Prescribed Heat Flux Conditions Research Articles

Thermal entry problem for a tube with prescribed heat flux condition using viscoplastic fluid: An extended Graetz problem for Casson fluid with axial conduction and viscous dissipation

AbstractThis study explores the impact of axial conduction and viscous dissipation on heat transfer inside a tube by employing the Casson fluid model. A semianalytical approach is employed to handle the considered problem. The application of the separation of variable technique converts the heat equation into a set of ordinary differential equations. A built‐in function bvp4c in Matlab is adopted for numerical solutions in terms of eigenvalues and eigenfunctions. The obtained results are thoroughly discussed through pictorial representations. The finding shows that the Peclet and Brinkman numbers could not be ignored where an accurate temperature is essential for the final product. The both Peclet numbers and Brinkman numbers have a strong influence on the entrance temperature profile of the tube. In addition, the viscoplastic parameter raises the local Nusselt number in developing and fully developed regions of the tube. This analysis may be helpful in the advancement of thermal devices that are used to diagnose many diseases.

Free convection flow of hybrid ferrofluid past a heated spinning cone

• Hybrid ferrofluid flow past a vertical spinning cone is numerically analyzed. • Hybrid ferrofluid is made of EG-water base fluid and Fe 3 O 4 + CoFe 2 O 4 ferroparticles. • IPS solutions are given for PST and PHF boundary conditions. • PST condition produces higher skin friction than PHF condition. • Hybrid ferrofluid yields highest skin friction and highest heat transfer. This paper analyzes the implementation of numerical computation based on the Iterative Power Series (IPS) method to investigate the steady boundary layer flow around and free convection from a spinning vertical cone placed in an otherwise still hybrid ferrofluid. The hybrid ferrofluid is prepared by suspending magnetite ( F e 3 O 4 ) and cobalt ferrite ( CoF e 2 O 4 ) ferroparticles in a 50%-50% solution of ethylene glycol (EG) and water ( H 2 O ). The investigations on heat transfer compare results for the Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF) boundary conditions. Similarity transformations are implemented for converting the partial differential equations into ordinary differential equations (ODEs). Numerical solution of the non-linear governing ODEs is obtained by employing the IPS method jointly with iterative shooting procedure. The present approach shows very good agreement with the findings of reported research for some special cases. The influence of governing parameters on the quantities of physical and engineering interest are presented using graphs and tables. It is found that skin friction is greater for PST boundary condition and the heat transfer is greater for PHF boundary condition. The hybrid ferrofluid yields maximum skin friction and maximum heat transfer compared to base fluids and simple nanofluids.

On development of heat transportation through bioconvection of Maxwell nanofluid flow due to an extendable sheet with radiative heat flux and prescribed surface temperature and prescribed heat flux conditions

This paper evaluates thermal output for the flow of Maxwell nanofluid over an extending sheet with bioconvection of micron size self‐motivated organisms. Radiative heat flux and two temperature boundary conditions, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF), are considered. The flow is influenced by a magnetic field and porosity effects of a medium. The motivation pertains to attain an enhancement in thermal transportation via nanoparticle inclusion. The possible settling of the nanoparticles may be avoided by bioconvection of microorganisms. The basic theoretical conservation of mass, concentration, momentum, and energy provides a nonlinear set of partial differential equations which are then transmuted into ordinary differential form. The implementation of Runge–Kutta method with shooting technique in Matlab coding resulted the numerical solution. A deep insight into the problem is inspected by varying the inputs of influential parameters of the dependent functions. It is perceived that the flow speed is hindered by the growing inputs of parameters of buoyancy ratio, magnetic field, Raleigh number, and porosity. The temperature of the fluid attains higher outputs directly with thermophoresis and Brownian movement of nanoparticles. Motile microorganisms χ(η) profile goes down when bioconvection Schmidt number intensified. The current numeric results are validated when compared within existing studies.

Rotating flow of carbon nanotubes subject to prescribed heat flux condition

This article intends to describe the three-dimensional flow of nanofluid consisting of carbon nanotubes (CNTs) subject to rotating frame. Disturbance in flow is generated by an exponentially stretching sheet. Prescribed heat flux condition is considered. Darcy-Forchheimer relation is employed to characterize the flow in porous space. System of dimensionless equations is obtained by utilizing adequate transformations. Optimal homotopy analysis algorithm is employed for solution development. Physical interpretation of emerging variables on flow fields and physical quantities is discussed. Skin friction coefficient enhances for local porosity parameter, nanoparticle volume fraction and Forchheimer number. Augmentation for heat transfer rate is noticed through solid volume fraction of nanoparticles.

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.

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.

Magnetohydrodynamic three-dimensional nonlinear convective flow of viscoelastic nanofluid with heat and mass flux conditions

The present research focuses on three-dimensional nonlinear convective flow of viscoelastic nanofluid. Here, the flow is generated due to stretching of a impermeable surface. The phenomenon of heat transport is analyzed by considering thermal radiation and prescribed heat flux condition. Nanofluid model comprises of Brownian motion and thermophoresis. An electrically conducting fluid is accounted due to consideration of an applied magnetic field. The dimensionless variables are introduced for the conversion of partial differential equations into sets of ordinary differential systems. The transformed expressions are explored through homotopic algorithm. Behavior of different dimensionless parameters on the non-dimensional velocities, temperature and concentration are scrutinized graphically. The values of skin friction coefficients, Nusselt and Sherwood numbers are also calculated and elaborated. It is visualized that the heat transfer rate increases with Prandtl number and radiation parameter is higher.

Simultaneous effects of heat generation/absorption and thermal radiation in magnetohydrodynamics (MHD) flow of Maxwell nanofluid towards a stretched surface

Mathematical analysis of magnetohydrodynamic (MHD) three-dimensional nonlinear convective flow of Maxwell nanofluid towards a stretching surface is made in this article. Characteristics of heat transfer are examined under thermal radiation, heat generation/absorption and prescribed heat flux condition. Nanofluid model includes Brownian motion and thermophoresis. Dimensional nonlinear expressions of momentum, energy and concentration are converted into dimensionless systems by invoking suitable similarity variables. A well-known homotopic technique is implemented for dimensionless expressions. Impact of different quantities on velocities, temperature and concentration are scrutinized graphically and discussed in detail. The expressions of Nusselt and Sherwood numbers are calculated and addressed comprehensively. It is also seen that thermal radiation parameter enhances the temperature field and heat transfer rate.

Time-Dependent Second-Order Viscoelastic Fluid Flow on Rotating Cone with Heat Generation and Chemical Reaction

AbstractThe present analysis deals with the study of time-dependent flow of a second-order fluid on a rotating cone in the presence of chemical reaction and heat generation or absorption effects under prescribed heat flux conditions. The boundary-layer nonlinear partial differential equations of second grade fluid are first reduced into a system of ordinary differential equations with the help of transformations and nondimensional similar and nonsimilar quantities, and then solved analytically by optimal homotopy analysis method (OHAM). The effects of relevant parameters such as chemical reaction, heat generation, or absorption on local skin friction coefficients, local Nusselt number, and local Sherwood number are discussed. These effects are illustrated graphically as well as in tabular form to describe special features of the solutions.

Effect of Viscous Dissipation, Internal Heat Source/Sink, and Thermal Radiation on a Hydromagnetic Liquid Film Over an Unsteady Stretching Sheet

In this study, the effect of magnetic field, viscous dissipation, nonuniform heat source, and/or sink and thermal radiation on flow and heat transfer in a hydromagnetic liquid film over an unsteady stretching sheet with prescribed heat flux condition is investigated. The governing equations are transformed into a set of ordinary differential equations with six free parameters by using a similarity transformation before being solved numerically. The temperature profiles depending on the governing parameters are displayed in graphical form and the relevant thermal characteristics are depicted in tabular representation. It is found that the dimensionless temperature profile, sheet temperature, and free surface temperature, with a specific unsteadiness parameter, are enhanced as the increase in magnetic parameter, Eckert number, space- and temperature-dependent parameters, and they are reduced for increasing effective Prandtl number.

Self-Similar Solution of Heat and Mass Transfer of Unsteady Mixed Convection Flow on a Rotating Cone Embedded in a Porous Medium Saturated with a Rotating Fluid

A self-similar solution of unsteady mixed convection flow on a rotating cone embedded in a porous medium saturated with a rotating fluid in the presence of the first and second orders resistances has been obtained. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear function of time. The system of ordinary differential equations governing the flow has been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. Both prescribe wall temperature and prescribed heat flux conditions are considered. Numerical results are reported for the skin friction coefficients, Nusselt number and Sherwood number. The effect of various parameters on the velocity, temperature and concentration profiles are also presented here.

Unsteady mixed convection from a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion

A semi-similar solution of an unsteady mixed convection flow over a rotating cone in a rotating viscous fluid has been obtained when the free stream angular velocity and the angular velocity of the cone vary arbitrarily with the time. Both the prescribed wall temperature and the prescribed heat flux conditions are considered in the present investigation. The non-linear coupled partial differential equations governing the mixed convection flow have been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical results are presented for the skin friction coefficients, Nusselt number and Sherwood number. The effects of various parameters on the velocity, temperature and concentration profiles are also reported here.

Unsteady mixed convection flow on a rotating cone in a rotating fluid

This paper deals with a new self-similar solution of unsteady mixed convection flow on a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear functions of time. The system of ordinary differential equations governing the flow has been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. Both prescribe wall temperature and prescribed heat flux conditions are considered. Numerical results are reported for the skin friction coefficients, Nusselt number and Sherwood number. The effect of various parameters on the velocity, temperature and concentration profiles are also presented here.

Unsteady mixed convection flow at the stagnation point

The unsteady mixed convection flow of an electrically conducting fluid at the stagnation point of a two-dimensional body and an axisymmetric body in the presence of an applied magnetic field has been studied. The effect of induced magnetic field has been included in the analysis. Both prescribed wall temperature and prescribed heat flux conditions have been considered. It is found that if the free stream velocity, applied magnetic field and square root of the wall temperature vary inversely as a linear function of time, i.e. as (1 − λt′) −1, the governing boundary layer equations admit a locally self-similar solution. If surface heat flux is prescribed, it should vary as (1 − λt ∗) − 5 2 for the existence of a local self-similar solution. The resulting ordinary differential equations have been solved using a finite element method as well as a shooting method with Newton's corrections for missing initial conditions. The skin friction and heat transfer coefficients and x-component of the induced magnetic field on the surface increase with the applied magnetic field or buoyancy force. Also they are found to change more for decelerating free stream velocity than for accelerating free stream velocity. Furthermore, they change little with the reciprocal of the magnetic Prandtl number. The buoyancy parameter causes overshoot in the velocity profile. For a given Prandtl number, beyond a certain critical value of the dissipation parameter, the hot wall ceases to be cooled due to the “heat cushion” provided by frictional heat.

On the principle of exchange of stabilities for the magnetohydrodynamic thermal stability problem in completely confined fluids

The principle of exchange of stabilities (exchange principle) for the thermal stability problem has been proved by Pellew & Southwell (1940) for fluids bounded by two infinite, horizontal parallel planes. Chandrasekhar (1952) discussed the establishment of the exchange principle for the same geometry when the fluid is an electrical conductor and when an arbitrary oriented, uniform, external magnetic field is applied in the vertical direction.In this paper, the exchange principle is examined for fluids completely confined in an arbitrary region with rigid bounding surfaces that are good electrical conductors with respect to the fluid. The uniform magnetic field is applied in an arbitrary direction. A generalized thermal boundary condition is imposed which includes the fixed temperature and prescribed heat-flux conditions as special cases.If no magnetic field is applied to the fluid, the present work reduces to a generalization (for completely confined fluids) of the Pellew & Southwell proof of the exchange principle. In the magnetohydrodynamic (MHD) thermal stability problem, the exchange principle is found to be valid if the total kinetic energy associated with an arbitrary disturbance is greater than or equal to its total magnetic energy. In a special case it is demonstrated that a sufficient condition which will establish the exchange principle is k ≤ η, where k is the fluid thermal diffusivity and η is the fluid electrical resistivity.