure water and this enhancement cannot be predicted by the Shah equation. Furthermore, the experimental results show that the convective heat transfer coefficient enhancement exceeds, by a large margin, the thermal conductivity enhancement. Therefore, we have discussed the various effects of thermal conductivities under static and dynamic conditions, energy transfer by nanoparticle dispersion, nanoparticle migration due to viscosity gradient, non-uniform shear rate, Brownian diffusion and thermophoresis on the remarkable enhancement of the convective heat transfer coefficient of nanofluids. Based on scale analysis and numerical solutions, we have shown, for the first time, the flattening of velocity profile, induced from large gradients in bulk properties such as nanoparticle concentration, thermal conductivity and viscosity. We propose that this flattening of velocity profile is a possible mechanism for the convective heat transfer coefficient enhancement exceeding the thermal conductivity enhancement.     

Design optimization of heat exchangers with high‐viscosity fluids

The thermal effectiveness and entropy generation of parallel and counter‐flow heat exchangers handling high‐viscosity fluids have been numerically investigated. Both the viscous friction and the viscosity variations with temperature were considered in the analysis. The results show that the thermal effectiveness–NTU curves deviate gradually from the curves obtained using the assumption that the effect of viscosity is negligible. Moreover, the consideration of the viscous frictional heating effect results in a considerable increase in the heat exchanger entropy. An optimum heat exchanger size could be determined from both first law and second law of thermodynamics points of view. The results show also that the effect of viscous friction with variable viscosity becomes more significant for lower inlet temperatures of high‐viscosity fluid. Copyright © 2002 John Wiley & Sons, Ltd.     

Thermophoresis particle deposition on unsteady two-dimensional forced convective heat and mass transfer flow along a wedge with variable viscosity and variable Prandtl number

In this paper, the effects of thermophoresis particle deposition on an unsteady two dimensional forced convective heat and mass transfer flow past a wedge taking into account the variation of fluid viscosity and fluid Prandtl number with temperature are studied. The local similarity equations are derived and solved numerically using Nachtsheim–Swigert shooting iteration technique along with the sixth order Runge–Kutta integration scheme. Comparisons with previously published work are performed, and the results are found to be in excellent agreement. Results for the non-dimensional velocity, temperature, concentration, Prandtl number and thermophoretic velocity are displayed graphically whereas thermophoretic deposition velocity is shown in the tabulated form for various values of the pertinent parameters. The obtained numerical results show that in modeling the thermal boundary-layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results, and therefore, it must be treated as a variable rather than a constant within the boundary layer. The results also show that the thermophoretic particle deposition velocity decreases as the thermophoretic coefficient increases.     

物性参数对环形空间流动和传热影响的模拟研究

利用有限容积法,建立了环形空间内单相流体竖直向上流动过程中流动和传热的稳态模型。模型将环形空间内管设置为具有固定生热速率的发热体;流体与内管壁之间设置流动和传热边界层,以更精确的描述壁面位置流体与固体之间动量和热量的耦合传递过程。通过与常物性模型的对比,流体密度、导热系数和黏度随温度变化的变物性模型,在传热能力上具有一定的减少,流体与固体传热面之间的界面剪切力稍有下降。通过比较常物性模型和变物性模型的Re和Ri,结果表明,随着流体强制循环速度的加大,流体物性变化对流动和传热过程的影响逐渐减小。     

扰流柱对间断交叉肋流动换热特性的影响研究

为了探究扰流柱对间断交叉肋通道流动与换热特性的影响,针对不同扰流柱数量和排布位置建立了不同的交叉肋模型,并通过数值模拟的方法,计算了各模型的阻力系数比、强化换热系数以及综合热效率3个性能指标的变化情况。研究结果表明：随着扰流柱数量的增大,阻力系数比和强化换热系数逐渐增大,而综合热效率不断下降;在进口雷诺数为20 000时,14柱模型与32柱模型相比,阻力系数比升高了15.4%,强化换热系数升高了32%,综合热效率提高了2.6%;将相同数量的扰流柱排布在通道内的不同位置对综合热效率的影响并不明显。     

Impact of variation of nanoparticle shape on free convective MHD water-based flow of Hamilton–Crosser model radiative nanofluids over a permeable surface

The present analysis explores the impact of shape of the nanoparticles on the conducting nanofluids past a porous surface. The electrically conducting fluid possesses enhanced physical properties due to the thermal buoyancy, and the radiative heat energy enhances the thermal properties of the water-based nanofluid. The suitable choice of a nanoparticle, that is, considering the metal particle like copper (Cu) and oxide particle such as TiO₂ in conjunction with the Hamilton–Crosser model thermal conductivity, augments the heat transfer properties. The appropriate transformation of similarity variable and the stream function helps to convert the leading partial differential equations to nonlinear ordinary differential equations (ODEs). Furthermore, these distorted ODEs are handled by using numerical technique such as Runge–Kutta–Fehlberg along with the shooting technique. The graphical presentation of the profiles of flow phenomena due to the interaction of relevant parameters is deployed for the physical significance, and the comparison of the present investigation shows a good agreement with the earlier results. However, the major outcomes are as follows; backflow occurs near the surface region due to the impermeable surface also increasing shape of the nanoparticle decelerates the fluid temperature and it is useful by considering the spherical shaped nanoparticles for the enhanced heat transfer.     

空气冷却式膜蒸馏构型的传热分析

在膜蒸馏的不同构型中,直接采用环境空气作为冷却媒介的空气冷却式构型很大程度上简化了系统配置。在强化传热的条件下,其跨膜通量与水冷构型接近。对空气冷却式膜蒸馏构型的传热过程进行理论分析,并通过量化分析各参数对膜蒸馏传热性能的影响,构建综合的传热模型。引入关联热阻系数这一概念,用以量化空气冷却的参数对膜蒸馏过程总传热系数的抑制作用。通过模拟计算研究了冷凝板导热系数、空气流速、冷凝板肋化系数、料液温度等参数对膜蒸馏传热性能的影响,并分析和量化多参数对关联热阻系数的综合影响。结果表明冷凝板导热系数、空气流速、冷凝板肋化系数是影响关联热阻系数的重要因素,各参数对膜蒸馏传热性能的综合影响得以量化。以上研究为后续传质模型的研究提供了指导。     

Effects of Variable Jet Nozzle Angles on Cross-Flow Suppression and Heat Transfer Enhancement of Swirl Chamber

This paper investigated the effects of variable jetting nozzle angles on the cross-flow suppression and heat transfer enhancement of swirl cooling in gas turbine leading edge. The swirl chamber with vertical jet nozzles was set as the baseline, and its flow fields and heat transfer characteristics were analyzed by 3D steady state Reynolds-averaged numerical methods to reveal the mechanism of cross-flow weakening the downstream jets and heat transfer. On this basis, the flow structure on different cross sections and heat transfer characteristics of swirl chamber with variable jetting nozzle angels were compared with the baseline swirl chamber. The results indicated that for the baseline swirl chamber the circumferential velocity gradually decreased and the axial velocity gradually increased, and the cross-flow gradually formed. The cross-flow deflected the downstream jets and drawn them to the center of the chamber, thus weakening the heat transfer. For swirl chamber with variable jetting nozzle angles, the air axial velocity is axial upstream, opposite to the mainstream, so that the impact effects of cross-flow on the jets were reduced, and the heat transfer was enhanced. Furthermore, with the increase of axial velocity along the swirl chamber, the jetting nozzle angle also gradually increased, as well as the effect of cross-flow suppression, which formed a relative balance. For all swirl chambers with variable jet nozzle angles, the thermal performance factors were all larger than 1, which indicated the heat transfer was enhanced with less friction increment.