Heat Transfer Biot Number Research Articles

Significance of Rosseland’s radiative heat transfer and dissipative heat on MHD viscous flow over a slandering sheet in the presence of Darcy-Forchheimer and Lorentz forces

The main emphasis of this research is to investigate computationally an innovative viscous, time-independent, and Darcy-Forchheimer flow of an electrically based incompressible nanofluid on a slandering stretched surface. The thermal conductivity and viscosity of this flow will be discussed. Incorporating an outer heat source into the thermal transfer process enhances the effect of dissipative heat and thermal radiation. When chemical processes are included, the effects of heat and solvent transport are influenced by the use of convective constraints at boundary. The flow characteristics are governed by the mathematical form which is further transferred to ordinary differential equations (ODEs) via appropriate assumptions regarding similarity variables and stream functions. The analytical technique for such highly nonlinear equations sometimes doesn't work effectively due to the strong nonlinearity. As a result, these transformed ODEs are solved numerically by means of bvp4c approach. Graphs depict the impacts of different substantial factors on velocity, temperature, and solutal concentration distributions. Numerical computations of physical quantities including magnetic parameters, inertial coefficient, permeable coefficient, thickness factor, heat transfer Biot number, Radiation parameter, Prandtl number, Eckert number, mass transfer Biot number, Schmidt number, heat source factor, and chemical reaction are evaluated and tabulated. The current findings are compared to previously known results, and they are in great agreement. The main outcomes of the study are thoroughly explained in the results and discussion section. Heat transfer Biot number raises the energy distribution and mass transfer Biot number strengthened the concentration profile while wall thickness quantity reduces the temperature and concentration of fluid as well. The enhanced variable viscosity is augmented by the longitudinal velocity profile and the rate of shear stress.

Cattaneo-Christov Heat Flux and Thermal Radiation in MHD Nanofluid Flow over a Bi-directional Stretching/Shrinking Surface

Nanofluids have gained popularity due to their better thermophysical properties and usefulness in daily life such as electronic design, solar energy, heat exchanger tubes, and cooling systems, among others. We have looked at the influence of thermal radiation, Cattaneo-Christov heat flux, and slippage on three-dimensional flow of MHD nanofluid along a surface which is stretched/shrinks in both directions in this study. The transformed ordinary differential equations are solved analytically, using homotopy analysis technique. A graphical analysis for the flows for numerous physical features has been presented. It has been observed that the fluids axial and transverse velocities are decreased by the magnetic field parameter, the suction/injection parameter, as well as by the slip parameter for stretching, whereas for shrinking, they are increased. The radiation parameter, heat transfer Biot number, and thermal relaxation parameter increases the nanofluids temperature. Bar charts were also used to evaluate how the physical parameters affect the skin friction coefficient and Nusselt number.

Modeling and analysis of Bödewadt hybrid nanofluid flow triggered by a stretchable stationary disk under Hall current

In the recent era of science and technology scientists have influenced by the hybridization of nanofluids due to their advanced thermophysical features. Hybrid nanofluids have superior response to thermal conductivity than any other conventional nanofluids. Therefore, the present study investigates the Bödewadt flow of hybrid nanoliquid above a stretchable static disk located in the plane z=0. Bödewadt flow describes a stable and uniform angular rotation of liquid at a higher distance from the static disk. Such flow is characterized through pressure gradient in radial direction and is balanced with centrifugal forces. An incompressible homogeneous electrically conducting flow occupies its space at z≥0. Hybrid nanofluid is a mixture of nanoparticles Cu (copper) and TiO2 (titanium dioxide) with water considered as a base-fluid. Titanium dioxide reveals excellent photo catalytic attributes and hence is implemented in antibacterial/antiseptic compositions. Moreover, copper nano-ingredients metallic particles suggest suitable dye diminution and catalytic potential properties. Hall effect is encountered in the momentum equations to measure the magnetic field while radiation term is considered to address the energy analysis. The convective flow phenomenon is normalized by executing similarity functions. The reduced governing system is then solved in numerical manner using Runge-Kutta-Fehlberg (RKF-45) procedure. The flow phenomenon on velocity and thermal fields is discussed in graphical way. Three-dimensional flow visualization with two-dimensional contours and streamlines are portrayed as well. Moreover, the numeric data of local-Nusselt number shear stresses is computed against selected values of the physical parameters. The modification in Hall current magnifies the radial velocity field and reduces the velocity field along axial direction. The temperature field is enhanced by the increased variations in heat transfer Biot number. The influence of volume fractions results in modification of thermal profiles.

Significance of heat and mass transport in peristaltic flow of Jeffrey material subject to chemical reaction and radiation phenomenon through a tapered channel

Abstract Using mathematical modeling and computational analysis, this study aims to examine the peristaltic blood flow of a non-Newtonian material in a tapered channel with radiative heat flux and response mechanisms. By utilizing a long-wavelength approximation, ignoring the wave number, and performing under conditions of low Reynolds number, closed form solutions for the velocity, temperature, and concentration fields are achieved. Several governing parameters and their effects on the system were analyzed, and relevant diagrams were provided. Increasing the Biot number, Jeffrey material, and thermal radiation parameter of the heat and mass transfer mechanism increases the velocity profile. When the heat source/sink parameter and the heat transfer Biot number increase, the temperature profile improves. The resultant concentration distributions are enhanced when mass transfer Biot number, heat radiation, and chemical processes are all raised. We observe that the pressure rate decreases in all three pumping zones when the heat transfer Grashof number and heat transfer Biot number rise. This is because the pressure rate is affected by the Grashof number and Biot number of heat transmission. The increase in thermal radiation parameter and heat transfer Biot number results in a slower rate of heat transfer than when Prandtl number and heat source/sink parameter increases. When the Soret number, Schmidt number, Biot number, and heat source/sink parameter are all raised, the mass transfer coefficient also rises. This rate, however, decreases as the heat radiation and chemical reaction parameters rise. The findings presented in this study have interesting implications for other aspects of human physiology. The preponderance of organs are permeable. Furthermore, fluids render the location of natural boundaries uncertain. The presented mathematical model can be used to derive predictions about the behavior of various systems. For the study of cancer treatment in biological systems, a mathematical model that includes nanoparticles, viscosity dissipation, and rotation holds much promise. Model development incorporated Soret–Dufour effects and thermal analysis of the digestive system.

A sensitivity analysis of MHD nanofluid flow across an exponentially stretched surface with non-uniform heat flux by response surface methodology

The current study investigates the MHD flow of nanofluid across an elongating surface while taking into account non-uniform heat flux. For this, we have considered the flow of a boundary layer over a stretched sheet containing (water-based) Al2O3 nanoparticles. The convective boundary conditions for temperature have been invoked. The flow created by a surface that is exponentially expanding in the presence of a magnetic field and a non-uniform heat flux has been mathematically formulated by using laws of conservation. Transformed non-dimensional systems of governing equations have been analyzed numerically by using Adam’s Bashforth predictor corrector approach. The effects of emerging parameters on the fluid velocity and temperature profiles have been further described by plotting graphs. An experimental design and a sensitivity analysis based on Response Surface Methodology (RSM) are used to examine the effects of various physical factors and the dependence of the response factors of interest on the change of the input parameter. To establish the model dependencies of the output response variables, which include the skin friction coefficient and the local Nusselt number, on the independent input parameters, which include the magnetic field parameter, the nanoparticle volume fraction, and the heat transfer Biot number, RSM is used. On the basis of statistical measures such as Q - Q residual plots, adjusted and hypothesis testing using p values, it is observed that both of our models for Skin Friction Coefficient (SFC) and the Local Nusselt Number (LNN) are best fitted. Further, it is concluded that the sensitivity of the SFC, as well as the LNN through heat transfer Biot number, is greater than that of nanoparticle volume fraction and magnetic field parameter. The SFC is sensitive to all combinations of the input parameters. At high levels of heat transfer Biot number, the LNN displays negative sensitivity via magnetic field parameters.

Entropy generation due to micro-rotating Casson's nanofluid flow over a nonlinear stretching plate: numerical treatment

Objective: This article numerically investigates the entropy generation due to micro-rotating Casson's nanofluid along with an impact of an inclined magnetic field past a nonlinear stretching surface. Heat and mass transfer analysis is carried out in association with the heat source/sink and chemical reaction coefficient. Furthermore, heat dissipation is computed via viscous dissipation and joule heating phenomena. Attributes of nanofluid are disclosed by taking Brownian motion and thermophoresis phenomena. Results and conclusion: Numerical solutions of out-coming differential equations are obtained employing Runge–Kutta fourth-order with shooting technique. The behavior of multiple parameters has been displayed via graphs. Entropy profile is developed effectively for accelerating values of Hartmann and Brinkman number. Moreover, the temperature profile accelerates significantly with an enhancement in the heat transfer Biot number. Practice implications: The study of entropy generation due to micro-rotating Casson's nanofluid has numerous applications in engineering and heat-storing devices such as pumped heat electricity storage, phase change material, solar and geothermal power systems. The minimization of entropy plays a significant role in the design of the mechanical system that relies on heat transfer.

Soret and Dufour effects on a Casson nanofluid flow past a deformable cylinder with variable characteristics and Arrhenius activation energy

In this study, the effects of variable characteristics amalgamated with chemical reaction and Arrhenius activation energy are analyzed on a two-dimensional (2D) electrically conducting radiative Casson nanoliquid flow past a deformable cylinder embedded in a porous medium. The surface of the cylinder is deformable in the radial direction i.e., the z-axis. The impression of Soret and Dufour's effects boosts the transmission of heat and mass. The flow is analyzed numerically with the combined impacts of momentum slip, convective heat, and mass conditions. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The dimensionless protuberant parameters are graphically illustrated and discussed for the involved profiles. It is perceived that on escalating the velocity slip parameter and porosity parameter velocity field depreciates. Also, on escalating the radiation parameter and heat transfer Biot number a prominent difference is noticed in an upsurge of the thermal field. For growing values of Brownian motion and thermophoretic parameters, temperature field augments. On escalating the curvature parameter and porosity parameter, drag force coefficient upsurges. The outcome of the Soret number, mass transfer Biot number, and activation energy parameter is quite eminent on the concentration distribution for the sheet in comparison to the deformable cylinder. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem.

Numerical simulation for Arrhenius activation energy on the nanofluid dissipative flow by a curved stretching sheet

In this paper, we have analysed a binary chemical nanofluid dissipative flow (in two cases i.e., 50% EG $$ + $$ 50% water/silica and 50% EG $$ + $$ 50% water/graphene oxide) due to a curved stretching sheet with activation energy. Appropriate transformations yield the nonlinear ordinary differential system. Shooting procedure (R-K 4th order based) is executed to solve the resultant equations. Graphical illustrations thoroughly demonstrate the features of the involved pertinent parameters. We have deliberated the behaviour of the alike parameters on the rate of transfers (heat and mass) and surface drag force (skin friction coefficient) by means of tables. This investigation reveals that (a) reaction rate parameter and temperature difference parameter are helpful to ameliorate the mass transfer rate (b) concentration enhances for higher estimation of activation energy variable (c) increasing the volume fraction of nanoparticles reflects an escalation in temperature (d) heat transfer rate enhancement is recognized for the influence of heat transfer Biot number. At the end this study, we came to know that the EG-Water $$ + $$ Graphene Oxide mixture has more heat transfer rate compared to EG-Water $$ + $$ Silica mixture. This outcome helps to conclude that, whenever the more heat transport required in manufacturing and industries, we can take the EG-Water $$ + $$ Graphene Oxide mixture.

Peristaltic motion of Maxwell fluid subject to convective heat and mass conditions

This article concentrates on peristalsis of Maxwell fluid in a symmetric channel with heat and mass convective conditions. Analysis is given in presence of viscous dissipation. The relevant problems statements are constructed and solved for the series solutions of stream function, temperature and concentration. Regular perturbation technique is adopted for small wave number. Heat transfer coefficient is also derived. Results of temperature, concentration and heat transfer coefficient are graphically analyzed. Trapping phenomenon is studied. It is observed that heat and mass transfer Biot numbers have opposite effects on fluid temperature and concentration. Concentration distribution decays with the increase in Schmidt number and Soret number. Heat transfer coefficient has oscillatory behavior and magnitude of heat transfer coefficient increases when heat transfer Biot number enhances. In addition, similar trapping pattern is observed for relaxation parameter and wave number.

Soret and Dufour features in peristaltic motion of chemically reactive fluid in a tapered asymmetric channel in the presence of Hall current

The present work examines heat and mass transfer characteristics of peristaltic motion of Johnson-Segalman fluid in a tapered asymmetric channel along with chemical reaction, by taking into account the Soret and Dufour effects. Effects of Hall current have also been discussed in mathematical modeling and analysis. Following the peristaltic wave procedure, the tapered asymmetric channel is based on the non uniform boundaries having diverse phases and amplitudes. The channel walls show excellent agreement with more realistic convective conditions. The modeled flow problem is directed into ordinary differential equations set with proper utilization of similarity quantities. The estimation of high wavelength as well as small Reynolds number are acknowledged to deduce the equations of Johnson-Segalman liquid model. The adopted solution procedure is constructed via homotopic algorithm. The results have been analyzed for various parameters of interest and sketched for better understanding. The velocity profile reveals decreasing behavior for increasing values of Weissenberg number and Hartman number while converse behavior is found for mean flow rate and Hall parameter. The temperature profile falloffs for heat transfer Biot number and Hartman number whereas it increases for Prandtl number, Brinkman number, Dufour number and Hall parameter. The concentration profile tends to decrease for mass transfer Biot number and increase for Schmidt constant.

Thermocapillary flow transition in an evaporating liquid layer in a heated cylindrical cell

Motived by recent ground-based and microgravity experiments investigating the interfacial dynamics of a volatile liquid (FC-72, Pr=12.34) contained in a heated cylindrical cell, we numerically study the thermocapillary-driven flow in such an evaporating liquid layer. Particular attention is given to the prediction of the transition of the axisymmetric flow to fully three-dimensional patterns when the applied temperature increases. The numerical simulations rely on an improved one-sided model of evaporation by including heat and mass transfer through the gas phase via the heat transfer Biot number and the evaporative Biot number. We present the axisymmetric flow characteristics, show the variation of the transition points with these Biot numbers, and more importantly elucidate the twofold role of the latent heat of evaporation in the stability; evaporation not only destabilizes the flow but also stabilizes it, depending upon the place where the evaporation-induced thermal gradients come into play. We also show that buoyancy in the liquid layer has a stabilizing effect, though its effect is insignificant. At high Marangoni numbers, the numerical simulations revealed smaller-scale thermal patterns formed on the surface of a thinner evaporating layer, in qualitative agreement with experimental observations. The present work helps to gain a better understanding of the role of a phase change in the thermocapillary instability of an evaporating liquid layer.

Electroosmotic flow of pseudoplastic nanoliquids via peristaltic pumping

The study of electroosmotic flow of biorheological fluids has been employed in the advancement of diversified biomicrofluidics systems. To explore more in this field, a mathematical model is developed to investigate the electroosmotic flow of pseudoplastic aqueous nanoliquids in microchannel. A tangent hyperbolic fluid model is employed to describe the rheological behavior of the pseudoplastic fluid. Here, analytical solutions for potential distribution, temperature and nanoparticle fraction are derived and perturbation solution for stream function, pressure gradient and volumetric flow rate are obtained. The convective boundary condition is applied on the channel walls. The authentic assumptions of Debye–Huckel linearization, long wavelength and small Reynold’s number are employed in the dimensional conservative equations. The influences of various emerging parameters are graphically computed for axial velocity, pressure gradient, thermal temperature, nanoparticle volume fraction, skin friction coefficient and Nusselt profiles. To observe the thermal radiation effects, a thermal radiative flux model is also deployed. It is noticed that the heat transfer Biot number increases with increasing thermal temperature; however, a reversed behavior is reported for the nanoparticle volume fraction. Therefore, the present model does not only provide a deep theoretical insight to interpret the electroosmotic flow systems, but it will also be applicable in designing the emerging tool for biomicrofluidic devices/systems under peristalsis mechanisms.

Chemical reaction in peristaltic motion of MHD couple stress fluid in channel with Soret and Dufour effects

Abstract This paper looks at the peristaltic motion of MHD couple stress fluid in an inclined asymmetric channel. Simultaneous effects of heat and mass transfer are considered. Soret and Dufour features lead to the coupled differential systems. Channel walls satisfy the convective conditions of heat and mass transfer. Exact solutions for the stream function and pressure gradient are derived. Temperature and concentration are obtained numerically. Graphical illustrations for axial velocity, temperature, concentration and streamline patterns are developed. Physical interpretation of obtained results has been presented. It can be seen that both Soret and Dufour numbers reduce the concentration field while reverse effect is seen towards temperature for both numbers. It is also observed that concentration reduces towards destructive chemical reaction and enhances for constructive chemical reaction. The heat transfer Biot number gives rise to fluid temperature. Further more the mass transfer Biot number decreases the concentration.

Numerical simulation for peristaltic activity of Sutterby fluid with modified Darcy’s law

The current work examines the peristaltic flow of Sutterby fluid in a planar symmetric channel. Electrically conducting fluid is considered via imposed magnetic field. An incompressible Sutterby fluid saturates the porous medium. Modified Darcy’s law has been employed for the porous medium effect. The channel walls are compliant. Convective conditions of heat and mass transfer are imposed. Viscous dissipation and Joule heating are retained. Problem for large wavelength are numerically solved. The graphs are obtained for the velocity, temperature, concentration and heat transfer rate. Velocity and concentration profiles are observed to have opposite behavior for increasing Darcy number. It is found that the effect of Hartman number on the velocity and temperature profiles is similar. Further heat transfer coefficient strengthened when heat transfer Biot number is increased.

Influence of convective conditions in radiative peristaltic flow of pseudoplastic nanofluid in a tapered asymmetric channel

This paper looks at the influences of magnetohydrodynamics (MHD) and thermal radiation on peristaltic transport of a pseudoplastic nanofluid in a tapered asymmetric channel. The tapered channel walls satisfy convective boundary conditions. The governing equations for the balance of mass, momentum, temperature and volume fraction for pseudoplastic nanofluid are first formulated and then utilized for long wavelength and small Reynolds number considerations. Effects of involved parameters on the flow characteristics have been plotted and examined. It is observed that the heat transfer Biot number shows a dual behavior on the temperature of nanofluid particles whereas the mass transfer Biot number with its increasing values enhances the fluid temperature.

Peristaltic flow with convective mass condition and thermal radiation

The primary objective of present investigation is to introduce the novel aspects of convective mass condition and thermal radiation in the peristaltic transport of fluid. Magnetohydrodynamic (MHD) fluid was considered in a symmetric channel. Heat and mass transfer characteristics were analyzed in the presence of Soret and Dufour effects, and the results were presented via two forms of thermal radiation. The temperature, concentration and pressure rise per wavelength were examined. It is observed that the velocity slip and magnetic field parameters have opposite effects on the pressure rise per wavelength. Temperature of fluid is a decreasing function of the radiation parameter. Further, the temperature of fluid decreases by increasing the heat transfer Biot number. It is notified that the heat transfer rate at the wall is a decreasing function of radiation parameter.

Convective boundary conditions effect on peristaltic flow of a MHD Jeffery nanofluid

This work is aimed at describing the influences of MHD, chemical reaction, thermal radiation and heat source/sink parameter on peristaltic flow of Jeffery nanofluids in a tapered asymmetric channel along with slip and convective boundary conditions. The governing equations of a nanofluid are first formulated and then simplified under long-wavelength and low-Reynolds number approaches. The equation of nanoparticles temperature and concentration is coupled; hence, homotopy perturbation method has been used to obtain the solutions of temperature and concentration of nanoparticles. Analytical solutions for axial velocity, stream function and pressure gradient have also constructed. Effects of various influential flow parameters have been pointed out through with help of the graphs. Analysis indicates that the temperature of nanofluids decreases for a given increase in heat transfer Biot number and chemical reaction parameter, but it possesses converse behavior in respect of mass transfer Biot number and heat source/sink parameter.

Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source

Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed. Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.

Mixed convective heat and mass transfer analysis for peristaltic transport in an asymmetric channel with Soret and Dufour effects

The present investigation addresses the simultaneous effects of heat and mass transfer in the mixed convection peristaltic flow of viscous fluid in an asymmetric channel. The channel walls exhibit the convective boundary conditions. In addition, the effects due to Soret and Dufour are taken into consideration. Resulting problems are solved for the series solutions. Numerical values of heat and mass transfer rates are displayed and studied. Results indicate that the concentration and temperature of the fluid increase whereas the mass transfer rate at the wall decreases with increase of the mass transfer Biot number. Furthermore, it is observed that the temperature decreases with the increase of the heat transfer Biot number.

A note on thermal-diffusion and chemical reaction effects on MHD pulsating flow in a porous channel with slip and convective boundary conditions

The present note investigates the effects of chemical reaction and Soret effects on hydromagnetic laminar viscous pulsating flow in a porous channel with slip and convective boundary conditions. The governing equations are solved analytically and the expressions for velocity, temperature, concentration, Nusselt number and Sherwood number distributions are obtained. The effects of various pertinent parameters on flow variables have been discussed numerically and explained graphically. Analysis indicates that the temperature distribution decreases for a given increase in heat transfer Biot number and Prandtl number while it increases with an increase in Hartmann number. Further, the concentration distribution increases with an increase in the mass transfer Biot number, Soret number and the heat transfer Biot number, while it decreases for a given increase in the chemical reaction parameter.