Grashoff Number Research Articles

Computational study on cilia transport of Prandtl nanofluid (blood-Fe3O4) enhancing convective heat transfer along microorganisms under electroosmotic effects in wavy capillaries

Purpose This study aims to focuse on the flow behavior of a specific nanofluid composed of blood-based iron oxide nanoparticles, combined with motile gyrotactic microorganisms, in a ciliated channel with electroosmosis. Design/methodology/approach This study applies a powerful mathematical model to examine the combined impacts of bio convection and electrokinetic forces on nanofluid flow. The presence of cilia, which are described as wave-like motions on the channel walls, promotes fluid propulsion, which improves mixing and mass transport. The velocity and dispersion of nanoparticles and microbes are modified by the inclusion of electroosmosis, which is stimulated by an applied electric field. This adds a significant level of complexity. Findings To ascertain their impact on flow characteristics, important factors such as bio convection Rayleigh number, Grashoff number, Peclet number and Lewis number are varied. The results demonstrate that while the gyrotactic activity of microorganisms contributes to the stability and homogeneity of the nanofluid distribution, electroosmotic forces significantly enhance fluid mixing and nanoparticle dispersion. This thorough study clarifies how to take advantage of electroosmosis and bio convection in ciliated micro channels to optimize nanofluid-based biomedical applications, such as targeted drug administration and improved diagnostic processes. Originality/value First paper discussed “Numerical Computation of Cilia Transport of Prandtl Nanofluid (Blood-Fe3O4) Enhancing Convective Heat Transfer along Micro Organisms under Electroosmotic effects in Wavy Capillaries”.

A comparative study of heat absorption and chemical reaction on MHD flow with fractional derivatives

In this article, Caputo and Prabhakar fractional derivatives are used to analyze the influence of heat flux on fractionalized second grade flow. The fluid model is generalized by Fick’s and Fourier’s laws. Moreover, radiation and slip effects are also taken into account additionally. Fractional governing models are solved semi-analytically by using Caputo and Prabhakar fractional derivatives. The method of Laplace method is applied to solve the dimensional model for temperature, velocity, and concentration profiles. The results are contrasted visually. A variety of graphs are used to illustrate the impacts of several parameters, including the heat absorption Q, fractional parameter, magnetic parameter M, and chemical reaction R. It is evident from the figure that the velocity distribution is affected less by chemical and magnetic field, while the fluid velocity is affected more by diffusion-thermodynamics and mass Grashoff number. Furthermore, comparisons among classical and fractional fluid models are made to check the validity of the result. It is noted that the classical approach is less convenient as compared to the fractional approach.

Thermal transport characteristics of fluid-particle suspension in a vertical uniform tube: A computational study on Rabinowitsch fluid with uniform heat source

Problem statement The thermal transport of fluid-particle suspension in Rabinowitsch fluid is discussed theoretically in a vertical uniform tube under the consideration of a uniform heat source. Methodology The fluid and particle phase models are used to develop the mathematical model in the form of partial differential equations which are solved through the symbolic software MATHEMATICA version 12.0 and present the exact solution of temperature distribution, velocity of fluid and particle phases, wall shear stress, pressure gradient, pressure rise, and stream function, etc. Computational results and findings The volume fraction density of the particles slows down the motion of the fluid particles. The velocity of Newtonian fluid is maximum as compared to pseudo-plastic and Dilatant fluids. The fluid phase velocity is superior to particle phase velocity distribution for all pertinent parameters of the analysis. The pressure rise increases in the case of Newtonian and pseudo plastic fluid and decreases in Dilatant fluid. The trapping phenomena are strongly associated with the volume fraction density of the particle. The shear stress shows a decreasing trend against the volume fraction density of the particles, Grashoff number, and heat source parameter. Special case The current fluid model (Rabinowitsch fluid) can be reduced in Newtonian, pseudo plastic, and Dilatant fluid for taking κ → 0 , κ < 0 , and κ > 0 , respectively. Applications The current analysis can be useful in biomedical engineering to observe the blood supply through the arteries, the removal of kidney stones, and also the passage of urine to the bladder from the ureter. Originality The present research is original and has not been published before.

Entropy generation analysis for hybrid nanofluid mobilized by peristalsis with an inclined magnetic field

The purpose of the present study is to analyse the entropy generation for the hybrid nanofluid mobilised by peristalsis. The hybrid nanoliquid is suspension of copper [Formula: see text] and iron-oxide [Formula: see text] nanoparticles in water. Impacts of magnetic field, Joule heating, mixed convection, heat source/sink and viscous dissipation are reckoned. Governing set of equations are simplified by using lubrication approach. Obtained system of differential equations are solved numerically. Special attention is paid to analyse the effects of hybrid nanomaterial, Hartman and Grashoff numbers on entropy generation, Bejan number, axial velocity, temperature, heat transmission rate at walls, pressure gradient, skin friction, Nusselt number. Flow behaviour is visualised through streamlines. The study reveals that velocity and temperature decrease on increasing the volume fraction of solid nanomaterials. Higher Grashoff and Hartman numbers augment both velocity and temperature. Better heat transfer performance is recorded for strong Hartman number. [Formula: see text] and [Formula: see text] improve Entropy generation and Bejan number. Higher Hartman number causes decrement in pressure gradient. Addition of nanoparticles concentration reduces skin friction. High flow rate increases trapping phenomenon.

Irreversibility estimation of MHD thermosolutal convection of Powell–Eyring fluid flow through an inclined microchannel

ABSTRACT Due to the impressive utility of the mass transport phenomena on microscales for various miniaturised devices, the theoretical and experimental studies in microchannel flows to analyse heat and mass transport find enormous interest in researchers. Investigations in microchannel flows have gigantic applications in biochips, drug delivery, and cooling of microchips. This article examines the combined heat and mass transport of Powell–Eyring fluid through a permeable inclined microchannel considering magnetism, thermo-diffusion, and Navier's slip effects under convective boundary conditions. To solve the nonlinear system numerically MATLAB bvp4c solver is employed. This analysis reveals that the entropy generation due to thermosolutal irreversibility is enhanced strictly with the thermo-diffusion effect and solutal Biot number. The Bejan number profile shows a dominating character of Reynold's number close to the upper channel wall and deteriorates with the immense solutal Grashoff number. Also, it achieves maximum and minimum values for the supreme thermal Biot number and Eckert number, respectively in the middle of the channel. The outcome of the study may provide significant insight into controlling flows through microchannels as well as manipulating microfluidic and biomedical devices for minimising energy loss and designing an efficient model for better thermal performance and transmission of chemical species.

Hall current effects on a fully developed combined convection flow in a vertical channel: A study of heat transfer

This paper the effect of magnetic field on free and forced convection flow between two vertical parallel plates is studied. The flow is assumed to be steady and fully developed. The vertical walls are kept at different uniform temperatures. The expression for velocity and bulk temperature are obtained in magnetic and in non-magnetic cases. Hall current effect plays a significant role in determining the flow pattern of an incompressible, viscous, conducting fluid under the influence of an external magnetic field. The effects of magnetic parameter or Hartmann number M, ratio of wall temperature differences (rT), ratio of Grashoff number and Reynolds number , the pressure gradient and the hall parameter (m) is studied numerically on velocity and bulk temperature.

MHD flow of third-grade fluid through a vertical micro-channel filled with porous media using semi implicit finite difference method

This study examines the complex dynamics of an incompressible, electrically conducting third-grade fluid (TGF) flow through a vertical micro-channel that is filled with porous media. The research utilizes asymmetrical convective cooling, a transverse magnetic field, and exothermic reactions to introduce a comprehensive model. The viscosity of the fluid, which is determined by the Naham-type law, changes significantly with temperature. Additionally, the convective heat transfer rates, which govern the asymmetric convective cooling at the surfaces of the micro-channel, are modeled using Newton's law of cooling, and Modified Darcy law is used to address the porous medium effect. To solve the complex system of nonlinear partial differential equations, we employ computational solutions derived from reliable and efficient finite difference methods (FDM). The method is tested for different time-steps and mesh sizes and it is found that the algorithms reliably produce the same results. Our investigation includes an evaluation of both spatial and temporal convergence of the FDM scheme. The study present qualitative discussions of graphical results, that highlight the impact of various flow parameters integrated into the system. The velocity and temperature profiles increases for higher values of thermal Grashoff number Gr and Reynolds number Re while opposite effect is noticed for increasing values of Hartman number M.

Double-diffusive mixed convection with four heated square blocks for different working fluids in a square cavity

This paper investigates the flow behavior of a 2D, steady-state, and double-diffusive mixed convection laminar flow inside a square cavity with heated square blocks. The set of computational equations is discretized using the finite volume method (FVM). The effect of various operating parameters, such as Richardson Number (0.01 ≤ Ri ≤ 10), Grashoff number (102 ≤ Gr ≤ 105), Prandtl number (0.054 ≤ Pr ≤ 7.0.), the size of the heated blocks (BR = 1/4, 1/6, 1/8) are analyzed. Results show that the Nuavg and Shavg on the block surfaces are increased with Ri and decrease with Pr at any block ratio. Denser crowding for contour lines of temperature and concentration along the block was observed for Pr = 7.0 compared to Pr = 0.054. The heat and species transfer rates enhance with increased Ri and BR. Further, an empirical correlation is developed for Nuavg and Shavg.

Heat and mass transfer analysis of non-Newtonian radiative nanofluid flow driven by the combined action of peristalsis and electroosmosis

The present numerical investigation uncovers the flow, heat, and mass transfer of ethylene glycol-based nanofluid (BN-EG) led by the combined impacts of peristaltic pumping and electroosmosis. The thermal conductivity of carrier liquid is deemed to change with temperature. Further, the features of electric field, Ohmic heating, radiative heat flux, mixed convection, and magnetic field are taken. Mathematical modeling is conducted under the assumption of lubrication theory. The nonlinear-coupled equations are addressed numerically by implementing Shooting method. The effective results of all physical constraints linked with the flow model are vigilantly studied and highlighted through various curves. The observations obtained from current analysis reveal that temperature augments with higher electroosmotic parameter. However, the Joule heating parameter increases the rate of heat transmission, while a lower rate of heat transfer is perceived for the radiation parameter. An increment in Helmholtz–Smoluchowski velocity increases the velocity profile. Pressure gradient rises in a forward way when electrical field favors peristaltic flow. Concentration of nanomaterial considerably declines when concentration Grashoff number is assigned higher values.

Turbulent natural convection heat transfer enhancement of nanofluids

This study investigates the enhancement of heat transfer for the fluid with the addition of nano-particles in a two-dimensional rectangular cavity. Thermo-physical properties of such fluids and volume fraction of nano-particles in those fluids and its heat transfer characteristics are studied. ANSYS Fluent code is utilized for this purpose. Validation of the computational model has been carried out against the benchmark data available from the literature. A heat transfer correlation in terms of the Nusselt number (Nu) average as a function of Grashoff number and volume fraction of the nano-particles in the base fluid for the turbulent flow is developed and formulated in this study.

Entropy Generation and Radiation Analysis on Peristaltic Transport of Hyperbolic Tangent Fluid with Hybrid Nanoparticle Through an Endoscope

The current study explores the impact of entropy generation, thermal jump, radiation, and inclined magnetic field on the peristaltic transport of hyperbolic tangent fluid containing molybdenum disulfide and silver nanoparticles through an endoscope with a long wavelength and low Reynolds number assumptions. Between two coaxial tubes, a non-Newtonian hyperbolic tangent fluid with silver nanoparticles is considered. The Second law of thermodynamics is used to examine the entropy generation. The Homotopy perturbation method (HPM) is applied to describe the solution of nonlinear partial differential equations. We were able to arrive at analytical solutions for velocity, temperature, and nanoparticle concentration. In the end, the impact of various physical parameters on temperature, nanoparticle concentration, velocity, entropy generation, and Bejan number was graphically depicted. The significant outcome of the present study is that the impact of Hartmann number and Brownian motion parameter declines the velocity profile, but the thermal Grashoff number enhances velocity, whereas Platelet-shaped nanoparticles achieve a higher speed as compare to Spherical-shaped nanoparticles.

Dynamical dissipative and radiative flow of comparative an irreversibility analysis of micropolar and hybrid nanofluid over a Joule heating inclined channel

This report scrutinized the influence of radiation and Ohmic heating on the dissipative flow of micropolar and hybrid nanofluid within an inclined length 2h channel under convective boundary conditions. Primary flow equations are renewed as the system of NODEs with the assistance of proper similarity conversions. In two circumstances, hybrid fluid flow and micropolar fluid flow, a blend of shooting and Runge–Kutta 4th order strategy, is used to achieve the desired results. The critical consequences of the current study are Larger pressure gradient minimizes the fluid velocity, and a more significant inertia parameter minimizes the rotation profile in the case of Newtonian fluid flow but facilitates the same in the case of hybrid nanofluid flow. It is perceived that the escalation in Brinkmann number causes the amelioration in the fluid temperature, and the radiation parameter mitigates the same. Furthermore, it is discovered that the Grashoff number enhances the Bejan number at the centre of the channel but lessens the same at other areas. Finally, validation is executed to compare the current outcomes with the former results and perceive a good agreement.

Heat transfer characteristics of magnetohydrodynamic two fluid oscillatory flow in an inclined channel with saturated porous medium

This investigation aims to examine the hydromagnetic flow of two liquid flows of fully developed incompressible Newtonian fluid in an inclined channel through the porous medium accounting for radiative heat flux, Joule heating, and viscous dissipation. The walls of the channel are maintained at different temperatures. A double perturbation method is employed to derive analytical results for velocity and temperature. Graphical results are presented for various arising parameters such as Hartmann number, Grashoff number, ratio of viscosity parameter, thermal conductivity ratio, and porous parameter. Further, the results for mass flux are presented in a tabular form and discussed. Reduction in the velocity and temperature distribution is observed by enhancing Darcy dissipation and frequency parameter. As the angle of inclination increases, there is a rise in flow and heat distribution. With the strength of the magnetic field and the rise in the Reynolds number, the mass flux decreases. A comparative study is carried out with the previously published work and the results are found to be in good agreement.

Soret effect on an unsteady MHD free convective flow past an infinite vertical plate with constant suction

The present study aims to numerically investigate the impact of flow parameters on an unsteady MHD free convective flow past an infinite vertical plate with constant suction. Specifically, the study considers the Thermo diffusion (Soret effect) on a moving infinite vertical plate with variable temperature and mass diffusion. the thermal diffusion, isthe tendency of a convection-free mixture to separate under a temperature gradient.Given the significance of suction in fields such as aerodynamics and space science, this study is motivated by the need to investigate the problem of combined heat and mass transfer of an unsteady MHD flow past an infinite plate with suction. The finite element method is used to solve the dimensionless governing equations of the problem, and numerical solutions for velocity, temperature, and concentration are obtained for various parameters including Grashoff number, mass Grashoff number, Prandtl number, Schmidt number, and Soret number. The results are presented in graphical form to observe the effect of the parameters on the problem under investigation, and the stability and convergence of the finite element method is established.

Non-similar mathematical and dynamical analysis of Cross nano-materials over a gravitationally effected surface

This research work is associated to the exploration of the significant phenomenon namely, three equations non-similar model of Cross liquid flow over a moving surface. The effects in the form of gravity, magnetic field and suction/injection are incorporated in this study. For the enhancement of thermal conductivity, the Buongiorno nano-liquid model is employed. The nonlinear PDEs are transformed into ODEs by utilizing the non-similar variables. In order to analyze the impact of stream-wise coordinate, the influence of Grashoff number is explored, while plotting the velocity, temperature and volume fraction. The velocity of this specific liquid is an increasing function of Wessenberg number, mixed convection and suction parameters, respectively. Additionally, Nt (Thermophortic forces) and Nb (Brownian motion parameter) escalated the temperature and volume fraction of the liquid, respectively and opposite behavior is determined, while plotting during the liquid temperature as well as liquid volume fraction.

Heat and Mass Transfer in a Vertical Channel Flow Through a Porous Medium in the Presence of Radiation

An analysis is made of heat and mass transfer in a three dimensional flow between two vertical porous plates through a porous medium. Analytical solutions have been obtained using the perturbation technique. The effect of non-dimensional parameters on velocity, temperature and concentration field are shown graphically. It is seen that the main flow velocity decreases with an increase in both the radiation parameter and Schmidt number but increases with an increase in the thermal Grashoff number, mass Grashoff number as well as the permeability parameter. Variations of the shear stress at the left plate are given in a tabular form. It is seen that the shear stress due to the primary flow at the left plate increases with an increase in the Reynolds number but decrease with an increase in the Schmidt number. With the increase of both the radiation parameter and Reynolds number the temperature decreases. The concentration field also decreases with an increase of the Schmidt number. Variations of mass flux at the left plate are given in tabular form. It is seen that the mass flux at the left plate increases with increase in both Schmidt number or Reynolds number.

Suction effect on MHD flow of Brinkman-type fluid with heat absorption and first-order chemical reaction

Suction/injection is a mechanical effect and used to control the energy losses in the boundary layer region by reducing the drag on the surface. In this study, unsteady MHD flow of Brinkman-type fluid with suction/injection, heat absorption, and chemical reaction is investigated and an analytical solution is established. The corresponding results for temperature, concentration, and velocity fields are obtained with the help of the Laplace transformation method analytically. The physical effects of thermal and mass Grashoff number, Prandtl number, Schmidt number, heat absorption parameter, first-order chemical reaction parameter, suction/injection, Brinkman parameter, and magnetic parameter have been discussed graphically. Finally, it is observed that in the presence of suction effect, fluid’s velocity decreases gradually by increasing the value of suction parameter while show an increasing trend for the increasing value of the injection parameter.

Numerical Study on the Thermal Enhancement of Phase Change Material with the Addition of Nanoparticles and Changing the Orientation of the Enclosure

The global demand of the heating and cooling applications gives a larger potential to study the thermal energy storage system. Phase change materials (PCM) that are used to charge, store, and discharge the heat energy are inferior in heat transfer characteristics. The properties of PCM can be improved by adding nanoparticles, changing the orientation of the enclosure or both. Two‐dimensional transient numerical analysis on the effect of Grashoff number (5000, 13000, and 20000), nanoparticle type (Al2O3, CuO, and MWCNT), and volume concentration (0%, 1%, 3%, and 5%) added in RT 42 PCM and orientation of square enclosure (30, 45, and 60°) to enhance the heat transfer rate is carried out. The thermophysical properties of the nano‐PCM are evaluated and presented. From the results, it is affirmed that the melt fraction of the PCM rises with the increase in Gr and volume concentration of the nanoparticles up to an optimum level. The MWCNT‐based nano‐PCM attained a larger portion of melt fraction followed by Al2O3, CuO, and pure PCM. It is noted that an orientation of 60° and 45° will convert more quantities of pure PCM and nano‐PCM into liquid fraction, respectively. The (3% MWCNT/RT‐42 PCM) filled in 45° oriented container attained the highest melt fraction by 3.4%, 2.04%, and 2.94% than (3% Al2O3/RT‐42 PCM), (1%CuO/RT‐42 PCM), and pure PCM. The variation in the maximum melt fraction of the nanomaterial is because of the change in thermophysical characteristics of the nano‐PCM.

Effects of Inclination angle and Free Convection on Velocity Profile for a Steady 2-Dimensional Magnetohydrodynamic Fluid Flow in an Inclined Cylindrical Pipe

Effects of inclination and free convection on velocity profile for magnetohydrodynamic (MHD) fluid flow in an inclined cylindrical pipe has been investigated. The governing partial differential equations are the equations of continuity, momentum and energy which are converted into ordinary differential equation by employing similarity transformation and solved numerically by the Runge- Kutta fourth order scheme with shooting method. The findings, which are presented in the form of tables and graphs reveal that; when Hartmann number, Grashoff number and Gamma are decreased, the velocity of the fluid increases. The results of the study may be useful for the different model investigations, especially, in various areas of science and technology in which optimal inclination and free convection are utilized.

Effects of Inclination angle and Free Convection on Velocity Profile for a Steady 2-Dimensional Magnetohydrodynamic Fluid Flow in an Inclined Cylindrical Pipe

Effects of inclination and free convection on velocity profile for magnetohydrodynamic (MHD) fluid flow in an inclined cylindrical pipe has been investigated. The governing partial differential equations are the equations of continuity, momentum and energy which are converted into ordinary differential equation by employing similarity transformation and solved numerically by the Runge- Kutta fourth order scheme with shooting method. The findings, which are presented in the form of tables and graphs reveal that; when Hartmann number, Grashoff number and Gamma are decreased, the velocity of the fluid increases. The results of the study may be useful for the different model investigations, especially, in various areas of science and technology in which optimal inclination and free convection are utilized.