Thermal Grashof Research Articles

Magnetized Flow of Maxwell Fluid over a Slippery Stretching Reactive Surface with Thermophoretic Deposition

This manuscript investigated mathematically magnetized Maxwell fluid over slippery stretching reactive surface with thermophoretic deposition. Similarity transformation was used to recast partial differential equations modeling flow problem to nonlinear coupled ordinary differential equations which were solved using fourth order Range-Kutta method and Newton-Raphson shooting technique. Numerical results were compared with literature-based results and found to be in good accord. Skin friction coefficient, Nusselt number, Sherwood number, velocity profiles, temperature profiles and concentration profiles which are of importance to engineers, were found to be influenced by thermo-physical parameters governing the dynamics of flow. Their effects were illustrated in tabular form and graphically. The study found that increasing Thermophoretic deposition parameter, Momentum slip parameter and Biot number amplified rate of heat transfer but decreased rate of mass transfer and Skin friction coefficients. Thermal Grashof, Solutal Grashof, and Damkohler numbers reduced skin friction coefficients but increased heat and mass transfer rates.

Mathematical modelling for peristaltic flow of fourth‐grade nanoliquid with entropy generation

AbstractNanomaterials having excellent thermal properties are employed in producing energy, extrusion processes, engineering processes, nuclear interactions, industrial domains and aero‐spaces, etc. Therefore, current study scrutinizes the aspects of entropy optimization and Ohmic heating on MHD peristalsis of fourth‐grade nanoliquid in a channel. Flexible channel walls retain concentration, thermal slip and velocity conditions. The consequences of viscous dissipation and Arrhenius activation have been accounted. The lubrication approximation is used in mathematical modelling. Nanofluid model is used by considering thermophoresis and Brownian motion. Furthermore, thermal radiation features are included in the energy equation. By using an appropriate similarity transformation, a system of PDEs is simplified to a solvable system of ODEs. Numerical techniques are used to solve the problem of governance. Detailed exploration of the sundry variables of concern on the flow quantities like velocity profile, nanoparticle concentration, temperature and entropy of the system is graphically examined. Heat transfer is examined in tabular form. Based on the derived outcomes, the velocity rises via thermal Grashof and slip variables. Further, an increment in Brownian motion and radiation parameters shows opposite behaviour on temperature.

A time-fractional model of free convection electro-osmotic flow of Casson fluid through a microchannel using generalized Fourier and Fick’s law

Electro-osmotic flow through a micro-channel has vast applications in the modern world, that is, in different fields like biochemistry and the biomedical industry. The present paper investigates the electro-osmotic flow of Casson (non-Newtonian) fluid through a vertical microchannel. The effect of heat and mass transfer is also studied in this fluid flow. The above physical phenomenon is modeled in the terms of partial differential equations. The derived system of the differential equations is non-dimensionalized using some appropriate dimensionless variables. Moreover, the dimensionless classical system is fractionalized using generalized Fourier and Fick’s law. The definition of the Caputo derivative is used for generalization. Laplace and Fourier’s techniques are applied jointly to obtain the exact solutions of the velocity, temperature, and concentration distributions. Furthermore, the effect of various physical parameters like Casson fluid parameter, fractional parameter, zeta potential parameter, thermal and mass Grashof number, Schmidt and Prandtl number on the velocity, temperature, and concentration distributions is shown and discussed graphically. Moreover, the results show that the velocity increases by raising the values of electrokinetic parameter k. This increase in velocity is the result of the fact that the larger value of k exhibits the thinner Electric Double Layer (EDL), which enhances the flow with the larger velocity gradient.

Thermo-Solutal Convection of a Nanofluid Utilizing Fourier’s-Type Compass Conditions

Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a vertical duct containing nanofluid. Numerical scrutiny for the double-diffusive free and forced convection within a duct encumbered with nanofluid is performed. Buongiorno’s model is deployed to define the nanofluid. Robin boundary conditions are used to define the surface boundary conditions. Thermal and concentration equations envisage the viscous, Brownian motion, thermosphores of the nanofluid, Soret and Dufour effects. Using the Boussi-nesq approximation the solutal buoyancy effect as a result of gradients in concentration are incorporated. The conservation equations which are nonlinear are numerically estimated using fourth order Runge-Kutta methodology and analytically ratifying regular perturbation scheme. The mass, heat, nanoparticle concentration and species concentration fields on eight dimensionless physical parameters such as thermal and mass Grashof numbers, Brownian motion parameter, thermal parameter, Prandtl number, Eckert number, Schmidt parameter, and Soret parameter are calculated. The impact of these parameters are outlined pictorially. The velocity and temperature fields are boosted with the thermal Grashof number. The Soret and the Schemidt parameters reduces the nanoparticle volume fraction but it heightens the momentum, temperature and concentration. At the cold wall thermal and concentration Grashof numbers reduces the Nusselt values but they increase the Nusselt values at the hot wall. The reversal consequence was attained at the hot plate. The perturbation and Runge-Kutta solutions are equal in the nonappearance of Prandtl number. The (E. Zanchini, Int. J. Heat Mass Transfer 41, 3949 (1998)). results are restored for the regular fluid. The heat transfer rate is high for nanofluid when matched with regular fluid.

Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

Abstract In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

Finite element computation of transient dissipative double diffusive magneto-convective nanofluid flow from a rotating vertical porous surface in porous media

This article aimed to investigate the transient dissipative magnetohydrodynamic double diffusive free convective boundary layer flow of electrically conducting nanofluids from a stationary or moving vertical porous surface in a rotating high permeability porous medium, considering buoyancy, thermal radiation and first-order chemical reaction. Thermo-diffusion (Soret) and diffuso-thermo (Dufour) effects are also considered. Darcy’s law is employed. The mathematical model is formulated by considering water-based nanofluids containing metallic nano-particles for both stationary and moving plate cases. Three nanofluids are examined, namely copper, aluminium oxide or titanium oxide in water. The transformed non-linear, coupled, dimensionless partial differential equations describing the flow are solved with physically appropriate boundary conditions using Galerkin weighted residual scheme. For prescribed permeability, numerical results are presented graphically for the influence of a number of emerging parameters. Validation of finite element solutions for skin friction and Nusselt number is achieved via comparison with the previously published work as special cases of the present investigation and very good correlation obtained. Increasing rotational parameter is observed to reduce both primary and secondary velocity components. Primary and secondary velocities are consistently elevated with increasing Soret, Dufour, thermal Grashof and solutal Grashof numbers. Increasing Schmidt number, chemical reaction and suction parameter both suppress nano-particle concentration whereas the converse behavior is computed with increasing Soret number. The study is relevant to high-temperature rotating chemical engineering systems exploiting magnetized nanofluids and also electromagnetic nanomaterial manufacturing processes.

Physical aspects of nanoparticles in non-Newtonian liquid in the presence of chemically reactive species through parabolic approach

An article is made to report physical aspects of nanoparticles along with mutual interaction of chemical reaction and mixed convection on boundary layer Eyring Powell fluid flow yields by stretching surface. The fluid flow is engaged due to no slip condition i-e the velocity of particles is directly related to velocity of surface due to stretching. The physical situation within the real concerned constraints is achieved in terms of differential equations as a boundary value problem. To make implementation of numerical algorithm possible partial differential equations are transformed into ordinary differential equations by means of appropriate transformation. Then these constructed ordinary differential equations are solved numerically by using shooting scheme charted with Runge-Kutta algorithm. The effect logs of an involved pertinent flow parameters are explored by way of graphical outcomes. It is observed that in the presence of nanoparticles Eyring-Powell fluid velocity increases for positive values of both thermal Grashof and solutal Grashof numbers. A parabolic curve fitting way of communication is executed to represent the impact of both thermophoresis parameter and Brownian motion parameter on heat and mass transfer rates. It is found that heat transfer rate is decreasing function of thermophoresis parameter but mass transfer rate exhibit an inciting nature towards Brownian motion parameter.

Axisymmetric Flow Over a Vertical Slender Cylinder in the Presence of Chemically Reactive Species

The Combined buoyancy effect due to thermal diffusion as well as species diffusion on the boundary layer flow over a slender cylinder in the presence of a chemical reaction is investigated. Using an appropriate transformation, the governing equations are transformed into a system of coupled non-linear ordinary differential equations and are solved numerically via finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in excellent agreement. The velocity, temperature, and the concentration profiles are presented graphically and analyzed for several sets of the physical parameters. The pooled effect of the thermal and mass Grashof number is to enhance the velocity and is quite the opposite for temperature and the concentration fields.

Simulation of Flow over a Cavity Using Multi-Relaxation Time Thermal Lattice Boltzmann Method

This article provides numerically study of the multi-relaxation time thermal lattice Boltzmann method (LBM) for compute the flow and isotherm characteristics in the bottom heated cavity located o n a floor of horizontal channel . A double-distribution function (DFF) was coupled with MRT thermal LBM to study the effects of various grashof number (Gr), Reynolds number (Re) and Aspect Ratio (AR) on the flow and isotherm characteristic. The results we re compared with the conventional single-relaxation time lattice Boltzmann scheme and benchmark solution for such flow configuration. The results of the numer ical simulation indicate that multi-relaxation time thermal lattice Boltzmann scheme demonstrated good agreement, which supports its validity in computing fluid flow problem.

Dissipation, MHD and Radiation Effects on an Unsteady Convective Heat and Mass Transfer in a Darcy-Forcheimer Porous Medium

This study investigates the effects of dissipation, magneto-hydrodynamics and thermal radiation on the natural convective heat and mass transfer of a viscous incompressible, gray absorbing-emitting fluid flowing past an impulsively started moving vertical plate in the Darcy-Forchheimer porous medium. The governing equations for the model are formulated in (${x}^\ast$, ${y}^\ast$, ${t}^\ast$) co-ordinates system with appropriate boundary conditions and the radiative heat flux takes the Rosseland diffusion approximation. The equations are simplified, non-dimensionalized and then solved using the Crank-Nicolsons method. The effects of Magnetic field, dissipation function, radiation-conduction and Forchheimer parameters with thermal Grashof, species Grashof, Prandtl, Schimdt and Darcy numbers are reported on the dimensionless velocity, temperature and species function distributions. Also, the variations of local skin friction, Nusselt and Sherwood numbers are computed.

Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection

The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied.

Transient Double-Diffusive Salinity in a Horizontal Fluid Layer

The transient double-diffusive stability problem for a horizontal layer of salty water bounded by two rigid isothermal surfaces was examined using both the frozen-time technique leading to an eigenvalue problem and the linear amplification theory leading to an initial value problem. Initially, the layer was subjected to zero temperature and salinity gradients. At the time t = 0, uniform step increases in both temperature and salinity were imposed at the bottom surface while the top surface is impermeable to the diffusion of salt. In the early developing stages scaling lengths based on thermal and mass boundary layer thicknesses were taken into consideration. Several parameters were considered in the analysis, namely, the thermal and solute Grashof numbers, Prandtl number, Schmidt number, time and wave size. Stability results based on the frozen-time technique and the linear amplification theory were compared in order to check the validity of the frozen-time technique within the range of the system parameters considered.

Combined Heat and Mass Transfer in Natural Convection on Inclined Surfaces

The combined heat and mass transfer characteristics of natural convection flow along inclined surfaces are studied analytically. The buoyancy forces arise from both temperature and concentration variations in the fluid. In the analysis, the diffusion-thermo and thermo-diffusion effects are neglected, as are the interfacial velocities resulting from mass diffusion. The surfaces are either maintained at a uniform temperature/concentration or subjected to a uniform heat/mass flux. The important parameters of the problem include Prandtl and Schmidt numbers, thermal and concentration Grashof numbers, the relative buoyancy force effect between species and thermal diffusion, and the angle of inclination from the vertical. Numerical results are presented for diffusion of common species into air and water. For both heating/diffusing conditions, the wall shear stress and the local Nusselt number are found to increase and decrease as the buoyancy force from species diffusion assists and opposes, respectively, the th...