Prescribed Surface Temperature Research Articles

NUMERICAL ASSESSMENTS OF PRESCRIBED HEAT SOURCES ON UNSTEADY 3D FLOW OF WILLIAMSON NANOLIQUID THROUGH POROUS MEDIA

The core theme of recent work is to describe the magnetohydrodynamic Williamson nanoliquid flow generated by an unsteady highly linear bidirectionally stretchable surface dipped in porous media. The effects of various heat modes, namely, prescribed surface temperature and prescribed heat flux, are also taken into considerations. The Buongiorno nanoliquid model has been used to analyze the amounts of heat plus mass transference. A suitable combination of variables has been used to transform the governing set of partial differential equations into the set of ordinary differential equations. Numerical assessment of heat and mass transference has been made by the courtesy of the Keller-Box scheme. Physical quantities of engineering importance have been discussed through various plots and through tabular arrangements. It is detected through the present contribution that escalating amounts of the unsteady parameter, expansion ratio parameter, and temperature-controlled index develop the rate of heat transfer, as well as enhance the rate of mass transfer. Moreover, it is also observed that the intensifying amounts of Williamson parameter, magnetic parameter, expansion ratio parameter, unsteady parameter, and porosity parameter improve the amounts of skin frictions. Furthermore, a better rate of heat transfer is achieved for prescribed surface temperature as compared to prescribed heat flux, whereas the better rate of mass transfer is attained for prescribed heat flux as compared to prescribed surface temperature.

COMPETENCE OF MAGNETIC DIPOLE AND RADIATION ON PERMEABLE SURFACE USING PRESCRIBED HEAT FLUX / PRESCRIBED SURFACE TEMPERATURE AND HOMOGENEOUS-HETEROGENEOUS REACTIONS

This paper mainly engrossed with homogeneous-heterogeneous reactions on the ferromagnetic fluid flow with thermal radiation subjected to prescribed heat flux and prescribed surface temperature. Self-similarity variables are employed to transmute the governing equations into ODE’s. Consequential ODE’s (ordinary differential equations) are fruitfully solved numerically by exploiting bvp4c with MATLAB solver. The pictorial illustrations are expressed on Nusselt number and skin friction coefficient, as well as velocity, temperature and concentration with an influence of active parameters (ferromagnetic parameter, porosity, thermal radiation, heat source parameter, viscous dissipation parameter, Schmidt number and chemical reaction) by considering two different kinds of thermal processes namely the sheet with prescribed surface temperature (PST) and the sheet with prescribed heat flux (PHF). The concentration profile depreciates with an increase in the chemical reaction in instances PST / PHF. The higher values of the viscous dissipation parameter increase the temperature profile for PST/ PHF cases. The heat transfer rate is very high at the maximum values of the radiation and minimum values of the ferromagnetic parameter. Streamlines pattern is presented to analyze the actual impact of ferromagnetic fluid flow on the wall. This theoretical investigation is of much significance for industrial, chemical, and technological areas such as rod-climbing, solar energy collectors, rotating X-ray tubes, vacuum chambers in the semiconductor industry, biomedical applications and electric engines.

MHD heat and mass flow of nano-fluid over a non-linear permeable stretching sheet

In this study, we examine the Magneto-hydrodynamics (MHD) heat and mass flow of nano-fluid over a non-linearly permeable stretching sheet. The resulting partial differential equations are converted to a system of ordinary differential equations using the similarity transformation and solved numerically using shooting technique with fourth order Runge-Kutta method. The effect of some fluid parameters on the momentum, thermal and nanoparticle volume fraction boundary layers were expatiated for prescribed surface temperature and constant surface temperature through graphs. An excellent agreement was found when the results obtained in this study were compared with results in previous literature.

Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power; then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.

Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium

In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation, and internal heat generation/absorption. Closed-form solutions for the boundary layer equations of viscoelastic, second-grade, and Walters’ B ′ fluid models are considered. The method of the solution includes similarity transformation. The converted equations of thermal and mass transport are calculated using the optimal homotopy asymptotic method (OHAM). The solutions of the temperature field for both prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are found. It is vital to remark that the interaction of the magnetic field is found to be counterproductive in enhancing velocity and concentration distribution, whereas the presence of chemical reaction, as well as a porous matrix with moderate values of the magnetic parameter, reduces the temperature and concentration fields at all points of the flow domain.

Memory response in a two‐dimensional transversely isotropic thick plate with varying heat source

AbstractThis present survey deals with a novel mathematical model of generalized thermoelasticity which investigates the transient phenomena in a two‐dimensional problem for a transversely isotropic thick plate having a heat source. The upper surface of the plate is stress‐free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the three‐phase‐lag thermoelastic model. The governing equations for displacement and temperature fields are obtained in the Laplace‐Fourier transform domain by applying the Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of the Laplace transform is done by using a method based on the Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the memory‐dependent derivative on the solutions has been studied.

Features of thermophoretic and Brownian forces in Burgers fluid flow subject to Joule heating and convective conditions

Here we investigate the aspects of thermal and solutal energy transport in MHD flow of Burgers nanofluid caused by a unidirectional stretching cylinder. The well-known Fourier’s and Fick’s laws are utilized to inspect the heat and mass transport phenomena. The convective energy transport at the surface of the cylinder is assumed and Fourier’s law of thermal conduction is modelled in terms of non-uniform heat source/sink and Joule heating. Additionally, the prescribed surface temperature (PST) is considered here. Governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by utilizing suitable similarity transformations. To deal with ODEs, a numerical technique namely BVP midrich scheme in Maple is utilized. The behavior of different physical parameters is explored and depicted in form of graphs and discussed with reasonable arguments. Basic physical intimation of gained results is that the higher Eckert number intensifies the thermal profile of nanofluid. Moreover, the nano particles concentration profile builds up for higher amount of thermophoretic force constraint Solutal distribution of Burgers nanofluid depicts growing trend for larger solutal Biot number

Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder

In this paper, the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied. The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow. Further, the novel features of heat generation/absorption, thermal radiation, and Joule heating are studied to control the rate of heat transfer. The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno. The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations (PDEs) and transformed into nonlinear ordinary differential equations (ODEs) with the help of the suitable flow ansatz. Numerically acquired results through the technique bvp4c are reported graphically with physical explanation. Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature (CWT) as compared with the prescribed surface temperature (PST). Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid. Moreover, the temperature distribution increases with increasing values of the radiation parameter and the Eckert number. It is also noted that an increase in Reynolds number reduces the penetration depth, and as a result the flow and transport of energy occur only near the surface of the cylinder.

Significances of prescribed heat sources on magneto Casson nanofluid flow due to unsteady bi-directionally stretchable surface in a porous medium

In this communication, bidirectional flow of Casson nanomaterial driven by an unsteady moveable surface in the region of boundary layer is analyzed. Moreover, the significances of porous space, magnetic field, prescribed surface temperature (PST), and prescribed surface heat flux are also incorporated. Furthermore, the aspects of Brownian motion and thermophoresis are also comprised through Buongiorno nanofluid model. Governing equations are firstly transformed into system of ordinary differential equations by using a suitable combination of variables, and then computational assessment is made through Keller-Box method. Graphical illustrations for temperature distribution, concentration distribution, local Nusselt number and local Sherwood number against escalating amounts of pertinent parameters are presented. It is observed that escalating amounts of unsteady parameter and temperature controlled indices reduce the temperature distribution, as well as the concentration distribution. It is also observed that increasing amounts of Casson parameter enhances the rate of heat transfer, and reduces the rate of mass transfer for PST case. Finally, a comparison benchmark for limited case has been presented to validate the present methodology.

Mixed Convection in Unsteady Stagnation Point Flow of Maxwell Fluid Subject to Modified Fourier’s Law

The extrusion process of polymers in the industry is greatly depends on the heat transport mechanism in the viscoelastic fluid flow for the better quality of product. Therefore, nowadays, the researchers deeply investigate the properties of thermal transport in the flow with various physical effects. This research article is proposed to study the rheology of stagnation point flow of viscoelastic fluid over the vertical stretching cylinder with the impact of buoyancy force. The non-Fourier’s heat flux model is considered here for the transportation of thermal energy in fluid flow. Additionally, the analysis for two types of surface heating agents, namely constant wall temperature (CWT) and prescribed surface temperature (PST) is performed. The resulting partial differential equations for governing the flow and heat transport problem are transformed into ordinary differential system through suitable similarity variables. Numerical solutions are obtained by utilizing bvp4c built in MATLAB technique. The acquired results for temperature field are presented graphically with the comparison of CWT and PST. The outcomes of present study reveal that higher rate of heat transfer is observed in the case of CWT. Moreover, it is noted that higher values of buoyancy parameter enhance fluid flow velocity for assisting mode. The increasing values of thermal relaxation time parameter decrease the heat transport in the fluid. A comparison is given of surface velocity gradient for magnetic parameter and Deborah number with existing literature.

Entropy analysis of a hydromagnetic micropolar dusty carbon NTs-kerosene nanofluid with heat generation: Darcy–Forchheimer scheme

The current paper on carbon nanotubes suspended magnetohydrodynamics micropolar dusty nanofluid impinging on a permeable extending sheet placed in a porous regime. The Darcy–Forchheimer scheme with heat source/sink and thermal radiation is taken into account. The shooting method is instrumental for obtaining numerical solutions of the transformed-converted system of nonlinear equations. The prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions are used. The impact of governing parameters on velocity, temperature, skin friction coefficient, Nusselt number, entropy generation rate and Bejan number are incorporated. The significant outcomes of the current investigation are that increment in the suction parameter decline the flow velocity and temperature (for both PST and PHF cases) while the injection uplift them. An enhancement in magnetic strength, the skin friction and heat transfer rate show the opposite trend for both SWCNT and MWCNT. Bejan number is increasing with the increase in nanoparticle volume fraction $$\phi$$ for both SWCNT and MWCNT.

Thermal Analysis of a Hydromagnetic Viscoelastic Fluid Flow Over a Continuous Curved Stretching Surface in the Presence of Radiative Heat Flux

This study deals with the flow and heat transfer of 2-D Maxwell fluid due to linear stretching of a curved surface. The heat transfer happens when temperature is specified on the boundary as prescribed surface temperature, PST, and prescribed surface heat flux, PSHF. The radiation and dissipation effects are incorporated in the energy equation. The modeling of the curved structure for a linear stretching velocity of Maxwell fluid is developed. The fluid is electrically conducted in the presence of varying applied magnetic field. The field quantities which describe the velocity, pressure, and temperature are calculated numerically. The effects of the radius of curvature, magnetic field, and non-Newtonian parameters are investigated and explained physically. This analysis adds to the mathematical understanding of boundary-driven flows in non-Newtonian fluids and enlarges the scope of its applications in the polymer industry for curved structures.

Magnetohydrodynamic micropolar fluid flow in a porous medium with multiple slip conditions

Theoretically, micropolar fluids are used in the biomedical investigations. This study analyzes the flow, heat and mass transfer in a magneto-micropolar reactive fluid over a nonlinear stretching sheet in a saturated non-Darcy porous medium. The impact of velocity, thermal and concentration slips with prescribed surface temperature and concentration boundary conditions are examined. Mathematical models are formulated and solved using an iterative technique spectral quasi-linearization method. The results of numerical simulations are depicted graphically. The present results when cross-checked with earlier reported data in the literature for limiting conditions exhibit good agreement. The results show that the momentum and thermal boundary layer thicknesses fall as the nonlinear stretching parameter increases while the opposite occur with a rise in the thermal conductivity parameter.

Unsteady Stagnation Point Flow of Maxwell Nanofluid Over Stretching Disk with Joule Heating

In advanced technology, the cooling systems are noteworthy in thermal devices which have been accomplished both active and passive heat transfer improvement methods. Scientist and engineers have developed numerous techniques for the enhancement of heat transport in the thermal systems. The nanofluids, Joule heating, magnetic field and surface heating agents are the emerging effect for the enhancement of heat transfer which have been continuously studied. The main aim of this paper is to study the thermal and solutal aspects of the magnetohydrodynamics unsteady flow of Maxwell nanofluid under the consideration of stagnation point over radially stretching disk. The impact of resistive heating and heat generation to the transportation of thermal energy in fluid is analyzed. Moreover, the prescribed surface temperature (PST) and constant wall temperature (CWT) are considered here. Additionally, the convective energy transport at the surface of disk is assumed and phenomenon of mass transfer is explored with effect of chemical reaction. The partial differential equations which govern the flow, heat and mass transport phenomena are reduced to nonlinear differential equations (ODEs) by introducing the suitable similar transformations. Also, for the solutions of ODEs the built in MATLAB program namely bvp4c is employed and outcomes presented graphically with comprehensive discussion. As a key outcome, it is noted that the higher values of unsteadiness parameter enhance the temperature field in the case of CWT but declines in the case of PST. The increase in Eckert number boosts up the temperature distribution in the Maxwell fluid significantly. The numerical values of surface temperature and concentration gradient for varying values of different parameters are given in tabular form.

Statistically Steady State Large‐Eddy Simulations Forced by an Idealized GCM: 1. Forcing Framework and Simulation Characteristics

AbstractUsing large‐eddy simulations (LES) systematically has the potential to inform parameterizations of subgrid‐scale processes in general circulation models (GCMs), such as turbulence, convection, and clouds. Here we show how LES can be run to simulate grid columns of GCMs to generate LES across a cross section of dynamical regimes. The LES setup approximately replicates the thermodynamic and water budgets in GCM grid columns. Resolved horizontal and vertical transports of heat and water and large‐scale pressure gradients from the GCM are prescribed as forcing in the LES. The LES are forced with prescribed surface temperatures, but atmospheric temperature and moisture are free to adjust, reducing the imprinting of GCM fields on the LES. In both the GCM and LES, radiative transfer is treated in a unified but idealized manner (semigray atmosphere without water vapor feedback or cloud radiative effects). We show that the LES in this setup reaches statistically steady states without nudging to thermodynamic GCM profiles. The steady states provide training data for developing GCM parameterizations. The same LES setup also provides a good basis for studying the cloud response to global warming.

Heat Transfer in Boundary Layer Magneto‐Micropolar Fluids with Temperature‐Dependent Material Properties over a Stretching Sheet

The process of heat transfer in boundary layer magneto‐micropolar fluid with temperature‐dependent material properties past a flat stretching sheet in a porous medium is investigated in this study. Two distinct cases of boundary heating conditions are analyzed for the heat transfer in this work, viz., prescribed surface temperature (PST) and prescribed heat flux (PHF). With the aid of similarity conversion analysis, the formulated equations of the flow and heat transfer have been translated into a system of nonlinear ordinary differential equations. Subsequently, Runge–Kutta–Fehlberg integration scheme in company of shooting techniques employed to obtain numerical solutions to the reduced equations. The findings are graphically illustrated and discussed in view of the two cases of boundary heating, while the results for the physical quantities of engineering concern are tabulated for various controlling parameters. In the limiting situations, the results generated are compared favourably with the earlier reported data in the literature, while the numerical solutions demonstrate a reduction in the rate of heat transfer and the viscous drag for both PST and PHF conditions with growth in the magnitude of material parameter K.

Global variability in radiative-convective equilibrium with a slab ocean under a wide range of CO2 concentrations

In radiative-convective equilibrium (RCE), radiative cooling of the troposphere is roughly balanced by the vaporization enthalpy set free by precipitating moist convection. Many earlier studies restricted the investigation of RCE to the dynamics of the atmosphere with constant boundary conditions including prescribed surface temperature. We investigate a GCM setup where a slab ocean is coupled to the atmosphere, and we explore a wide range of CO2 concentrations. We obtain reliable statistical quantities from thousand-year-long simulations. For moderate CO2 concentrations, we find unskewed temporal variations of 1–2 K in global mean surface temperature, with an almost constant climate sensitivity of 2 K. At CO2 concentrations beyond four times the preindustrial value, the climate sensitivity decreases to nearly zero as a result of episodic global cooling events as large as 10 K. The dynamics of these cooling events are investigated in detail and shown to be associated with an increase in large-scale low-level stratiform cloudiness in the subsiding region, which is a result of penetrative shallow convection being capped by an inversion and thus not ventilating the lower troposphere. These dynamics depend on the CO2 concentration: both through the effect of temperature on stratification and through the changing spatial scale of organization of the flow, which determines the spatial scale and temporal coherence of the stratiform cloud sheets.

Numerical solution for flow of a Eyring–Powell fluid in a pipe with prescribed surface temperature

In the current study, the flow and heat transfer of MHD Eyring–Powell fluid in a circular infinite pipe is discussed. The rheology of fluid is described by constitutive equation of Eyring–Powell fluid. The solution is constructed for both constant and variable viscosity cases. For variable viscosity case, the viscosity function is defined by Reynolds and Vogel’s models. The solution of each case is calculated numerically with the help of eminent iterative numerical technique. The effects of thermo-fluidic parameters on flow and heat transfer phenomenon are highlighted through graphs. The velocity and temperature profiles diminish against magnetic parameter $$(M_{e} )$$ and material parameter (M) in all cases, whereas both velocity and temperature profiles rise via magnitude of the pressure gradient and material parameter Y. The validity of our numerical results due to shooting method is presented by comparing them with the numerical results produced by pseudo-spectral collocation method. Relative absolute errors are plotted, and achieved accuracies are of the order four and five in w and $$\theta$$, respectively. The outcomes of current investigation may be useful in thin film, catalytic reactors, polymer solutions and paper production, etc.

Bi-directional stretched nanofluid flow with Cattaneo-Christov double diffusion

Bi-directional unsteady flow of nanomaterial has been explored in the existence of Cattaneo-Christov double diffusion. Brownian motion, thermophoresis and heat sources namely PST (prescribed surface temperature) and PHF (prescribed heat flux) are included. The obtained nonlinear systems are computationally solved by employing Keller box method. Graphs have been created for temperature and concentration fields for distinct amounts of involved parameters. Tables have been generated and discussed for skin friction, heat and mass transfer rates. It is assessed that temperature and concentration are reducing fields of thermal and relaxation factors for prescribed heat flux. Obtained effects are linked with the formerly published results and found favorable agreement.

Magnetohydrodynamic Boundary Layer Flow of a Viscoelastic Fluid Past a Nonlinear Stretching Sheet in the Presence of Viscous Dissipation Effect

This paper numerically investigates the viscous dissipation effect on the boundary layer flow of an electrically-conducting viscoelastic fluid (Walter’s B liquid) past a nonlinear stretching sheet. The partial differential equations governing the flow problem are transformed into ordinary differential equations through similarity variables. The transformed equations are then solved using the Keller box method. A careful evaluation of the influence of the pertinent parameters on the velocity field and temperature distributions through various plots is done for the prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions. The computed coefficient of skin friction, the rate of heat transfer (Nusselt number), and the temperature at the wall are also presented in tabular form. It is revealed from this table that the magnitude of the heat transfer is reduced with the increase in the Eckert number E c , viscoelastic parameter K, and magnetic parameter M for the PST case by about 12%, 20%, and 29%, respectively. Similarly, the temperature at the wall for the PHF case also decreases with the increase in E c and M by about 8% and 24%, respectively. It is obvious that the application of the PST condition excels at keeping the viscoelastic fluid warmer than the PHF condition. This implies that applying the PHF condition is better for cooling the sheet faster. The temperature at the wall is unchanged with the changes in the pertinent parameters in the PST case, and it is ascertained that the present results are in close agreement with the previous published results.