Exponential Heat Research Articles

Theoretical investigation of hybrid nanomaterials transient flow through variable feature of Darcy–Forchheimer space with exponential heat source and slip condition

Nanomaterials have achieved remarkable importance in cooling small electronic gadgets like akin and microchips devices. The role of nanoparticles is essential in various aspects, especially in biomedical engineering. Thus hybrid nanomaterials is introduced to strengthen the heat exchangers' performance. In view of the above practical and existing applications of nanomaterials. Our aim is to examine the consequences of Darcy–Forchheimer's radiative and Hall current flow of nanomaterials over a rotating porous disk with variable characteristics. Stretching disk accounting for the slip condition. Nanoparticles ZnO and CoF2O4 are dispersed in based fluid water. The present model is utilized for thermo-physical attributes of hybrid nanomaterials with the impact of shape factor. Transformations convert the modeled PDEs into ODEs. The obtained highly non-linear system is tackled numerically by the NDSolve technique through the software Mathematica. The outcomes of significant variables against different profiles are executed and elaborated in detail. Obtained results show that both nano and hybrid nanofluid radial velocity have reverse behavior against variable porosity and permeability parameters, whereas it decays for larger Forchheimer numbers. Further, it is worthy to point out that, hybrid nanophase has a higher impact on distinct profiles when compared with nano and common liquid phases.

Triple stratification impacts on an inclined hydromagnetic bioconvective flow of micropolar nanofluid with exponential space-based heat generation

The present work aims to analyze the effects of magnetohydrodynamics, heat and mass transfer, and gyrotactic microorganism behavior on the bioconvective micropolar nanofluid flow subject to triple stratifications and Cattaneo–Christov double diffusion over a stretched surface. The dimensional system of differential equations has been simplified to dimensionless with suitable non-dimensional quantities and suitable similarity transformations. An efficient numerical technique bvp4c through MATLAB has been implemented to devise the solution of the non-dimensionalized system of governing equations. The significant outcomes of the current analysis are that the amplification of magnetic parameter intensifies the flow velocity and shows the reverse effect for the fluid temperature. The enhancement of micropolar parameter upgrades microrotation, while it exhibits opposite effect for the fluid temperature and nanoparticle concentration. Microorganism concentration peters out with a rise in Peclet number. Gyrotactic microorganism thermal stratification augmentation leads to the diminution of velocity and thermal boundary layer thickness. When gyrotactic microorganism concentration difference parameter rises from 0.1 to 0.8, skin friction whittles down by 12.5%, and wall motile microorganism number ameliorates by 50%.

Exponential space and thermal-dependent heat source effects on electro-magneto-hydrodynamic Jeffrey fluid flow over a vertical stretching surface

This paper deals with the study of an incompressible electro-magneto-hydrodynamic (EMHD) Jeffrey fluid flow over a vertical nonlinear stretching surface of variable thickness. Heat and mass transfer effects are analyzed by considering different source terms like viscous dissipation, Ohmic heating, thermophoresis, Brownian motion, thermal heat source, exponential heat source and activation energy. Governing equations for the flow system are converted into dimensionless forms using appropriate similarity transformations. The solution for the resulting governing equations is obtained by using the shooting technique with RK-4 method. The effects of various physical parameters such as magnetic field parameter [Formula: see text], Grashof number (Gr), solutal Grashof number [Formula: see text], Brownian diffusion parameter [Formula: see text], thermophoresis diffusion parameter [Formula: see text], thermal heat source parameter [Formula: see text], exponential heat source parameter [Formula: see text], Prandtl number (Pr) and Lewis number (Le) are presented with the help of graphs. It is observed that the heat transfer effects increase by increasing thermal and exponential heat sources, and mass transfer effects enhance by increasing the activation energy. Entropy generation for this flow system is also analyzed. Entropy decreases with an increase in the electric field parameter. In contrast, the Bejan number initially increases with an increase in the electric field parameter. After some particular value of electric field parameter, it changes its behavior in the boundary layer and decreases with an increase in the electric field parameter. Entropy and Bejan number increase with an increment in the concentration difference parameter. The accuracy of the results is validated by those of published literature and found in reasonable justification. The present results may be helpful in many engineering and industrial applications like manufacturing lubrication, natural gas networks, cooling nuclear reactors and spray processes.

Numerical investigation of double diffusion heat flux model in Williamson nanofluid over an exponentially stretching surface with variable thermal conductivity

This investigation examines the Williamson nanofluid flow over an exponentially stretched surface with variable thickness. Cattaneo-Christov double diffusion (CCDD) heat flux model is applied while examining two cases of heat transfer, i.e., prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF). A mathematical model of the problem based on momentum, mass, and energy conservation. The governing non-linear partial differential equation (PDEs) are converted into non-linear ordinary differential equations (ODEs) via similarity transformations. The velocity, temperature, and concentration profiles are obtained numerically. Additionally, the impacts of numerous physical parameters of engineering significance are visually depicted through graphs and tables. It is noted that by raising the thermal relaxation parameter γ 1 , the temperature profile decreases. When the concentration relaxation parameter γ 2 rises, then the concentration distribution also decays. When the magnetic parameter M increases, then the velocity profile decreases. For the selected numeric values of the Prandtl number Pr , the temperature profile decreases for both PEST and PEHF cases.

Analytical Solution of Non Linear DPL Bioheat Transfer Model for Temperature Dependent Metabolic Heat Source During Thermal Therapy

In this research paper, the simulation based modelling of heat transfer in tissue under periodic boundary condition has been considered. The dual phase lag bioheat transfer (DPLBHT) model is implemented for computation of the temperature based thermal therapy treatment. The elements of volumetric heat source such as perfusion of blood, metabolism heat source and external heat source are considered in nonlinear DPL model. In this paper we have taken three cases for metabolic heat source namely, constant, linear and exponential. The combined two numerical methods which are based on finite difference scheme and Runge Kutta (4,5) scheme are exerted to solve the non-linear problem. We compute the exact solution for particular case. Numerical conclusions which are computed by numerical hybrid method are equated with exact result. It has been found that non linear DPL model with exponential metabolic heat source is closed to exact solution. We also expressed the effect of different parameters such as relaxation time, perfusion rate, metabolic heat source parameter, associated blood perfusion heat, heat source because of heat flux and temperature gradient etc.

Comparative appraisal of nanofluid flows in a vertical channel with constant wall temperatures: an application to the rocket engine nozzle

ABSTRACT This study aims to investigate the entropy generation of fully developed nanofluid flow in a spongy medium between two fixed absorbent vertical plates with a transpiration cooling mechanism. For heat transfer analysis exponential space-dependent heat source and thermal dependent heat source along with linear radiation are employed. Three distinct scenarios for thermal wall boundary conditions are investigated: i) Constant walls temperature ii) Convective boundary condition on the left wall of the channel and iii) convective boundary conditions on both walls of the channel. Two nanofluids combinations i.e. copper (cylindrical shape) nanoparticles immersed in water and silver (platelet shape) nanoparticles in water are used. It is also noted that studies on the transpiration of nanofluid in rocket engines for cooling purposes are scrutinized when walls are stretchy. But the walls of the rocket engine are fixed. Keeping this in mind, we analyzed the cooling process of the rocket nozzle with a fixed wall channel. The numerical solution of the model equations is attained using the bvp4c method in MATLAB. Findings indicate that the copper/water nanofluid combination performs better than silver/water as for as cooling the nozzle of a rocket engine is concerned. Moreover, convective boundary conditions lower the fluid temperature.

Hydrothermal features in the swirling flow of radiated graphene – Fe3O4 hybrid nanofluids through a rotating cylinder with exponential space-dependent heat generation

The current analysis tries to establish the hydrothermal characteristic for two hybrid nanofluids and a familiar nanofluid flow over a stretchable swirling cylinder. Graphene and Ferrous nanoparticles among present fluids water were appropriated by the affected flow. Moreover, the significant characteristics of aggressive space-dependent convective boundary conditions and heat source/sink were studied for flow and thermal mechanisms. Applicable comparison transformations were furnished to clarify those fluid equations for partial differential equations to ordinary differential equations. Every highest capable finite element method was enforced by clearing up consequent equations and boundary conditions. It’s extraordinary to the validity and reliability of the present numerical explanation in admirable accord with extant clear-cut solutions for the literature. Fluctuations by the confusions of swirling velocity, temperature, and axial velocity to certain related parameters are drawn over the design. The Nusselt number and twain components for skin friction coefficient values of more investigated elements are disclosed in the tables. The investigation finally confirms that nanoparticles were preferred to familiar fluids for improving heat transfer. Both the velocities are reduced for the magnetic flux, whereas temperature kept increasing.

Improving the thermal performance of (ZnO-Ni /H2O) hybrid nanofluid flow over a rotating system: the applications of Darcy Forchheimer theory

The present study focused on the effect of Lorentz force and Hall current on hybrid nanomaterial flow over a transient stretching and rotating disk. Darcy-Forchheimer law was utilized. A porous stretching disk accounted for the slip effect. Energy expression is modeled through heat dissipation, radiation, and exponential heat source. Hybrid nanomaterial is used for the current model, which is the combination of ZnO and Ni with water as a base liquid. The modeled PDE system is converted to ODEs employing suitable variables. The obtained ODEs are approximated by the ND-Solve technique. Our analysis conveys that the rate of heat transfer is higher in nanomaterial compared with hybrid nanomaterial. Hall current enhances the fluid motion, whereas the inertia factor shows the opposite behavior. Additionally, it is found that the Lamina shape of nano-particles has a higher rate of heat transfer than other shapes.

Study of radiative magneto-non-Newtonian fluid flow over a nonlinearly elongating sheet with Soret and Dufour effects

Casson fluid model is extensively used for modeling of blood flow in thin arteries at low shear rates. The current article investigates the Soret and Dufour effects on free convective flow of Casson fluid over a nonlinearly elongating sheet embedded in a porous medium. Free convection: Flows arising solely due to the difference in density caused by temperature differences. The exponential space-based heat source/sink and thermal radiation are also incorporated in the heat transfer equation. Similarity solution was obtained by using suitable transformations and the transformed equations are solved by using the Runge–Kutta fourth-order method with a shooting technique by the help of the MATLAB code. The impacts of operating parameters on velocity, temperature, and concentration distributions are explained through graphs and tables. Important findings of the analysis are: Dufour and Soret effects serve as the surface coolant and maintenance of solutal deposition-free surface. Applied magnetic field and heavier diffusing species with suction lead to thinner boundary condition preventing vorticity diffusion.

Entropy generation analysis for mixed convective flow of Casson fluid in a vertical microchannel with the influence of nonlinear radiation by maintaining inconstant viscosity

AbstractThe study of entropy generation in the fluid flow has great importance in the field of engineering. The present analysis is to investigate the entropy production in Casson fluid flow in a vertically placed porous‐filled microchannel. The flow is influenced by the nonlinear radiation and exponential heat source. Viscosity is kept varying throughout the flow. The equations which govern the considered flow are nonlinear and are nondimensionalized by considering the appropriate nondimensional variables. The flow problem is tackled by converting the ordinary differential equation (ODE) by assigning the new variables. The flow problem is tackled by using the effective mechanism which involves the finite difference technique by converting the equations into a set of first‐order ODE. The results attained are discussed using the graphs. It is noted that by maintaining the lesser values for the Casson parameter and mixed convection parameter, entropy production can be reduced. The Bejan number profile has the highest magnitude for the variation of mixed convection parameter and the same is found to be less for the nonlinear radiation parameter.

Three-dimensional numerical analysis of flow and heat transfer of bi-directional stretched nanofluid film exposed to an exponential heat generation using modified Buongiorno model

The heat transfer characteristics of copper/water nanofluid flow over a bi-directional stretched film are theoretically studied. The used mathematical model accounts for nanofluid effective dynamic viscosity and thermal conductivity. The model of the current study utilizes the modified Buongiorno model to scrutinize the effect of haphazard motion, nanoparticles' thermo-migration, and effective nanofluid properties. 3D flow is driven by having the nanofluid film elongation in two directions. The thermal analysis of the problem considers the nonlinear internal heat source and Newton heating conditions. In modeling the problem, the Prandtl boundary layer approximations are employed. Moreover, the nonlinear problem set of governing equations for investigating the transport of water conveying copper nanoparticles was non-dimensionalized before being treated numerically. The current parametric study investigates the impact of governing parameters on nanoparticles velocities, temperature, and concentration distributions. The presence of copper nanoparticles leads to a higher nanofluid temperature upon heating. The temperature enhances with the nanoparticles Brownian movement and thermo-migration aspects. Furthermore, involving a heat source phenomenon augments the magnitude of the heat transfer rate. Moreover, the velocity ratio factor exhibits decreasing behavior for x-component velocity and increasing behavior for y-component velocity. In conclusion, the study results proved that for larger values of Nb and Nt the temperature is higher. In addition, it is clear from the investigations that the Lewis number and Brownian motion factor decline the nanoparticle concentration field.

Bio-convection effects on Williamson nanofluid flow with exponential heat source and motile microorganism over a stretching sheet

This article studies the bio-convection impacts on Williamson nanofluid flow and covers the nonlinear thermal radiation and chemical reaction effects on stretching sheet. The fundamental focus is to enhance heat transfer. Nanofluids are the most important source of effective heat source, having many applications in scientific and technological processes. Nanomaterials with superior thermal characteristics offer a wide range of uses in medicine, energy generation, heat exchange, and electronic cooling systems, among others. The present physical problem involving this flow is contained the nonlinear partial differential equations (PDEs). An appropriate transformation is used to convert the partial differential equations (PDEs) to ordinary differential equations (ODEs), which are then numerically settled utilizing bvp4c method in MATLAB. The physical features of nanofluids such as fluid velocity, volumetric concentration, temperature, and profiles of motile organisms are studied in relation to various factors. Additionally, the skin friction coefficient, Nusselt number, Sherwood number as well as motile microorganism number are calculated numerically using tables. It is found that the velocity profile decreases for the boosted values of Walliamson fluid parameter, magnetic parameter, angle of inclination and buoyancy ratio parameter. The temperature grows by increasing the values of thermophoresis parameter, exponential space and thermally based heat source/sink parameter. A survey of the available literature corroborates the aforementioned results.

Effect of exponential heat source on parabolic flow of three different non-Newtonian fluids

This study examined the flow and thermal transfer feature of MHD (magnetohydrodynamic) Casson, Carreau, and Williamson fluid movements over a parabolic extending region with exponential heat generation effect. The mathematical model is transformed into Ordinary Differential Equations (ODEs) by utilizing appropriate similarity variables and resolved using bvp5c Matlab package. The influence of applicable limits on transfer facts is illustrated via plots and tabular values. The current study outcomes reveal the comparisons of flow, thermal profiles, wall friction, and local Nusselt number of these (Casson, Carreau, and Williamson) different non-Newtonian liquids. Casson fluid shows more excellent thermal conductivity when compared to Carreau and Williamson fluids and observed that the drive and thermal gradient of three non-Newtonian fluids are not uniform. Also, the magnetic force tends to condense the stream and thermal transport rate of these three fluids. The rate of thermal transport is amplified by growing the magnitude of Prandtl and exponential parameters.

Importance of induced magnetic field and exponential heat source on convective flow of Casson fluid in a micro-channel via AGM

The study of the natural convective flow of a fluid in the presence of an induced magnetic field has always been of considerable importance due to its many applications in various areas of science, technology, and industry, such as the operation of magnetohydrodynamic generators. This study addresses an analysis of exponential heat source and induced magnetic field on the second-class convection of Casson fluid in a microchannel. The flow is in a vertical microchannel organized by two vertical plates. The answer to governing equations has been grabbed for temperature field, induced magnetic field, and velocity via Akbari-Ganji's method (AGM). Nusselt number, skin friction coefficient, and current density are approximated. Graphs that describe the conclusion of influential physical variables on velocity, temperature, current density, induced magnetic field, and skin friction coefficient distributions are shown. Comparison of results with numerical method (Runge-Kutta-Fehlberg, RKF-45), homotopy perturbation method (HPM), and AGM confirms the accuracy of answers obtained with AGM.

Bio-convective Darcy-Forchheimer oscillating thermal flow of Eyring-Powell nanofluid subject to exponential heat source/sink and modified Cattaneo–Christov model applications

Nanofluid thermal applications considerably enhanced the heat and mass transfer patterns, which plays novel role in many bio-technological, renewable energy and engineering applications. Many prime applications off nanomaterials have been inspected in solar energy and thermal engineering issues to benefit human society. Furthermore, motile microorganisms, that have applications in petroleum sciences, enzymes biotechnology, biofuels, pharmaceutical, and other fields, greatly improve the stability of nanofluids. The current study examines the Darcy-Forchhiemer accelerating flow of Eyring-Powell nanofluid over an oscillating surface which contains the thermal radiations and gyrotactic microorganisms. The extension in the heat and mass transfer expression is suggested by following the relations of Cattaneo–Christov theory. Furthermore, the non-uniform heat source/sink phenomenon is also being focused to improve the thermal aspect of model. The flow problem model is consisting of non-linear PDEs that are solved by using the homotopy analysis scheme. After highlighting the convergence zone, physical characteristics for parameters are listed.

Corrigendum: Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux

Corrigendum: Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux

Scrutinization of thermodynamic second law for the steady flow of couple stress nanofluid in an inclined microchannel by varying thermal conductivity

AbstractThis study comprises the flow of Ti6Al4N nanoparticle alloy allowed to flow within the microchannel kept at a certain angle. Engine oil is the base fluid in which nanodimensional particles are immersed. The flow is caused by the influence of linear and exponential heat sources. The microchannel is a permeable media with the suction/injection at the microchannel extremes. During the flow, the impact of the microstructure of these particles is concerned, thus reporting the rotational interaction amidst the particles. The obtained nonlinear equations are solved using the effective numerical method, namely, finite difference code improved by using the Lobatto IIIA formula and the findings are discussed using the graphs. The results attained claim that linear and exponential space‐dependent heat source parameter has augmented the thermal profile. Also, consideration of the couple stress of the fluid is known to retard the flow.

Activation energy with exothermic/endothermic reaction and Coriolis force effects on magnetized nanomaterials flow through Darcy–Forchheimer porous space with variable features

Nanomaterials have a remarkable role in contributing to industrial and medical applications like cooling of compressors, domestic refrigerators, brain tumors, and engines. Therefore, this report develops the theoretical investigation of magnetized nanomaterials Darcy–Forchheimer flow with zero mass flux. Rotation and stretching of disk cause the flow. Variable permeability and porosity are explored via Darcy–Forchheimer expansion. Activation energy with exothermic/endothermic reaction, Joule heating, exponential, and thermal heat source are additionally added to the energy equation. For the analysis of nanomaterials, Boungiorno model is considered. The modeled equations are altered to systems of ordinary differential equations by using Von Karman variables. ND-Solve scheme numerically approximated the converted system. Variation of physical quantities against distinct parameters is interpreted. It is noted that exothermic/endothermic reaction improves the temperature of nanomaterials.

Activation energy impact on unsteady Bio-convection nanomaterial flow over porous surface

<abstract> <p>Nanofluid is an advanced technology to enhance heat transportation. Additionally, the thermal conductivity of nanofluids is high therefore, they are more useful for heat transportation. Evaluation of entropy generation has been a helpful technique for tackling improvements in thermal features because it provides information that cannot be obtained via energy analysis. For thermodynamic irreversibilities, a good approximation is the rate of entropy generation. As a result of a reduction of entropy production, energy transport infrastructure has become more efficient. This study aims to analyse the bioconvective flow of nanofluid flow through a stretching sheet in the occurence of gyrotactic motile microorganisms. A magnetised nanomaterial model with thermophoretic and Brownian diffusion properties is analysed. The impacts of activation energy, temperature dependent and exponential base heat source are investigated in this analysis. The entropy generation of the system is also observed for nanofluid flow. The mathematical model is developed as partial differential equations. The governing equations are reduced to a dimensionless system of ordinary differential equations by applying similarity transformations. The ODEs are tacked numerically with the aid of shooting scheme in commercial software MATLAB. For graphical and numerical results of flow controlling parameters versus subjective fields, the commercial software MATLAB tool bvp4 is used with the shooting scheme. The novelty of this analysis computes numerical computation of bioconvective nanofluid flow with temperature-dependent and exponential base heat source investigated. Furthermore, the consequence of thermal radiation and entropy of the system is considered. The porous medium with activation energy is also taken into consideration. The results show that the velocity field is reduced with increased bioconvection Rayleigh number. The thermal field is increased via an exponential space-based heat source. The concentration is reduced via Lewis number. the microorganisms profile declines for larger bioconvection Lewis number. The Brinkman number Br, magnetic and permeability characteristics all showed a rising trend when plotted against the entropy production rate.</p> </abstract>

Nanoparticle aggregation kinematics on the quadratic convective magnetohydrodynamic flow of nanomaterial past an inclined flat plate with sensitivity analysis

The study focuses on the aggregation kinematics in the quadratic convective magneto-hydrodynamics of ethylene glycol-titania ([Formula: see text]) nanofluid flowing through an inclined flat plate. The modified Krieger-Dougherty and Maxwell-Bruggeman models are used for the effective viscosity and thermal conductivity to account for the aggregation aspect. The effects of an exponential space-dependent heat source and thermal radiation are incorporated. The impact of pertinent parameters on the heat transfer coefficient is explored by using the Response Surface Methodology and Sensitivity Analysis. The effects of several parameters on the skin friction and heat transfer coefficient at the plate are displayed via surface graphs. The velocity and thermal profiles are compared for two physical scenarios: flow over a vertical plate and flow over an inclined plate. The nonlinear problem is solved using the Runge–Kutta-based shooting technique. It was found that the velocity profile significantly decreased as the inclination of the plate increased on the other hand the temperature profile improved. The heat transfer coefficient decreased due to the increase in the Hartmann number. The exponential heat source has a decreasing effect on the heat flux and the angle of inclination is more sensitive to the heat transfer coefficient than other variables. Further, when radiation is incremented, the sensitivity of the heat flux toward the inclination angle augments at the rate 0.5094% and the sensitivity toward the exponential heat source augments at the rate 0.0925%. In addition, 41.1388% decrement in wall shear stress is observed when the plate inclination is incremented from [Formula: see text] to [Formula: see text].