Prescribed Surface Temperature Case Research Articles

Nonlinear radiative thermal analysis of magneto-micropolar fluid over a bidirectionally extending sheet with varied thermal conditions

Thermal fluid flow analysis occasioned by stretching surfaces offers practical industrial and engineering applications, such as extrusion and drawing processes and materials experiencing heating and cooling conditions. Thus, this study explores magnetohydrodynamic micropolar fluid flow under varied thermal conditions and nonlinear thermal radiation over a dually stretched sheet subject to surface mass flux and an internal heat source. The study thus provides insight into the dynamics of heat transfer mechanisms for improving material processing techniques in many engineering processes. The flow dynamics with the thermal analysis are evaluated by applying two thermal conditions in the heat equation: the prescribed surface temperature (PST) and the prescribed heat flux (PHF). The formulated partial derivative equations that describe the current problem are changed into ordinary derivatives using some similarity quantities, while the converted equations are tackled with the combined techniques of shooting and Runge–Kutta Fehlberg. Consequently, diverse tables and figures are displayed to deliberate on the impacts of the physical terms on the dynamics of flow and heat transmission processes. The consequence of the analysis reveals a higher heat gradient in the prescribed surface temperature case than the uniform temperature distribution, as the Prandtl number magnifies. The micropolar material term reduces the surface frictional factor and depletes heat transmission, but the magnetic field term raises the skin friction coefficient.

Investigation of heat and mass transfer performance in Casson fluid flow over nonlinear stretching sheet: Impact of novel similarity transformations

This article primarily aims to utilize novel similarity transformations that were created to overcome a limitation found in previous research. These similarity methods have proven to be effective in finding solutions to systems of partial differential equations. The study analyzed mass and heat transfer in a Casson fluid near a boundary on a stretchy, permeable surface, considering radiative heat transmission and non-homogeneous thermal effects. It focused on two heating methods: prescribed surface temperature (PST) and prescribed surface heat flux (PHF). Prior research involving stretchable surfaces has mostly used non-dimensional similarity metrics related to one variable that is not dependent on others (e.g., only or), which resulted in certain errors. To tackle this issue, we have introduced a novel set of similarity transformations that encompass all the independent variables in the equations. that are being studied (that is, x and y ). This novel strategy seeks to significantly improve the accuracy of our results. The equations that dictate the behavior were transformed into nonlinear ordinary differential equations by employing specific similarity transformations. The Runge–Kutta-Fehlberg approach proved to be highly efficient in computing solutions, yielding fourth- and fifth-order approximations. The solutions were found to rely on various physical parameters, including the Casson fluid factor, Prandtl and Schmidt numbers, heat source and sink components, radiation parameters, and suction and injection factors. These parameters elucidate the behavior of velocity, concentration, and temperature profiles. When the Casson parameter increases by 212.5%, the temperature increases by 0.5270% for the PST case and by 1.4050% for the PHF case under suction conditions, and similarly, rises by 1.3238% for the PST case and by 5.7224% for the PHF case under blowing conditions.

Consistent ramifications of prescribed surface temperature and prescribed heat flux boundary conditions for the slip flow of Walter B fluid in a stretching channel

ABSTRACT The present work delves into the Walter B fluid flow across the channel with the elongating enclosures when enthralled by linear radiation. The magnetic field is contemplated throughout the examination. The fluid suction and injection is permitted through the lower permeable wall. The slip regime is confined at the boundaries of the channel. Heat transfer in the channel is brought to light under two heating processes, namely prescribed surface temperature and prescribed surface heat flux case. The modeled equations are non-dimensionalized and then solved by the Runge-Kutta Fehlberg method in association with shooting scheme. Results deduce that the Reynolds number magnifies the velocity in the channel. Under two different heat boundary conditions, it is recorded that temperature is more pronounced for prescribed surface temperature case than prescribed heat flux. Flow profile for the varying viscoelastic parameter deciphers that at the lower end of the channel, the velocity is augmented and reverse response is recorded at the upper half of channel. Entropy profile magnifies with the augmentation of the magnetic parameter and shows depleting nature for higher Reynolds number. Examining the Walter B fluid flow in the channel enclosed with stretchable walls deliberates the flow of blood in the arterial wall under the exertion of strong magnetic field.

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.

Impact of surface temperature and convective boundary conditions on a Nanofluid flow over a radially stretched Riga plate

The current work provides the optimal homotopic analytical methodology for the steady circulation over a non-isothermal radially stretched Riga plate/disc unit. The attributes of the heat, along with the mass transfer process, are assessed in the existence of variable transport and magnetic features. Radial stretched Riga disc is considered along with additional realistic boundary heating conditions, namely, prescribed surface temperature as well as prescribed surface concentration, convective boundary conditions and also zero mass flux concentration on the surface area of the Riga disc. The model tracks Brownian motion as well as the thermal diffusion of nanoparticles in fluid circulation all at once. Regulating equations, which are highly coupled, are changed right into non-dimensional equations using appropriate transformations of similarity. Through assembling series solutions, the resulting framework is planned and examined. Graphic summaries are offered for the rheological qualities of various parameters in size for velocity, temperature, as well as nanoparticles. The modified Hartman number improves the velocity distribution and reduces the temperature distribution in both prescribed surface temperature and convective boundary condition cases. The effect of the chemical reaction parameter shows the reduced concentration distribution for the prescribed surface temperature case. In contrast, it is precisely the opposite in the convective boundary condition case.

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.

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.

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.

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

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.

Heat transfer in a hydromagnetic flow over a stretching sheet

Exact solutions are obtained for the heat transfer in an electrically conducting fluid past a stretching sheet subjected to the thermal boundary with either a prescribed temperature or a prescribed heat flux in the presence of a transverse magnetic field. The solutions for the heat transfer characteristics are evaluated numerically for different parameters, such as the magnetic parameterN, the Prandtl numberPr, the surface temperature indexs, and the surface heat flux indexd. It is observed that for the prescribed surface temperature case the fluid temperature increases due to the existance of the magnetic field, and decreases as the Prandtl number or the surface temperature index increases; for the prescribed surface heat flux case, the surface temperature decreases as the Prandtl number of the surface heat flux index increases, and the magnetic parameter decreases. In addition, varying the prescribed surface temperature indexs affects the mechanism of heat transfer.