Expressions For Nusselt Number Research Articles

EFFECTS OF ROTATIONAL MODULATION ON CONVECTION IN ETHYLENE GLYCOL-BASED HYBRID NANOFLUIDS WITH INTERNAL HEATING

The rotational modulation effects on Rayleigh-Bénard convection in ethylene glycol-based hybrid nanofluids with internal heating are investigated. Due to their improved thermophysical properties as compared to base fluid, nanofluids are frequently used in numerous heat transfer applications. Hybrid nanofluids with suitable nanoparticle combinations can have better thermophysical characteristics than mono nanofluids. As a result, this study investigates the impact of hybridizing the base fluid on system stability and heat transfer. A single-phase model is employed to perform a linear and weakly nonlinear stability analysis of the nanofluid. The nonautonomous Ginzburg-Landau equation is derived and solved, and the solution is used to obtain the Nusselt number expression. Based on the linear analysis, the critical Rayleigh number attained in the case of hybrid nanofluids is less than the value found in the case of mono nanofluids. Therefore, the convection onset is faster in a hybrid nanofluid than in a mono nanofluid. The study further shows that hybrid nanofluid ethylene glycol-alumina-copper increases the heat transportation rate as compared to the mono nanofluid ethylene glycol-alumina, presenting evidence that hybrid nanofluid facilitates heat transfer better than the mono nanofluid. Increasing the volume of hybrid nanoparticles qualitatively improved heat transfer by up to 5.96%. Further, the effects of important fluid parameters on heat transfer are presented. Among other results, we found that increasing the modulation's amplitude improves heat transmission in the hybrid nanofluid.

Implementation to cardiovascular disorders under the action of magnetohydrodynamics in a non‐Newtonian peristaltic blood flow of nanofluid

AbstractThe issue of vascular stenosis has recently received significant innovative interest among researchers. Due to the buildup of adipocytes and other constituents of atherosclerotic, arteries can generate an abnormal condition called arterial stenosis. It optimizes blood circulation to prevent myocardial illness. In light of this, the current scientific report assembled a Casson fluid model to assess the MHD peristaltic transit of blood supply via a mildly stenotic artery when copper nanoparticles are added. A relevant simulation model is often used to outline the issue, acquiring non‐dimensional variables and approximations for the stenosis. Temperature has quantitative approaches, and the result for velocity is derived numerically in MATHEMATICA. The expressions for Nusselt number, wall shear stress, flow resistance distribution and stream function are attained. The under action of copper nanoparticles, the consequences of several new physiological measures on arterial blood circulation properties are visually displayed and explained briefly. A pictorial explanation of the trapping phenomena is also provided. In comparison to arteries devoid of stenosis, arteries with stenosis have a higher temperature distribution throughout the fluid flow and velocity. In addition, high temperature and velocity increase in the middle of the artery and decrease as one gets closer to the arterial wall. Further, the concentration, Grashof number and heat source and sink parameters of the nanoparticles reduce the wall shear stress of the blood in the arteries since the arterial wall contributes heat to the flow zone. The discovery could have medical applications as well as bioinformatics. Furthermore, the current work contributes to the cure of different cardiac illnesses.

Natural convection MHD mass transfer through an infinite vertical porous plate in the existence of radiation embedded in porous medium

AbstractThis research focuses on studying the effects of heat and mass transfer convective flow passing through an infinite vertical plate embedded in porous media under radiation and chemical reaction with constant heat and mass flux. A magnetic field of strength is functional throughout the fluid region. The novelty of the present work is to examine the heat and mass transfer magnetohydrodynamics flow in the presence of thermal radiation. The equations governing the flow, heat and mass transfer are solved analytically using the perturbation technique. Expressions for velocity, temperature, concentration, skin‐friction, Nusselt, and Sherwood numbers are obtained. The influence of physical parameters on the flow domain is described graphically and in tabular form. It is found that increase in radiation parameter reduces the velocity and temperature. Moreover, internal friction of the plate decreased with increasing values of radiation parameter.

Enhancing solar air heater efficiency with 3D cylinder shaped roughness elements

Solar air heaters (SAHs) harness solar radiation to warm the air. This study investigates the efficacy of 3D cylindrical roughness features in enhancing heat transfer and reducing friction losses within SAHs. The configuration involves inline and staggered placement of 3D cylindrical roughness elements beneath the absorber surface. Through ASHRAE standard 93–77 testing, heat transfer and friction factors are examined across various cylinder roughness setups, with parameters such as relative roughness pitch (p/h) and gap (w/h) considered. The channel aspect ratio (W/B) is set at 5, and a relative roughness height (h/D) of 0.06 is maintained and flow Reynolds number (Re) is varied from 3000 to 8000. Regression analysis reveals a significant relationship between heat transfer and friction. Notably, at Re = 7910, p/h = 20, and w/h = 8 for staggered cylinder roughness, average friction factor (fav) increases by 171.3 %, and average nusselt number (Nuav) increases by 69.7 %. Similarly, the efficiency index (η) peaks at 0.8192 with inline roughness at Re = 2969, p/h = 20, and w/h = 8. The introduced 3D cylinder roughness elements disrupt the laminar sub-layer, amplifying convective heat transfer while curbing friction losses. This approach optimizes SAH performance within the studied parameter range, showcasing potential improvements for utilizing solar energy. Experimental results, along with expressions for average friction factor (fav) and average Nusselt number (Nuav), underscore the benefits of cylinder-shaped roughness geometries while maintaining h/D = 0.06. These findings introduce an innovative convective heat transfer method, enhancing SAH efficiency. Furthermore, the anticipated average friction factor (fav) and average Nusselt number (Nuav) values align within error limits of ±6.63 % and ±6.62 %, respectively, with improved regression coefficients indicating the stronger relationship and the influence of independent variables on dependent variables.

ROLE OF SUCTION/INJECTION ON MIXED CONVECTION FLOW IN A VERTICAL MICROCHANNEL FILLED WITH POROUS MATERIAL

A suction/injection controlled mixed convection flow of an incompressible and viscous fluid in a vertical microchannel filled with porous material with asymmetric plate temperature is presented. The governing equations are derived and solved using the method of undetermined coefficient. The closed form expression for temperature field, velocity field, skin friction and Nusselt number for the steady fully developed flow are obtained analytically. The effects of the governing parameters on the microchannel hydrodynamic and thermal behaviors are determined. It is interesting to point out that growing the Darcy number as well as the suction S accelerate the fluid motion while they reduce the critical values of the ( at which flow reversal sets in ) on both plates. The stability of the flow is affected by variation in the permeability of the porous material.

Mathematical analysis of MHD hybrid nanofluid flow with variable viscosity and slip conditions over a stretching surface

There are number of real-world uses for hybrid nanofluids. Studies have shown that hybrid nanofluid is better at transferring heat than nanofluid with only one type of nanoparticle. It can be used in new ways, like in microfluidics, dynamic sealing, heat dissipation, and so on. The use of hybrid nanofluids in MHD flow over a stretching surface with varying viscosity can enhance heat transfer rates. This has various applications in industries such as, cooling systems in electronics, thermal management in aerospace, and energy system. But the properties of boundary layer flow and rate of heat transfer for hybrid nanofluids could be studied more in a space with more dimensions and with other physical assumptions around the flow of fluids. The current study's major purpose is to investigate the flow of a three-dimensional hybrid nanofluid over a stretched sheet as its viscosity changes. Furthermore, the effects of the Smoluchowski temperature and Maxwell velocity slip boundary conditions are considered. Hybrid nanofluid was created by dispersing copper (Cu) and alumina (Al2O3) nanoparticles in a base fluid (H2O). Similarity variables are employed to transform a set of nonlinear partial differential equations (PDEs) that govern fluid flow and heat transfer into a system of higher-order ordinary differential equations (ODEs). The RKF method in Mathematica solves the higher-order nonlinear ODEs. Graphical analyses and in-depth discussions examine how leading variables affect velocity and temperature profiles. The expressions for skin friction and local Nusselt number are explicitly formulated, and graphs illustrate the variations of these two quantities across different parameter values. When velocity slip parameter goes up, velocity profile f′ηgoes down, and the temperature profile θ(η) also goes down when the temperature slip parameter goes up. As the velocity slip parameter goes up, skin friction goes down, while the Nusselt number goes up as the temperature slip parameter goes up. When results of this study are compared to some of results that have already been published, they are found to be very interesting as heat transfer increases due to the impacts of physical parameters.

Heat and Mass Transfer on Unsteady MHD Kuvshinski Fluid Flow Past an Inclined Porous Plate with Multiple Slip Effect

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD free convection Kuvshinski fluid flow immersed in a porous medium over inclined plates with radiation absorption and chemical reaction effects. The systems of non-dimensional governing linear partial differential equations are solved analytically by using the perturbation technique. The expressions for the fields of velocity, temperature and concentration are obtained. With the aid of these the expressions for skin friction, Nusselt number and Sherwood number are derived. The effects of various physical parameters on the flow quantities are studied through graphs and tables. For the validity, we have checked our results with previously published work and found in good agreement.

Droplet heating and evaporation: A new approach to the modeling of the processes

A new model for mono-component droplet heating/evaporation is developed, tested, and applied to the analysis of in-house experimental data. The new model links the previously developed liquid phase model, using the analytical solution to the heat transfer equation at each time step, and the gas phase model, using the solution to the equations of the conservation of mass, momentum, and energy leading to an explicit expression for the Nusselt number and implicit expression for evaporation rate of the droplet. The latter expressions are used as boundary conditions for the liquid phase model. The new model is verified using a comparison between its predictions of the droplet temperatures and radii for very large liquid thermal conductivity [1000 W/(m K)] and those of the model, using the assumption that the thermal conductivity of liquid is infinitely large. The closeness between the predictions of these models supports the reliability of both. The model is validated using the experimental data obtained at the Heat and Mass Transfer laboratory of Tomsk Polytechnical University with regard to the heating/evaporation of droplets. The deviations between the measured and predicted droplet radii and temperatures in most cases are shown to be within experimental error margins.

Mathematical analysis of radius and length of CNTs on flow of nanofluid over surface with variable viscosity and joule heating

The transfer of heat is a phenomenon that is significant in a variety of contexts due to the different ways in which it may be utilized in industrial settings. To increase the rate at which heat is transferred, carbon nanotubes (CNTs), which can either be single-wall or multi-walled, are suspended in base fluids, and the resulting mixture is referred to as a “nanofluid. This study looks at how heat transfers through nanofluids that are suspended in carbon nanotubes with different lengths and radii over a stretching surface. It also looks at how changing viscosity and joule heating affect motion. Water is taken as base fluid. This study looks at both carbon nanotubes with one wall and those with more than one. The flow is governed by a series of partial differential equations, which, to control the flow, are transformed into a series of nonlinear ordinary differential equations. Similarity transformation is used to convert the obtained nonlinear ordinary differential equations and accompanying boundary conditions into a form that is dimensionless. To numerically solve the transformed equation, RK-4 with shooting method is used. Graphs and in-depth discussions are used to look at how velocity and temperature profiles are affected by the leading variables. The expression for skin friction and local Nusselt number are written down and graphs show how these two numbers change for different parameter values. The temperature profile goes down when the viscosity parameter goes down, but the velocity profile goes up. When the magnetic parameter goes up, the velocity profile f′(η), goes down, but the velocity profile g(η) and temperature θ(η) both go up at the same time. The rate of heat transfer increases with the addition of φ and S. When the suction parameter (S = 2.1) with 1% of φ is used, it is reported that rate of heat transfer increases by 1.135% for Single walled and 1.275% for Multi Walled carbon nanotubes. To determine whether or not the proposed numerical model is legitimate, a comparison is made between the current results and those that have previously been published.

Induced by heat source on unsteady MHD free convective flow of Casson fluid past a vertically oscillating plate through porous medium utilizing finite difference method

In this research, the unsteady MHD flow of a Casson fluid past a vertical plate that oscillates while maintaining a constant wall temperature and the heat source is the subject of this article. The fluid is electrically conductive and moves through a porous media. Partial differential equations with initial and boundary conditions are used to model this phenomenon. There are a few appropriate non-dimensional variables introduced. Using the finite difference method(FDM), the consistent dimensionless equations with circumstances are resolved. The energy and velocity equations are solved precisely. Expressions for Nusselt number and skin friction are also assessed. The outcomes of computations are analyzed for newly developing flow parameters. Additionally, skin friction and the Nusselt number effects are explained using table values. Furthermore, increasing the heat source parameter causes a rise in temperature and velocity.

Unsteady EMHD free convective second grade fluid flow past an exponentially accelerated vertical porous plate

This paper presents a detailed account of unsteady, incompressible, viscous, electrically conducting, unidirectional, free convective second grade fluid through an exponentially accelerated vertically infinite plate with both applied electric field and magnetic field being present. The equation of motion and energy manifested as nonlinear partial differential equation are represented as algebraic equations using implicit finite difference scheme and solved numerically by implementing the damped-Newton method. With the help of the momentum and energy equation, we defined the expressions for skin friction and Nusselt number. The cases n = 1(constant acceleration) and n = 0.5(variable acceleration) are also taken into consideration. The solution obtained is eventually simulated using MATLAB and the resulting graphs representing the influence of non-dimensional parameters on flow field and temperature field are discussed thoroughly. We have also validated the results obtained from the present methodology with the results obtained from already existing methodologies under some limited cases. It is interesting to note that when the plate is being cooled by free convection current, with increase in viscoelastic parameter the viscous forces are dominated by the elastic effects which results in accelerating the velocity flow profile. For comparatively smaller values of Ec the temperature distribution decreases with increasing Re as the suction propagation facilitates decrease in boundary layer thickness which consequently enhances heat transfer rate. The effect of Ec is to raise the temperature profile due to enhancement in viscous dissipation effects. Practically, the combined effects of the physical parameters are remarkably important in various engineering, medical and industrial applications.

Double-Slope Solar Still Productivity Based on the Number of Rubber Scraper Motions

In low-latitude areas less than 10° in latitude angle, the solar radiation that goes into the solar still increases as the cover slope approaches the latitude angle. However, the amount of water that is condensed and then falls toward the solar-still basin is also increased in this case. Consequently, the solar yield still is significantly decreased, and the accuracy of the prediction method is affected. This reduction in the yield and the accuracy of the prediction method is inversely proportional to the time in which the condensed water stays on the inner side of the condensing cover without collection because more drops will fall down into the basin of the solar-still. Different numbers of scraper motions per hour (NSM), that is, 1, 2, 3, 4, 5, 6, and 7, are implemented to increase the hourly yield of solar still (HYSS) of the double-slope solar still hybrid with rubber scrapers (DSSSHS) in areas at low latitudes and develop an accurate model for forecasting the HYSS. The proposed model is developed by determining the best values of the constant factors that are associated with NSM, and the optimal values of exponent (n) and the unknown constant (C) for the Nusselt number expression (Nu). These variables are used in formulating the models for estimating HYSS. The particle swarm optimization (PSO) algorithm is used to solve the optimization problem, thereby determining the optimal yields. Water that condensed and accumulated inside the condensing glass cover of the DSSSHS is collected by increasing NSM. This process increases in the specific productivity of DSSSHS and the accuracy of the HYSS prediction model. Results show that the proposed model can consistently and accurately estimate HYSS. Based on the relative root mean square error (RRMSE), the proposed model PSO–HYSS attained a minimum value (2.81), whereas the validation models attained Dunkle’s (78.68) and Kumar and Tiwari’s (141.37).

The Soret effect on MHD flow with Hall current and induced magnetic field

We analyse the influence of the Soret parameter on the MHD mixed convection flow of a viscoelastic fluid over a vertical surface. The induced magnetic field and Hall effects are applied. The governing equations are solved analytically by the perturbation method. The pertinent parameters affecting velocity, induced magnetic field (i.m.f), temperature and concentration are discussed graphically. The main goal and novelty of the research are to investigate the impact of the Soret effect and i.m.f along with Hall current on the flow field. The important findings are as follows: with the rise in S0, the induced magnetic field falls in the primary flow direction, whereas a reverse trend is noticed for the secondary flow direction. We also found that the Soret effect enhances the fluid temperature and both the components of velocity profiles. The expression of Skin friction, current density, Nusselt and Sherwood number over the magnetised vertical surface (m.v.s) are obtained and represented computationally through tabular forms.

Temperature Dependence on Transient Hydrodynamic Gravity Driven Flow Down an Inclined Plane

Transient hydrodynamic gravity driven flow of a viscous incompressible fluid down an inclined plane occupying a semi-infinite region of space bounded by an infinite hot plate is studied. The effect of modified Froude number plays an important role in determining the flow situation. Exact solution is obtained by employing Laplace transform method. This problem is concerned with a car – following theory subjected to traffic flow with a decisive importance to a variation of depth with a slope leading to a flood wave. A reducible influence of a frictional drag has an active influence to the flow reversal characteristics with time variation satisfying the separation due to the existance of a modified Froude number. The stabitity of a roll wave is determined by the critical Froude number in a time varying flow. Numerical results of velocity distributions and frictional shear stress are depicted graphically for different values of flow parameters. Numerical results of a critical Froude number are presented in tables. Temperature analysis has been presented analytically with a view to point out the expression of Nusselt number at the plate.

Application of Exponential Temperature Dependent Viscosity Model for Fluid Flow over a Moving or Stationary Slender Surface

The problem of laminar flow around a moving thin needle or slender surface with free stream velocity is analyzed when viscosity is supposed to have an exponential temperature dependency. Additionally, the temperature dependence in thermal conductivity is retained. Consideration of variable viscosity and thermal conductivity makes the governing equations coupled and non-linear. A self-similar solution of the problem is achieved, which depends on a parameter θw, which is the quotient of wall and ambient temperatures. A comparison of present findings is made with those of inversely linear temperature-dependent viscosity and constant viscosity cases. The size of the needle plays an important part in enhancing thermal boundary layer thickness. The expressions of skin friction coefficient and local Nusselt number in case of exponential temperature dependent viscosity are just derived in this study. An important observation is that computational results are qualitatively like those noticed for the case of inversely linear temperature dependency.

Study of Baffles Arrangement Influence on the Natural Convection into a Heated Square Channel

The present experimental paper is officiated to study the heat characteristics and performance of air flow through a square cross-sectional heated channel under natural heat convection conditions. The influence of baffles arrangement and perforated baffles on the rate of heat transfer through a channel are studied. Four cases of a heated channels are studied, one is a plain channel and other three channels with a baffle namely, three inline baffles, three staggered baffles and three staggered perforated baffles arrangements. The outer tested channels surfaces are electrically heated with a constant surface heat flux condition. All tested channels are fabricated by cold forming with constant dimensions using aluminum plate has thickness of 1.0 mm. The heat performance is assessed for all tested channels. The results of present paper are approved than the available data in the previous paper and a good convergence are noticed. Obtained experimental results appear that a three staggered perforated baffles arrangement is a best selection as it improves heat transfer rate in expression of Nusselt number, it higher about 22% to 27% than that the plain channel for same conditions.

Linear and weakly non-linear stability analysis of oscillatory convection in rotating ferrofluid layer

In the present paper, the problem of ferroconvection in the presence of uniform vertical rotation is considered to investigate the linear and weakly non-linear oscillatory stability. Two-dimensional convective roll instability is discussed with finite-amplitude disturbances. For linear stability, as a first-order problem, the expressions for Rayleigh numbers for stationary and oscillatory convection are derived and the effects of Coriolis force and magnetic parameters on the onset of ferromagnetic convection are studied, numerically. In weakly nonlinear oscillatory analysis, the second-order and third-order stability problems are discussed and the complex Ginzburg-Landau equation describing the amplitude of convection cell in rotating ferrofluid is derived and consequently, the expression for Nusselt number representing the heat transfer rate is obtained. From the present analysis, we observed that the rotation has the usual stabilizing effect on the linear stability in ferroconvection, however, the magnetic number (M1) and the measure of nonlinearity of magnetization (M3) both have a destabilizing effect on the onset of linear instability. Also, we found that for non-linear convection, the heat transfer rate (the Nusselt number) increases with increasing values of Taylor number, magnetic number, and the measure of nonlinearity of magnetization.

Analysis of time‐dependent dynamics of micropolar fluid subject to Lorentz force, energy flux due to a concentration gradient and viscous dissipation

This study deals with an analysis of the time-dependent dynamics of micropolar fluid flow subject to Lorentz force, diffusion thermal, and viscous dissipation effect past a uniformly moving semi-infinite porous plate in the presence of chemical reaction. Expressions of velocity, microrotation, concentration, temperature, skin friction, Sherwood number, and Nusselt number are established and the effect of several parameters on them are represented graphically. Equations governing the flow and heat transfer are solved by adopting the regular perturbation technique. It is noticed that temperature distribution as well as the coefficient of friction is enhanced due to the diffusion thermo effect. It is observed that the microrotation increases with increasing magnetic parameters. Furthermore, the study confirms a drop in fluid concentration under the composition of species.

MHD Mixed Convective Slip Flow along an Inclined Porous Plate in Presence of Viscous Dissipation and Thermal Radiation

The present study investigates the mixed convective MHD flow of Newtonian fluid along an inclined permeable plate which is saturated in porous medium. A non-uniform magnetic field along with viscous dissipation and thermal radiation is also considered in the model. Velocity and thermal slip conditions are applied at the plate. Expressions for skin friction and Nusselt number are obtained with the help of suitable similarity transformation. Governing equations are solved numerically by Runge-Kutta fourth order method with shooting technique. Graphs of the fluid velocity and temperature are plotted and their behaviours are discussed. Numerical values of skin friction and Nusselt number are tabulated and analysed.
 HIGHLIGHTS
 
 Rate of heat transfer can be enhanced by decreasing Eckert number or radiation parameter
 Higher fluid velocity with lesser skin friction can be obtained by using larger values of velocity slip parameter
 Mixed convection plays a significant role in enhancing fluid velocity
 
 GRAPHICAL ABSTRACT

Soret and heat generation effects on unsteady MHD Casson fluid flow in porous medium

This article studies motion with quadratic speed on the unsteady free convective MHD Casson fluid flow in a porous medium. The fluid in electrically conducting and bounding plate has ramped the surface concentration. The characteristics of heat and mass transfer are analyzed with thermal diffusion, heat generation, chemical reaction, and thermal radiation. The governing dimensionless equations are solved using the Laplace transform technique, and analytical expressions for velocity, temperature, and concentration are obtained. For both boundary conditions, the expression for Skin friction, Nusselt number, and Sherwood number are obtained and represented in tabular form. Effects of several pertinent parameters on velocity, temperature, and concentration distribution are presented graphically. It is seen that the mass buoyancy force increases with Soret number which leads to accelerated fluid flow. Chemical reaction and porosity of the fluid tend to reduced Skin friction coefficient, while Casson fluid and magnetic field tend to reverse effect on it.