Prescribed Heat Flux Research Articles

Effects of prescribed surface temperature and heat flux with electrical conductivity via microbial chemotaxis to enhance nanoparticle

The purpose of the current investigations in to explore the three-dimensional magnetohydrodynamic (MHD) Oldroyd-B nanofluid flow over an exponential stretchable surface with variable thermal conductivity. Impact of thermal radiation and gyrotactic motile organism also incorporated in the present study. A fluid that has tiny particles, also referred to as nanoparticles, scattered throughout a base fluid is called a nanofluid. These nanoparticles can be formed from metals, oxides, carbon-based compounds, or other nanomaterials, and their usual sizes range from 1 to 100 nanometers. Water, oil, ethylene glycol, or other common liquids can be used as the foundation fluid. Because of their improved physical qualities, greater heat transfer, and thermal conductivity, nanofluids have many uses in a variety of sectors. Two type of boundary conditions are associated here like prescribed surface temperature (PST) and prescribed heat flux (PHF). Exploring nanoparticles influence on a fluid viscoelasticity, and vice versa, advanced understanding of three-dimensional nanofluid flow over a porous, stretchable surface. The research also probed microorganisms' and reactions' impact on heat/mass transfer. Employing MATLAB and a similarity approach converted Navier-Stokes equations into ordinary differential equations. Outcomes included velocity profile, temperature profiles, concentration profiles, and microbe behavior. Thus, this significantly contributed to modelling collectors and thermal storage. The concentration profile flattens when the Schmidt number (Sc) is increased, indicating that the fluid flow behavior is clearly influenced. Moreover, these findings established ways to improve energy systems' efficiency by elucidating heat transport and fluid flow parameters. This enables sustainable energy solutions to tackle global challenges. The influence of various convergence parameters is illustrated through graphically and in the form of table. Also, our results are validated with the previously published data and found tremendous agreement.

The effects of bioconvection, non‐Fourier heat flux, and thermal radiations on Williamson nanofluids and Maxwell nanofluids transportation with prescribed thermal conditions

AbstractThe utilization of nanoentities in common fluids has opened new opportunities in the area of heat transportation. The rising requirements to enhance the efficiency of compact heat exchangers can be achieved by using various nanofluids. In this article, the thermal output of Maxwell and Williamson nanofluids transport over a prolonging sheet with bioconvection of self‐motivated organisms is scrutinized. A magnetic flux and the porous effects of a medium influence the flow of fluids. The fundamental principles for conservation of mass, concentration, momentum, and energy yield a nonlinear set of partial differential equations that can then be altered into ordinary differential form. A heat transfer flux is presented along with temperature boundary conditions, PST, and PHF (prescribed surface temperature and prescribed heat flux). The numerical results are acquired by executing the Runge–Kutta method with a shooting procedure in MATLAB coding. By fluctuating the inputs of influential variables of the dependent functions, a precise overview of the scheme is acquired. It can be seen that velocity decreases with the rising values of buoyancy ratio, magnetic force, Raleigh number, and porosity. Also, the temperature of the fluids begins to rise directly with the rising values of thermophoresis and Brownian motion parameters. The present study addresses bioconvection, non‐Fourier heat flow, and thermal radiations while combining the special properties of Williamson and Maxwell nanofluids. The field of biomedical engineering may benefit from this study, particularly with regard to therapies for hyperthermia and drug delivery systems. This study can be useful in cutting‐edge cooling systems, bioengineering, solar energy conversion and biotechnology.

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.

An analytical study on the influence of magnetic field-dependent viscosity on viscous and ohmic dissipative second-grade fluid boundary layers

This article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Numerical treatment for double diffusion phenomenon with generalized heat flux effects in 3d nanomaterial flow over bi-directional stretched wall

Current study aims to numerically investigate the bi-directional flow of nanofluids in the presence of Cattaneo–Christov double diffusion for two heat sources, namely, prescribed surface temperature (PST) along with prescribed heat flux (PHF). The conventional mathematical model in partial differential equations (PDEs) of the system have been reduced into an equivalent set of ordinary differential equations (ODEs). The system dynamics in the form of approximate solutions of the ODEs is presented by Adams and Explicit Runge Kutta numerical solvers. For better understanding the influence of physical parameter of interest including Brownian movement parameter, thermophoresis parameter, concentration relaxation parameter, Schmidt number, Prandtl number, thermal relaxation parameter, temperature ratio parameter, stretching ratio parameter and Deborah number on temperature, as well as concentration profiles are presented exhaustively. Appropriateness of the scheme is ascertained through close resemblance of results for different state of the art counterparts with negligible error around 10–05 to 10–09.

Quality and quantity trade-offs in clear ice making

This paper is aimed at clear ice making. To this end, a purpose-built apparatus that controls the solidification rate was specially designed and constructed to assess the trade-offs between ice clearness (quality) and production rate (quantity). An image-based ice clearness evaluation technique was devised and adopted to compute a figure-of-merit for the ice quality. 30 ml ice cube samples were produced in a closed ice tray for either prescribed heat flux (650, 1300 and 1700 W m−2) or surface temperature (−4, −8 and −12 °C) at the bottom wall, while a 25 mm EPS insulation was adopted for top and lateral walls. The experiments were carried out using both tap and boiled water, whose initial amount of dissolved gas was monitored. The results pointed out the heat transfer and initial air concentration conditions that rule the quality and quantity trade-offs in clear ice making.

Prescribed thermal effects on the dynamics of radiative and chemically reactive hyperbolic tangent nanofluid

ABSTRACT The dynamics of hyperbolic tangent nanofluid, coupled with thermal radiation and chemical reactions, find extensive applications in various fields, including drying processes, oil emulsions, ceramics, prevention of crop damage from freezing, and dehydration processes. Therefore, the primary objective of the present contribution is to scrutinize the dynamic behavior of hyperbolic tangent nanofluid with consideration for both chemical reactions and thermal radiation effects subject to a prescribed thermal system. To model the nanofluid’s behavior, we have employed Buongiorno’s nanofluid model, which incorporates random motion and thermo-diffusion of nanostructured particles. The thermal performance of the hyperbolic tangent nanofluid is analyzed under two boundary conditions: prescribed surface temperature (PST) and prescribed heat flux (PHF). To facilitate the analysis, we have transformed the transport PDEs in Cartesian configuration into ODEs. Subsequently, we have employed the highly efficient HAM (homotopy analysis method) to solve the obtained system. The study explores the influence of various flowing constraints on key configurations such as temperature formation, velocity formation, concentration formation, local drag formation, Nusselt number, and Sherwood number. Notably, the Nusselt number diminishes with the inclusion of thermo 0.2 ≤ N t ≤ 1.1 and Brownian 0.3 ≤ N b ≤ 1.1 diffusions of nanoparticles, while it increases with an escalation in the thermal radiation 0.0 ≤ R d ≤ 2.5 parameter.

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.

Supergranule aggregation: a Prandtl number-independent feature of constant heat flux-driven convection flows

Supergranule aggregation, i.e. the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh–Bénard convection at a fixed Rayleigh number ${Ra} \approx 2.0 \times 10^{5}$ across $4$ orders of Prandtl numbers ${Pr} \in [10^{-2}, 10^{2}]$ by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio $\varGamma = 60$ . Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of ${Pr}$ on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes.

Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection

Jeffrey fluid flow past an inclined stretchable sheet affected by magnetic dipole and suction/injection was investigated. The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. Considering the prescribed surface temperature (PST) and prescribed heat flux (PHF) heat processes, the effect of inclination angle, the Grashof number, and other parameters on the velocity and temperature of the fluid were documented by graphs and tables. Without the angle of inclination, the solutions from this paper were found to agree with those of the Generic algorithm and Nelder Mead method. The fluid is slower when the plate is inclined at a larger angle and this tends to allow for higher fluid temperature. The ferromagnetic interaction parameter and the ratio of relaxation to retardation time have the same effect on fluid velocity and temperature as the angle of inclination. The suction parameter and Prandtl number amplify the Nusselt number, while, as the suction increases, the skin friction increases for all inclination angles. With these results, engineers in chemical/polymer industries can make appropriate changes that can lead to more quality production.

Entropic behavior in bidirectional flow of CeO2-ZnO/water hybrid nanofluid with prescribed surface temperature/heat flux aspects

PurposeThe present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid.Design/methodology/approachThe transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters.FindingsIt is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints.Originality/valueTo the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation.

EMHD flow and convective heat transfer over a prescribed surface temperature (PST) and prescribed heat flux (PHF) heating condition

Mixed convection describes the combined effects of free and forced convection. It’s used extensively in technical projects including solar collectors, electronics, and nuclear power plants. When buoyancy force dominates the forced convective process or when forced flow dominates the free convective process, such a process is taking place. The authors of this study pondered the situation in which a non-Newtonian micropolar fluid flows steadily and incompressible past an expanding sheet. We have used elements of EMHD, velocity slip, and mixed convection to achieve this. The set of equations administered flow of fluid is converted into ordinary differential equation by suitable variables. MATLAB software’s bvp4c code is used to find the solutions of reduced equations. The influence of different parameters on velocity profile and temperature profile are illustrated. From the outcomes, it is stipulated that the increasing parameter the and temperature distributions exhibit an increasing trend. Additionally, when we increase the value of we see a decreasing trend in the temperature distribution for both the and instances.

Unsteady magnetized flow of micropolar fluid with prescribed thermal conditions subject to different geometries

Due to realistic implementations of heat transfer flows, this study communicates with the two cases of the prescribed thermal process. A comparative analysis of the time-dependent flow of a micropolar fluid between two problems of linear stretching sheet and exponential stretching sheet is demonstrated. In the context of the linear stretching sheet, the investigation covers situations involving prescribed surface temperature (PST) and prescribed heat flux (PHF). Likewise, for the exponential stretching sheet, the study examines cases of prescribed exponential order temperature (PEST) and prescribed exponential order heat flux (PEHF). For both problems, the two cases of the thermal process are examined for heat transfer analysis considering joule heating and nonlinear thermal radiation. The two-dimensional flow in the presence of a variable magnetic field is explored for both the linear and exponential stretching sheet problems. Graphical representations are employed to provide a comparative illustration of flow properties concerning relevant parameters for both cases. From the graphical and tabular analysis, we deduce that an exponential stretching sheet provides more consequential results as compared to a linear stretching sheet. Furthermore, the material parameter demonstrates an increase in the velocity field for both of the considered sheets.

Framing the features of nanolayer and diameter of carbon nanotubes in the flow of blood over a stretching cylinder in presence of magnetic induction

This study explores the slip boundary layer electrically conducting flow of nanofluid over a stretching cylinder. Flow type in present study is considered to be steady and incompressible flow with mixture of SWCNTs/MWCNTs and human blood. Thermal conductivity of present flow model is measured by merging the consequence of diameter of SWCNTs/MWCNTs nanoparticles and solid–liquid interfacial-layer. Velocity slip, non-linear radiation, and induced magnetic-flux are considered in flow. The mode of heat transmission in flow is presented in appearance of dual heat flux, that is, Cattaneo-Christov heat flux and prescribed heat flux. By executing similarity exploration, we modernize the leading PDEs of the acknowledged flow model into ODEs. The consequential equations are solved numerically by recalling Runge–Kutta–Fehlberg fourth-fifth order scheme through shooting system. Deliberations on consequence of flow features on flow specific are organized accurately via graphs and charts. The professed numerical consequences are novel and distinctive. These consequences can contribute to other scholars on electing the suitable factors to enlarge the heat conduction technique in medical science, society, and the industry.

Graetz problem for the casson fluid model with prescribed heat flux in a circular duct

Graetz problem for the casson fluid model with prescribed heat flux in a circular duct

Influence of PST and PHF heating conditions on the swirl flow of Al+Mg+TiO2 ternary hybrid water-ethylene glycol based nanofluid with a rotating cone

Swirl flow heat exchangers are commonly used in industrial processes such as power generation, chemical processing, and refrigeration. They can be used for both heating and cooling applications and can be designed to handle a wide range of fluid flow rates and temperatures. This study investigated the influence of PST (prescribed surface temperature) and PHF (prescribed heat flux) heating conditions on the swirl flow of Al+Mg+TiO2 ternary hybrid water-ethylene glycol (50/50) based nanofluid with a heated rotating cone. The governing ordinary differential equations were derived from the partial differential equations using the proper similarity transformations. The problem was solved using the Shifted Legendre Collocation Method (SLCM), which is a powerful numerical method. The results showed that the PST heating conditions had a significant impact on the flow and heat transfer characteristics of the ternary hybrid nanofluid. Under PHF heating conditions, the swirl velocity distribution was leading to a noteworthy influence. The use of the Al+Mg+TiO2 ternary hybrid water-ethylene glycol based nanofluid resulted in a significant enhancement in the convective heat transfer coefficient. The SLCM method provided accurate and efficient numerical solutions for the problem, demonstrating its suitability for simulating complex fluid flow and heat transfer problems.

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.

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.

The Effect of Biot Number on a Generalized Heat Conduction Solution

Abstract Analytical solutions for thermal conduction problems are extremely important, particularly for verification of numerical codes. Temperatures and heat fluxes can be calculated very precisely, normally to eight or ten significant figures, even in situations involving large temperature gradients. It can be convenient to have a general analytical solution for a transient conduction problem in rectangular coordinates. The general solution is based on the principle that the three primary types of boundary conditions (prescribed temperature, prescribed heat flux, and convective) can all be handled using convective boundary conditions. A large convection coefficient closely approximates a prescribed temperature boundary condition and a very low convection coefficient closely approximates an insulated boundary condition. Since a dimensionless solution is used in this research, the effect of various values of dimensionless convection coefficients, or Biot number values, are explored. An understandable concern with a general analytical solution is the effect of the choice of convection coefficients on the precision of the solution, since the primary motivation for using analytical solutions is the precision offered. An investigation is made in this study to determine the effects of the choices of large and small convection coefficients on the precision of the analytical solutions generated by the general convective formulation. Results are provided, in tabular and graphical form, to illustrate the effects of the choices of convection coefficients on the precision of the general analytical solution.

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.