Comparative Numerical Analysis of Heat and Mass Transfer Characteristics in Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg Fluids on a Stretched Surface

In the current research,a thorough examination unfolds concerning the attributes of magnetohydrodynamic(MHD)boundary layer flow and heat transfer inherent to nanoliquids derived from Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg compositions.Such nanoliquids are subjected to an extending surface.Consideration is duly given to slip boundary conditions,as well as the effects stemming from variable viscosity and variable thermal conductivity.The analytical approach applied involves the application of suitable similarity transformations.These conversions serve to transform the initial set of complex nonlinear partial differential equations into a more manageable assembly of ordinary differential equations.Through the utilization of the FEM,these reformulated equations are solved,considering the specified boundary conditions.The outcomes attained are graphically depicted by means of plots and tables.These visual aids facilitate a comprehensive exploration of how diverse parameters exert influence over the distributions of velocity,temperature,and concentration.Furthermore,detailed scrutiny is directed towards the fluctuations characterizing pivotal parameters,viz.,Nusselt number,skin-friction coefficient,and Sherwood number.It is identified that the Nusselt number showcases a diminishing trend coinciding with increasing values of the volume fraction parameter(φ).This trend remains consistent regardless of whether the nanoliquid under consideration is Al_(2)O_(3)-Eg or TiO_(2)-Eg based.In contrast,both the skin-friction coefficient and Sherwood number assume lower values as the volume fraction parameter(φ)escalates.This pattern remains congruent across both classifications of nanoliquids.The findings of the study impart valuable insights into the complex interplay governing the characteristics of HMT pertaining to Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg nanoliquids along an extending surface.

CFD-Based Simulation and Analysis of Hydrothermal Aspects in Solar Channel Heat Exchangers with Various Designed Vortex Generators

The hydrothermal behavior of air inside a solar channel heat exchanger equipped with various shaped ribs is analyzed numerically.The bottom wall of the exchanger is kept adiabatic,while a constant value of the temperature is set at the upper wall.The duct is equipped with a flat rectangular fin on the upper wall and an upstream V-shaped baffle on the lower wall.Furthermore,five hot wall-attached rib shapes are considered:trapezoidal,square,triangular pointing upstream(type Ⅰ),triangular pointing downstream(type Ⅱ),and equilateral-triangular(type Ⅲ)cross sections.Effects of the flow rates are also inspected for various Reynolds numbers in the turbulent regime(1.2×10^(4)-3.2×10^(4)).The highest performance(η)value is given for the Ⅱ-triangular rib case in all Re values,while the square-shaped ribs show a significant decrease in the η along the achieved Re range.The η value at Remax is 2.567 for the Ⅱ-triangular roughness case.Compared with the other simulated cases,this performance is decreased by about 3.768%in the case of Ⅰ-triangular ribs,15.249% in the case of Ⅲ-triangular ribs,20.802% in the case of trapezoidal ribs,while 27.541% in the case of square ribs,at the same Remax.Also,a comparison ismade with air-heat exchangers that have non-rough walls and contain cross-shaped VGs presented previously,in order to highlight the effectiveness of the rough surface presence in the baffled and finned channels.The obtained results indicated that the triangular-shaped rib(type Ⅱ)has the most significant hydrothermal behavior than the other cases.This indicates the necessity of roughness heat transfer surfaces for finned and baffled channels to improve significantly the performance of the air-heat exchangers they contain.

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H_(2)O nanofluid on a flat surface in a porous medium:A stability analysis

The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H_(2)O nanofluid on a flat surface in a porous medium is examined.Moreover,the thermal radiation and viscous dissipation effects are considered.The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method.The computed results can reveal many vital findings of practical importance.Firstly,dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows,the solution is unique.The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium.But different shapes of nanoparticles are not disturbing the dual solution existence range,though it has a considerable impact on thermal conductivity of the mixture.Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid,i.e.,the water here.On the other hand,the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium.Regarding the cooling rate of the heated surface,it rises with the permeability parameter,shape factor(related to various shapes of Cu-nanoparticles),and radiation parameter.The surface drag force becomes stronger with the permeability parameter.Also,with growing values of nanoparticle volume fraction,the boundary layer thickness(BLT)increases and the thermal BLT becomes thicker with larger values of shape factor.For decelerating unsteady flow,the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed.The thermal BLT is thicker with radiation parameter.Due to the existence of dual solutions,a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.

Darcy-Forchheimer relation in Casson type MHD nanofluid flow over non-linear stretching surface

Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments.A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation.Slip boundary conditions are used for velocity,temperature and concentration of the nanoparticles.Brownian diffusion and thermophoresis is attended.An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid.The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity.A fourth order Runge-Kutta(RK)scheme is enforced to solve the system numerically.Graphs are prepared for various progressive values of non-dimensionalized parameters whereas;variation in wall drag factor,heat and mass transfer rates is analyzed through numerical data.Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow.Temperature is found as a progressive function for the Brownianmotion factor and thermophoresis.The magnitude of wall drag factor,heat transfer and masstransfer rates shows reduction for progressive values of slip parameters.

Magnetohydrodynamic(MHD)boundary layer heat and mass transfer characteristics of nanofluid over a vertical cone under convective boundary condition

This paper investigates the boundary layer flow,heat and mass transfercharacteristics over a vertical cone filled with nanofluid saturated porous medium with theinfluence of magnetic field,thermal radiation and first order chemical reaction subject to theconvective boundary condition.Similarity transformation technique is used for the purpose ofconverting non-linear partial differential equations into the system of complex ordinarydifferential equations.The computational Finite element method has been employed to solvethe flow,heat and mass transfer equations together with boundary conditions.The impact ofvarious pertinent parameters on hydrodynamic,thermal and solutal boundary layers isinvestigated and the results are displayed graphically.Furthermore,the values of local skin-friction coefficient,rate of temperature and rate of concentration is also calculated and theresults are presented graphically.The comparisons with previously published work is made andfound good agreement.The thickness of thermal boundary layer is increased with increase inthe values of Brownian motion parameter(Nb)and thermophoresis parameter(Ni).

Investigations of Soret,Joule and Hall effects on MHD rotating mixed convective flow past an infinite vertical porous plate

We made an elaborate scrutiny on the Soret and Joule effects of MHD mixed convective flow of an incompressible and electrically conducting viscous fluid past an infinite vertical porous plate taking Hall effects into account.Perturbation technique is used to solve the non-dimensional equations.The effects of the various non-dimensional parameters on velocity,temperature and concentration within the boundary layer are examined.Besides that,computational deliberations or discussions are also undertaken on the effects of the pertinent or significant parameters on the skin-friction coefficient and rates of heat and mass transfer in terms of the Nusselt and Sherwood numbers respectively.The concentration distribution increases with increase in Soret effect and decrease with increase in chemical reaction parameter.An increase in Prandtl number results to decrease the temperature distribution.Both the primary and secondary velocity components and temperature increases with increasing heat source parameter.Skin friction coefficient decreases with an increase in permeability parameter,whereas it shows reverse effect for thermal and mass Grashof numbers.Nusselt number increases with an increase in Prandtl number.Sherwood number reduces with increasing Soret number.

Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamie and thermal radiation effects

The problem of unsteady magnetohydrodynamic(MHD)boundary layer flow of a non-Newtonian Maxwell nanofluid over a stretching surface with thennal radiation is considered.The Maxwell model is used to characterize the non-Newtonian fluid behaviour.An appropriate similarity transformation Is employed to transform the governing partial differential equations of mass,momentum,energy and nanoparticle concentration into ordinary differential equations.Tbe coupled non-linear ordinary differential equations are solved by using the variational finite element method.The flow features and the heat transfer characteristics and nanoparticle volume fraction are analyzed and discussed in detail for several sets of values of the governing flow parameters.Tbe results for the skin-friction coefficient,local Nusselt number and the local Sherwood number are presented in tables for various values of the flow controlling parameters.

Insight into the relationship between non-linear mixed convection and thermal radiation:The case of Newtonian fluid flow due to non-linear stretching

The current research focuses the light on the characterization of buoyancy-driven non-linear mixed convection and non-linear radiation in a Newtonian flow over a nonlinearly stretching vertical sheet,and this type of flow has useful applications in many industrial processes,such as the paper and pulp industry,polymer industry,electronic device cooling,solar collectors,gas turbine plants,and nuclear power.Using appropriate transformations,governing PDEs for non-linear mixed convection are reduced to higher-order non-linear ODEs and those are numerically solved.Along with tabular presentations of computed results,the graphical representations are generated to elucidate the effects of involved parameters on convection transport properties and their inter-relations.It demonstrates that flow velocity increases near the surface and decreases away from the surface as the non-linear convection parameter increases.Furthermore,increments in the thermal buoyancy,temperature ratio and non-linear radiation parameters result in the boost of velocity.The temperature decreases as linear and non-linear buoyancy-related parameters(non-linear convection and thermal buoyancy parameters)are of higher levels.In contrast,the temperature rises with two non-linear thermal radiation-related parameters(thermal ratio and non-linear radiation parameters).For greater values of the non-linear stretching related parameter,a lower velocity and a higher temperature are witnessed.The non-linear convection,thermal buoyancy,thermal ratio and non-linear radiation parameters contribute toward the reduction of the magnitude of surface-drag force and growth of the surface cooling rate.But,with the non-linearity in surface stretching there are significant percentage hikes of surface-drag force magnitude and surface cooling rate.

Regression analysis and features of negative activation energy for MHD nanofluid flow model:A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic(MHD)stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions.Negative activation energy is scarce in practice,but the impact of negative activation energy could not be neglected as it is noticed in chemical processes.The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies,such as exothermic binding of urea or water.In some processes,the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies.The present mathematical model is solved with successive linearization method(a spectral technique).A comparison of results is made for negative and positive values of activation energy.Apart from it,the quadratic multiple regression model is discussed briefly and explained with bar diagrams.It is observed that with rise in unsteadiness parameter from 0 to 1(taking positive activation energy),skin friction and Sherwood number are increased by 9.36%and 19%respectively,and Nusselt number is decreased by 26%.However,for negative activation energy,9.36%and 112%enhancement is observed in skin friction and Sherwood number,respectively.

Interaction of Radiation and Turbulent Natural Convection:A Pseudo-Direct Numerical Study

This paper presents a hybrid lattice Boltzmann solver for turbulent buoyancy-driven flow coupled with surface thermal radiation.The two-relaxation time scheme for the Boltzmann equation combined with the implicit finite difference scheme for the energy equation is implemented to compute the heat transfer and fluid flow characteristics.The accuracy and robustness of the hybrid approach proposed in this study are assessed in terms of the numerical and experimental data of other researchers.Upon performing the simulation,the Rayleigh number is ranged from 108 to 1010 whereas the surface emissivity is changed from zero to unity.During computations,it is found that the overall temperature of the cavity is increased as a result of enhancing the surface radiation.Convective plumes are formed both at the isothermal and the thermally-insulated walls with the Ra109 and#0.6.In the conditions under study,the overall heat transfer rate is raised by around 5%when taking into account the surface thermal radiation.