Exponential Space Dependent Heat Source Research Articles

Prandtl-eyring couple stressed flow within a porous region counting homogeneous and heterogeneous reactions across a stretched porous sheet

The movement of a non-Newtonian incompressible Prandtl-Eyring fluid layer over a stretching/shrinking permeable plate is shown in the current work. The flow is stressed by an additional couple stress, altered by a uniform normal magnetic field, and saturated in a permeable material. Heat transmission is demonstrated using a temperature-dependent heat source, an exponential space-dependent heat source, Joule heating, and viscous dissipations. Momentum, energy, and chemical type concentration equations, coupled with appropriate boundary conditions, support the mathematical structure. The novel aspect of the current work comes from considering species mass transfer using heterogeneous and homogeneous biochemical reactions along with the effects of thermal diffusion in the aforementioned flow. The reaction processes are isothermal with identical coefficients of chemical species. The leading nonlinear partial differential equations are transformed into ordinary differential equations utilizing appropriate similarity transformations. The homotopy perturbation method examines these equations. As a result, the primary objective distributions' analytical solutions are derived, and a graphical representation of them is produced to show the effects of the pertinent physical elements. The heterogeneity reaction serves as a dual role parameter in this diffusion, while the homogeneity reaction has been discovered to be a decreasing factor for particle diffusion. The ability of suction or injection via a permeable surface is observed to reduce the velocity and heat transmission, meanwhile, increasing chemical species condensation.

Heat transfer analysis of magnetized Cu-Ag-H2O hybrid nanofluid radiative flow over a spinning disk when the exponential heat source and Hall current are substantial: Optimization and sensitivity analysis

The main motive of the instigated mathematical model is to observe the impact of Hall current on the hybrid nanofluid flow over a disk that is rotating. The copper and silver metal nanoparticles have been considered with volume fraction φ1=φ2=0.01(0.01)0.04 and are suspended in water to form the hybrid nanofluid. Diverse characteristics like magnetic field, thermal radiation, and (ESHS) exponential space dependent heat source are incorporated to investigate the nature of the flow. The present mathematical model is initiated with partial derivative equations (PDEs) which are redrafted as ordinary derivative equations (ODEs) with appropriate transformations of similarity. The results are attained through a blend of the Runge-Kutta method, shooting procedure, and the influences of parameters on the flow of nanofluid and hybrid nanofluid are compared and illustrated both as tables and graphs. The present numerical research is unique because by employing a complete quadratic CCD framework using the RSM strategy, the sensitivity and optimization analysis of the heat transmission improvement for the volume fraction, ESHS, and thermal radiation parameters have been performed. The R-squared and adjusted R-Squared are obtained as 100%. The residual graphs and contour diagrams of the same are also shown. The current study establishes that the Hall parameter increases the radial velocity, but it also controls the energy and cross-radial velocity. The rate of heat transmission is increased by thermal radiation even at low levels of ESHS. The rate of heat transmission is more sensitive (0.024670) to the volume fraction of the hybrid nanofluid when ESHS is at an intermediate level. The lowest sensitivity (-1.269967) value towards ESHS is observed For thermal radiation and ESHS parameter values, the heat transmission rate of the mono nanofluid is not as great as that of hybrid nanofluid. The current study finds applications in the generation of hydroelectric power, air cleansing and rotating equipment, healthcare devices, and many other industries.

Thermally radiated micro-polar fluid with space-dependent heat source: Modified Cattaneo-Christov heat flux theory

The principle aim is to investigate the micro-inertia for vertex viscosity effects that were utilized about design to act on heat energy. Heat transfer was imposed out that unsteady distributed stagnation point flow by micro-polar fluid. That define the energy equation, Cattaneo-Christov heat flux figure was used for formal Fourier's law. Effects on exponential space-dependent heat source and linear thermal radiation were more comprise on the interpreted model. Numerical technique finite element method was occupied about the results to ordinary differential equations that were acquired against governing partial differential equations below the convenient equal transformations. This flow reach toward the departure domain displayed the absorbed flow aspect and opposite flow aspect susceptible on that physical parameters elaborate into the analysis. In view of acquired results, we observed that thermal profile downturn about extra sizably higher values of relaxation time, during increase into increasing radiation factor. An increase in vertex viscosity increases angular motion. Moreover, space-dependent heat digestion is extra applicable about cooling process. That more, the acceptance of current results was entire as growing analogy into actual circulated work.

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.

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].

Implication of Bio-convective Marangoni flow of non-Newtonian material towards an infinite disk subject to exponential space-based heat source

In recent years, the research for enhanced thermal transportation is centered around the utilization of nanostructures to avail the prospective benefits in areas of biomedical, metallurgy, polymer processing, mechanical and electrical engineering applications, food processing, ventilation, heat storage devices, nuclear systems cooling, electronic devices, solar preoccupation, magnetic sticking, bioengineering applications, etc. The thermal aspects of nanoliquids and associated dynamics properties are still necessary to be explored. In this thermal contribution, the flow of Casson nanofluid configured by an infinite disk is analyzed. The significance of Marangoni flow with activation energy, thermal and exponential space-dependent heat source, nonlinear thermal radiation and Joule heating impacts is also incorporated. Similarly, variables are affianced to recast the governing flow expressions into highly coupled nonlinear ODEs. The numerical simulation for the prevailing model is elucidated by applying the bvp4c built-in function of computational commercial software MATLAB. Consequences of sundry parameters, namely, magnetic parameter, Prandtl number, radiation parameter, exponential space-dependent heat source parameter, thermal-dependent heat source parameter, Eckert number, Dufour parameter, Soret number, Schmidt number, Marangoni number and Marangoni ratio parameter, mixed convection parameter, buoyancy ratio parameter, bioconvection Rayleigh number, activation energy parameter, thermophoresis parameter, Brownian motion parameter, bioconvection Lewis number, Peclet number microorganisms difference variable versus involved flow profiles like velocity, temperature, concentration of nanoparticles and microorganism field are obtained and displayed through graphs and tabular data.

A study of quadratic thermal radiation and quadratic convection on viscoelastic material flow with two different heat source modulations

In many practical applications such as plastic manufacturing and the polymer industries, the temperature difference is substantially large as a result the density of the working fluid alters nonlinearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, as it has a considerable impact on the flow and heat transport characteristics of the working fluid. Here, the non-Newtonian viscoelastic material flow driven by stretching of elastic sheet subjected to NBA and quadratic form of Rosseland thermal radiation is investigated. Two different heat source modulations, viz., exponential space-dependent heat source, and a temperature-related heat source are analyzed. The viscoelastic material obeys the quadratic Boussinesq approximation. The fluctuation of plate temperature is linear and the transpiration (plate mass suction) is also accounted. The Darcy law is employed for a porous medium. The dimensionless profiles of the velocity, heat transport rate, and temperature are simulated by solving the nonlinear two-point boundary value system by employing the finite difference-based routine. The significance of key parameters involved in the problem is studied on various flow fields via surface and streamline plots. It is found that the quadratic convection mechanism enhanced the Nusselt number; however, the quadratic thermal radiation aspect reduced the Nusselt number. The higher velocities are captured in the case of quadratic thermal convection as compared with its absence. Whereas this trend is quite opposite for the thermal field. The velocity of viscoelastic material positively correlated with the viscoelastic material parameter. Further, the outcome of this investigation helps in determining the key parameters which facilitate the desired heat transport rate.

Heat transfer optimization of hybrid nanomaterial using modified Buongiorno model: A sensitivity analysis

Sensitivity analysis of the heat transfer rate in the flow of the hybrid nanoliquid C2H6O2−H2O (base liquid) +MoS2−Ag (nanoparticles) over a wedge using the Response Surface Methodology (RSM) is carried out. The nanomaterial is modeled using the modified Buongiorno nanofluid model (MBNM) that considers the major slip mechanisms and the effective properties of the hybrid nanoliquid. Two distinct heat sources- linear thermal heat source and an exponential space-dependent heat source are taken into account. The governing nonlinear two-point boundary-layer flow problem is treated numerically. The effects of pertinent parameters on the flow fields in the boundary layer region are represented graphically with suitable physical interpretations. The exponential heat source and slip mechanisms are used to study the sensitivities of the heat transfer rate. Both heat source mechanisms lead to an improvement in the temperature profile, in which the effect of the exponential space-related heat source is predominant. The Brownian motion parameter was found to be the most sensitive to the heat transfer rate.

Influence of exponential space-based heat source and Joule heating on nanofluid flow over an elongating/shrinking sheet with an inclined magnetic field

ABSTRACT One thing that is not yet knows is the effect of increasing space-dependent internal heat source on the dynamics of recyclable iron oxide-supported copper oxide nanocatalyst in the industry. This study presents not only the effect of exponential space-dependent heat source (ESHS) and Joule heating on such dynamics using the nanofluid model but also the impact of magnetic strength proportional to Lorentz force. The dimensional governing equations, suitable to model the boundary layer flow of water conveying and nanoparticles through the porous medium on a convectively heated surface, were modelled using the Darcy model. Similarity solution of the problem was obtained using the suitable similarity solution. Numerical solution of the corresponding boundary value problem was sought for using MATLAB-based bvp4c package. Magnetic parameter declines the motion of the nanofluids (water conveying copper nanoparticles and water conveying cupric nanoparticles) but accelerates the temperature profile.

Quadratic convective transport of Cu‐Al2O3hybrid nanoliquid with Hall current, variable suction, and exponential heat source

The time‐dependent slip flow and heat transport of the Cu‐Al2O3hybrid nanofluid through a vertical permeable plate with Hall current and variable suction is investigated. An exponential heat source and quadratic convection effects are considered. The dimensionless governing equations are solved analytically using the regular perturbation method. The graph of variation of the different flow fields with respect to the distance from the plate is drawn for the analysis. It is established that the exponential heat source aspect increased the temperature profile while the quadratic convection aspect decreased the temperature profile. The applied magnetic field and nonlinear convection aspects reduce the axial velocity field. The quadratic convection and exponential space‐dependent heat source phenomena are favorable to friction factors. Furthermore, the global heat transfer is increased in the presence of an exponential space dependent heat source and hybrid nanoparticles.

Importance of activation energy and heat source on nanoliquid flow with gyrotactic microorganisms

This article addresses salient features of gyrotactic microorganism and activation energy in flow of nanofluid by rotating disk. An exponential space dependent heat source (ESHS) process is implemented to examine the thermal transport characteristics. Additionally nanoparticles mass flux condition is considered. The solutions are numerically computed. Impacts of various physical variables appearing in the solutions of non-linear systems are carefully analyzed. The current work identifies that temperature distribution of nanoliquid enhances for higher values of thermophoresis and Brownian motion variables. Moreover activation energy and temperature difference parameters diminish the nanoparticles concentration. Comparative study is provided in order to validate our outcomes.

Significance of Induced Magnetic Field and Exponential Space Dependent Heat Source on Quadratic Convective Flow of Casson Fluid in a Micro-channel via HPM

Significance of Induced Magnetic Field and Exponential Space Dependent Heat Source on Quadratic Convective Flow of Casson Fluid in a Micro-channel via HPM

Simulation of nanofluid thermal radiation in Marangoni convection flow of non-Newtonian fluid

Purpose The purpose of this study is to study the impacts of exponential space-dependent heat source (ESHS) and thermal radiation in Marangoni convective flow of Cross fluid. The passively controlled model is developed to exhibit the nanoparticles’ concentration on the surface. Design/methodology/approach The resulting problem under consideration is tackled by using the shooting approach. Findings Temperature field augments with enhancement of the thermophoretic, exponential-based space heat source (ESHS) and radiation parameters, whereas it decays with the increase of the Marangoni ratio parameter. Originality/value To the best of the authors’ knowledge, no such analysis has yet been reported.

MHD flow of SWCNT and MWCNT nanoliquids past a rotating stretchable disk with thermal and exponential space dependent heat source

The main purpose of this investigation is to analyze the impacts of a novel exponential space dependent heat source on MHD slip flow of carbon nanoliquids past a stretchable rotating disk. The flow is created due to rotation and stretching of the disk. Aspects of the convective condition and cross-diffusion (Soret and Dufour effects) are also accounted. A comparative study of nanofluids made up of SWCNT’s (single-walled carbon nanotube) and MWCNT’s (multi-walled carbon nanotube) is presented. The governing partial differential equations system is reduced to nonlinear ordinary boundary value problem. The Runge–Kutta–Fehlberg is utilized for numerical simulations. Embedded dimensionless parameters on the flow fields are examined via graphical illustrations. The rate of heat mass transfer can be controlled by cross-diffusion, exponential space-based heat source and thermal-based heat source effects. It is also proved that A novel idea of the exponential space dependent heat source is implemented in the investigation of the slip flow over a rotating deformable disk under the effects of cross-diffusion, temperature based heat source and magnetic field for the first time. A comparison between two different fluids namely SWCNT-H2O nanoliquid and MWCNT-H2O nanoliquid are studied.

Brinkman‐Forchheimer slip flow subject to exponential space and thermal‐dependent heat source in a microchannel utilizing SWCNT and MWCNT nanoliquids

AbstractThis communication examines the impact of carbon nanotubes (single‐wall carbon nanotubes [SWCNT] and multi‐wall carbon nanotubes [MWCNT]) on magnetohydrodynamic Brinkman and Forchheimer flow in a planar microchannel with multiple slips. Flow through a porous medium is modeled via Brinkman and Forchheimer theory. The impacts of thermal‐dependent heat source (THS) and exponential space‐dependent heat source (ESHS) are deployed. Aspects of Joule and viscous dissipations are also retained. The dimensionless equations are solved using the Runge‐Kutta‐Fehlberg joint with shooting methodology. The significance of various nondimensional parameters on the flow distributions as well as skin‐friction and Nusselt number is illustrated and analyzed. Closed form solution of momentum quantity is developed for a particular case. Obtained numerical results are in perfect agreement with analytical results. Further, the results of SWCNT and MWCNT are compared.

Exploration of activation energy and binary chemical reaction effects on nano Casson fluid flow with thermal and exponential space-based heat source

PurposeThe purpose of this paper is to explore the effects of binary chemical reaction and activation energy on nano Casson liquid flow past a stretched plate with non-linear radiative heat, and also, the effect of a novel exponential space-dependent heat source (ESHS) aspect along with thermal-dependent heat source (THS) effect in the analysis of heat transfer in nanofluid. Comparative analysis is carried out between the flows with linear radiative heat process and non-linear radiative heat process.Design/methodology/approachA similarity transformation technique is utilised to access the ODEs from the governed PDEs. The manipulation of subsequent non-linear equations is carried out by a well-known numerical approach called Runge–Kutta–Fehlberg scheme. Obtained solutions are briefly discussed with the help of graphical and tabular illustrations.FindingsThe effects of various physical parameters on temperature, nanoparticles volume fraction and velocity fields within the boundary layer are discussed for two different flow situations, namely, flow with linear radiative heat and flow with non-linear radiative heat. It is found that an irregular heat source/sink (ESHS and THS) and non-linear solar radiation play a vital role in the enhancement of the temperature distributions.Originality/valueThe problem is relatively original to study the effects of activation energy and binary chemical reaction along with a novel exponential space-based heat source on laminar boundary flow past a stretched plate in the presence of non-linear Rosseland radiative heat.

Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects

Abstract Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Karman transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect.

Nonlinear Gravitational and Radiation Aspects in Nanoliquid with Exponential Space Dependent Heat Source and Variable Viscosity

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid’s temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface

This research intends to elaborate Soret-Dufour characteristics in mixed convective radiated Casson liquid flow by exponentially heated surface. Novel features of exponential space dependent heat source are introduced. Appropriate variables are implemented for conversion of partial differential frameworks into a sets of ordinary differential expressions. Homotopic scheme is employed for construction of analytic solutions. Behavior of various embedding variables on velocity, temperature and concentration distributions are plotted graphically and analyzed in detail. Besides, skin friction coefficients and heat and mass transfer rates are also computed and interpreted. The results signify the pronounced characteristics of temperature corresponding to convective and radiation variables. Concentration bears opposite response for Soret and Dufour variables.

Marangoni convection radiative flow of dusty nanoliquid with exponential space dependent heat source

Abstract The flow of liquids submerged with nanoparticles is of significance to industrial applications, specifically in nuclear reactors and the cooling of nuclear systems to improve energy efficiency. The application of nanofluids in water-cooled nuclear systems can result in a significant improvement of their economic performance and/or safety margins. Therefore, in this paper, Marangoni thermal convective boundary layer dusty nanoliquid flow across a flat surface in the presence of solar radiation is studied. A two phase dusty liquid model is considered. Unlike classical temperature-dependent heat source effects, an exponential space-dependent heat source aspect is considered. Stretching variables are utilized to transform the prevailing partial differential system into a nonlinear ordinary differential system, which is then solved numerically via the Runge-Kutta-Fehlberg approach coupled with a shooting technique. The roles of physical parameters are focused in momentum and heat transport distributions. Graphical illustrations are also used to consider local and average Nusselt numbers. We examined the results under both linear and quadratic variation of the surface temperature. Our simulations established that the impact of Marangoni flow is useful for an enhancement of the heat transfer rate.