Prescribed Heat Flux Case Research Articles

Semi-Numerical Investigation of Boundary Layer Flow and Heat Transfer of Magnetohydrodynamics Nano-Fluid Flow in Presence of Chemical Reaction Over a Non-Isothermal Porous Medium

Abstract The technical brief presents, analysis of boundary layer flow and heat transfer in nanofluids under the influence of magnetic field, thermal radiation and chemical reaction over non-isothermal stretching surface through permeable porous medium. The self-similarity equations obtained from governing equations are solved using shifted Chebyshev and Haar wavelet collocation methods. The prescribed surface temperature, prescribed heat flux cases and impact of various flow governing parameters are discussed in detail. The established results are compared with earlier results and are comparable.

Comparative appraisal of mono and hybrid nanofluid flows comprising carbon nanotubes over a three-dimensional surface impacted by Cattaneo–Christov heat flux

Carbon nanotubes (CNTs) are nanoscale tubes made of carbon atoms with unique mechanical, electrical, and thermal properties. They have a variety of promising applications in electronics, energy storage, and composite materials and are found as single-wall carbon nanotubes (SWCNTs) and double-wall carbon nanotubes (DWCNTs). Considering such alluring attributes of nanotubes, the motive of the presented flow model is to compare the thermal performance of magnetohydrodynamic (MHD) mono (SWCNTs)/Ethylene glycol) and hybrid (DWCNTs- SWCNTs/Ethylene glycol) nanofluids over a bidirectional stretching surface. The thermal efficiency of the proposed model is gauged while considering the effects of Cattaneo-Christov heat flux with prescribed heat flux (PHF) and prescribed surface temperature (PST). The flow is assisted by the anisotropic slip at the boundary of the surface. The system of partial differential equations (PDEs) is converted into a nonlinear ordinary differential system by the use of similarity transformations and handled using the bvp4c numerical technique. To depict the relationship between the profiles and the parameters, graphs, and tables are illustrated. The significant outcome revealed that the fluid temperature rises in the scenario of both PST and PHF cases. In addition, the heat transfer efficiency of the hybrid nanoliquid is far ahead of the nanofluid flow. The truthfulness of the envisioned model in the limiting scenario is also given.

Insight into the Significance of Viscous Dissipation and Heat Generation/Absorption in Magneto-Hydrodynamic Radiative Casson Fluid Flow With First-Order Chemical Reaction

This study is an attempt to explore two-dimensional magneto-hydrodynamic Casson fluid flow with heat generation or absorption, chemical reaction, and viscous dissipation under the effect of thermal radiation. Prescribed surface temperature (PST) and prescribed heat flux (PHF) cases have been taken into account to investigate the problem. The constitutive relations for Casson fluid incorporated with suitable boundary layer approximation theory have been utilized to achieve the flow model equations. The obtained highly non-linear partial differential equations cannot be solved analytically, so we transform them into first-order differential equations, then tackle them with the boundary value problem (BVP-4c) technique in Matlab. Radiation increment decreases primary and secondary velocity profiles abruptly in both cases. Heat generation and absorption augmentation decrease the thermal and momentum boundaries for both studied cases. The skin coefficient for PHF cases has decreased 80% when compared with PST cases. The increment in Casson parameter has enhanced the Nusselt number by 75% for the PST case, whereas the decline in Nusselt number has doubled for the PHF case with the increase in magnetic field. It is concluded that, with the increment in Casson fluid, magnetic, radiation, and permeability parameter the Nusselt number has significantly increased for the PST case. However, for these parameters, an abrupt decline in Nusselt number has been observed for the PHF case. Results reported in this study for shear stress and Sherwood number are in complete agreement with already published previous work.

MHD micropolar fluid flow over a stretching/shrinking sheet with dissipation of energy and stress work considering mass transpiration and thermal radiation

An inclined MHD (Magnetohydrodynamics) micropolar fluid flow due to stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined in the present analysis. The governing non-linear PDEs (Partial differential equations) are altered into ODEs (Ordinary differential equations) by using similarity variables. These types of flow problems have many industrial applications such as polymer extrusion, glass blowing and so on. The flow and heat problems were examined analytically especially heat transfer analysis is examined under two different cases namely PST (Prescribed surface temperature) and PHF (Prescribed heat flux) cases, then these solutions are expressed in terms of Kummer's function. Thermal radiation is also taken into account in heat equation and the analysis is carried out by using the microrotation parameter throughout the equation. Coefficient of Skin friction and local Nusselt number are also examined, analytically. Furthermore, graphical scenario have been considered by using different physical parameters namely Prandtl number, Chandrasekhar's number, radiation parameter, mass transpiration and so on. By using these results, it is cleared that microrotation parameter helps to increase Nusselt number, but dual nature behavior is observed for shrinking sheet condition. The induces magnetic field slightly increases the surface skin friction and slightly reduces the surface mass transfer.

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.

Nonlinear Thermal Buoyancy on Ferromagnetic Liquid Stream Over a Radiated Elastic Surface with Non Fourier Heat Flux

The current article discusses the heat transfer characteristics of ferromagnetic liquid over an elastic surface with the thermal radiation and non-Fourier heat flux. In most of the existing studies, the heat flux is considered as constant, but whereas we incorporated the non-Fourier flux to get the exact performance of the flow. Also, we excluded the PWT and PHF cases to control the boundary layer of the flow. The governing equations related to our contemplate are changed into non-linear ordinary differential equations (ODE’s) by utilizing appropriate similarity changes, which are at the point enlightened by Runge–Kutta based shooting approach. The equations are broken down concerning boundary conditions and to be explained prescribed wall temperature (PWT) and prescribed heat flux (PHF) cases. The impacts of diverse non-dimensional physical parameters on velocity and temperature profiles are laid out graphically. Also, the assortment of skin friction and local Nusselt number for both PWT and PHF cases for various assessments of non-dimensional parameters have been sorted out. Towards the wrap-up of the examination, we suspect that the friction factor coefficient is higher in the PWT case compared to the PHF case. This result helps to conclude that the flux conditions are useful for cooling applications.

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.

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.

Convective heat transfer in a dusty ferromagnetic fluid over a stretching surface with prescribed surface temperature/heat flux including heat source/sink

The aim of the present paper was to investigate the boundary layer flow and heat transfer in a dusty fluid with ferromagnetic particles over a flat stretching sheet including the effect of magnetic dipole. By using suitable similarity transformations, the governing partial differential equations of momentum and energy were reduced into non-linear ordinary differential equations. The resulting differential equations with corresponding boundary conditions were solved numerically by employing shooting based fourth order Runge-Kutta method. The effect of controlling parameters such as ferromagnetic interaction parameter, mixed convection parameter, Eckert number, Prandtl number, the number of dust particles and heat generation/absorption parameter on the temperature and velocity profiles are considered graphically for two types of heating processes, namely, the prescribed surface temperature (PST) and the prescribed heat flux (PHF). The value of skin friction coefficient and Nusselt number are presented in tabular form for different values of the governing parameters. It is found that the value of local Nusselt number increases with an increase of the value of heat source/sink parameter for both PST and PHF cases. The present results were compared with previously published data for a special case and an excellent agreement was found.

Cattaneo -Christov heat flux model for magnetohydrodynamic flow in a suspension of dust particles towards a stretching sheet

Abstract In the present paper, the flow of an incompressible, electrically conducting dusty fluid over a stretching sheet is considered. The Cattaneo- Christov heat flux theory is employed to control the thermal boundary layer. The flow equations are transformed into nonlinear ordinary differential equations (NODEs) and which are solved with help of Runge-Kutta 4th order method. Flow equations are examined with respect to boundary conditions namely prescribed wall temperature (PWT) and prescribed heat flux (PHF) cases. In general PWT and PHF boundary conditions are very useful in the industrial as well as manufacturing up and down processes. Impact of the emerging parameters on the dimensionless velocity and temperature as well as friction coefficient and local Nusselt number are examined. We also validated my results with already available literature. It is found that the heat transfer rate of the flow in PWT case is higher than that of PHF case. These results can help us to conclude that for higher heating processes (Heating industries) PWT case and lesser heating processes (Cooling industries) PHF boundary condition is useful.

Fe3O4–(CH2OH)2 nanofluid analysis in a porous medium under MHD radiative boundary layer and dusty fluid

In this paper, magnetohydrodynamic (MHD) boundary layer flow and heat transfer of an incompressible Iron (II,III) oxide (Fe3O4)-ethylene glycol ((CH2OH)2) nanoparticle on micropolar fluid with homogeneously suspended dust particles over a stretching sheet in the presence of thermal radiation and Joule heating are investigated. After transforming the partial differential equations (PDEs) governing the problem into the ordinary differential equations (ODEs), Runge–Kutta Fehlberg fourth fifth order numerical method is applied. The main criterion of this paper is to study the effects of different parameters and dimensionless numbers on velocity and temperature distribution in two phases of fluid and dust for two prescribed surface temperature (PST) and prescribed heat flux (PHF) cases. Velocity reduction in both fluid and dust phases is due to the Lorentz force against flow by increasing Hartman number, enhancement of temperature and thickness of thermal boundary layer are due to the increase of radiation parameter and Eckert number for both PST and PHF cases are the most important results. Also, in the final section of this paper, the effect of changes in the value of different parameters on skin friction coefficient and local Nusselt number in (PST and PHF PHF) have been discussed. These results indicated increasing the Hartman parameter (Ha) would cause an increase skin friction coefficient, also increasing the Eckert number would cause an increase local Nusselt number in PST case and reverse effect in PHF case.

On heat transfer analysis of axisymmetric flow of viscous fluid over a nonlinear radially stretching sheet

This article deals with the exact solutions regarding heat transfer of viscous fluid over a non-linear radially stretching sheet. The effects of viscous dissipation on the heat transfer characteristics are considered in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function and graphically sketched to see the influence of pertinent parameters on the temperature profiles. In addition the results for the wall temperature gradient (Nusselt number) are also presented in graphical form and discussed in detail. It is found that Prandtl number decelerates the temperature profiles in both PST and PHF cases. Thermal boundary layer thickness increases by increasing the Eckert number.

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of a Nanofluid Over Non-Isothermal Stretching Sheet

The boundary-layer flow and heat transfer over a non-isothermal stretching sheet in a nanofluid with the effect of magnetic field and thermal radiation have been investigated. The transport equations used for the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., thermal radiation parameter R, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order nonlinear ordinary differential equations. These equations were numerically solved using a fourth-order Runge–Kutta method with shooting technique. The analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to see the effects of governing parameters for various physical conditions. Numerical results are obtained for distribution of velocity, temperature and concentration, for both cases i.e., prescribed surface temperature and prescribed heat flux, as well as local Nusselt number and Sherwood number. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le. Besides, it is found that the surface temperature increases with an increase in the Lewis number Le for prescribed heat flux case. A comparison with the previous studies available in the literature has been done and we found an excellent agreement with it.

Heat transfer for two types of viscoelastic fluid over an exponentially stretching sheet with variable thermal conductivity and radiation in porous medium

An Analysis has been carried out to study the boundary layer flow and heat transfer characteristics of second order fluid and second grade fluid with variable thermal conductivity and radiation over an exponentially stretching sheet in porous medium. The basic boundary layer equations governing the flow and heat transfer in prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformations. Numerical solutions of the resulting boundary value problem are solved by using the fourth order Runge-Kutta method with shooting technique for various values of the physical parameters. The effect of variable thermal conductivity, porosity, Prandtl number, radiation parameter and viscoelastic parameters on velocity and temperature profiles (in PST and PHF cases) are analyzed and discussed through graphs. Numerical values of wall temperature gradient in PST case and wall temperature in PHF case are obtained and tabulated for various values of the governing parameters. In this study Prandtl number also treated as variable inside the boundary layer because it depends on thermal conductivity. The results are also verified by using finite difference method.

MHD flow and heat transfer for Maxwell fluid over an exponentially stretching sheet with variable thermal conductivity in porous medium

An analysis is made to study MHD flow and heat transfer for Maxwell fluid over an exponentially stretching sheet through a porous medium in the presence of non-uniform heat source/sink with variable thermal conductivity. The thermal conductivity is assumed to vary as a linear function of temperature. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using implicit finite difference scheme known as Keller-box method. The effect of the governing parameters on the flow field, skin friction coefficient, wall temperature gradient (in prescribed surface temperature case), wall temperature (in prescribed heat flux case) and Nusselt number are computed, analyzed and discussed through graphs and tables. The present results are found to be in excellent agreement with previously published work [1,2] on various special cases of the problem.

Heat Transfer Analysis for Couple Stress Fluid over a Nonlinearly Stretching Sheet

An investigation has presented to analyze the heat transfer in a boundary layer flow of an incompress- ible couple stress fluid over a nonlinear stretching sheet. The heat transfer problem have been analyzed for the two heating processes, 1) PST (prescribed surface temperature case) and 2) PHF (prescribed heat flux case). The govern- ing partial differential equations for flow and heat transfer are transformed to ordinary differential equations. The nu- merical solutions have been obtained by using fourth order Runge-Kutta method coupled with shooting method. The effects of dimensionless surface temperature, couple stress parameter , Prandtl number Pr , Eckert number Ec, non- linear stretching sheet parameter n and 1; 2 have been observed by graphical illsurations. Chen (8) described the effects of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. Alinejad (9) investigate the flow and heat transfer characteristics of viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation, Khan et al. (10) presented an analysis of the axisymmet- ric flow of a non-Newtonian fluid over a radially stretch- ing sheet, Mehmood et al. (11) investigates the theoretical study of steady stagnation point flow with heat transfer of a second grade nano fluid towards a stretching surface, Khan et al. (12) gives an analytical study for the effects of slip factors on unsteady stagnation point flow and heat transfer towards a stretching sheet. Asghar (13) reveals all possible similarity transformations for the flow of power-law fluid over a stretching surface by a Lie group analysis. The rota- tion of the fluid particles and its effect has studied under the theory of couple stresses which describes the rotation field in specification of the velocity field. The examples of cou- ple stress fluids include blood, rheologically complex flu- ids, lubricant oil with long chain additives, polymeric sus- pensions, etc. Stokes (14) considered the effects of couple stresses in fluids. Soundalgekar (15) carried out an analysis for the dispersion of a solute in a channel flow of fluid with

Nanofluid Flow over a Rotating Disk with Prescribed Heat Flux

An analysis is carried out to study the problem of the steady flow and heat transfer over a rotating disk with a prescribed heat flux in nanofluid. Nanofluid considered is Copper (Cu) with water as the base fluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, which are then solved using the Nachtsheim-Swigert Shooting iteration technique along with the fourth order Runga Kutta method. The features of the flow and heat transfer characteristics are analyzed and discussed. The radial velocity, tangential velocity and the axial velocity for copper-water nanofluid are calculated and are represented graphically. Numerical results for dimensionless temperature, the radial skin friction coefficient and the tangential skin friction coefficient of the nanofluid flows are obtained and computations are carried out for the various values of Prandtl number. It is found that for the prescribed heat flux case (PHF case), the effect of Prandtl number is to reduce the temperature as it increases for copper-water nanofluid.

Free convection flow about a vertical spinning cone under a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a heated down-pointing cone spinning with a constant angular velocity about the symmetry axis. Boundary-layer velocity and temperature profiles were determined numerically for prescribed surface temperature or heat flux and for various values of the magnetic and spin parameters and the Prandtl number. The spin of the body augments the velocity profiles increasing the skin friction and compresses the temperature profiles toward the surface increasing the surface heat flux for the prescribed surface temperature case and decreasing surface temperature for the prescribed heat flux case. The magnetic field suppresses the velocity profiles and decreases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in lower surface heat flux for the prescribed surface temperature case and higher surface temperature for the prescribed heat flux case.

Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field

An analysis is performed for flow and heat transfer of a steady laminar boundary layer flow of an electrically conducting fluid of second grade in a porous medium subject to a transverse uniform magnetic field past a semi-infinite stretching sheet with power-law surface temperature or power-law surface heat flux. The effects of viscous dissipation, internal heat generation of absorption and work done due to deformation are considered in the energy equation. The variations of surface temperature gradient for the prescribed surface temperature case (PST) and surface temperature for the prescribed heat flux case (PHF) with various parameters are tabulated. The asymptotic expansions of the solutions for large Prandtl number are also given for the two heating conditions. It is shown that, when the Eckert number is large enough, the heat flow may transfer from the fluid to the wall rather than from the wall to the fluid when Eckert number is small. A physical explanation is given for this phenomenon.

The effects of thermal modulation upon the onset of Marangoni–Bénard convection

The effects of thermal modulation with time on the thermocapillary instability of a thin horizontal fluid layer with a deformable free surface are investigated on the basis of linear stability theory. First, a sinusoidal heating with a mean component is applied at the lower wall, corresponding to boundary conditions either in the form of prescribed temperature or heat flux. For finite-wavelength convection the thermal modulation exerts a strong effect, giving rise to a family of looped regions of instability corresponding to alternating synchronous or subharmonic responses. In the case of prescribed heat flux, the critical curve consists of significantly fewer loops than in the case of prescribed temperature. Thermal modulation with moderate modulation amplitude tends to stabilize the mean basic state, and optimal values of frequency and amplitude of modulation are determined to yield maximum stabilization. However, large-amplitude modulation can be destabilizing. A basic state with zero mean is then considered and the critical Marangoni number is obtained as a function of frequency. The effects of modulation are also investigated in the long-wavelength limit. For the case of prescribed temperature, the modulation does not affect the onset of the long-wavelength mode associated with the mean basic state and a purely oscillating basic state is always stable with respect to long-wavelength disturbances. For the case of prescribed heat flux both at the wall and free surface, by contrast, thermal modulation exerts a significant effect on the onset of convection from a mean basic state and long-wavelength convection can occur even for a purely oscillating basic state. The modulation can be stabilizing or destabilizing, depending on the frequency.