Surface Heat Transfer Rate Research Articles

Darcy-Forchheimer flow and heat transfer of water-based Cu nanoparticles in convergent/divergent channel subjected to particle shape effect

The current study provides a comprehensive numerical investigation of flow and heat transfer of water-based Cu nanoparticles over a convergent/divergent channel. In order to control the random motion of nanoparticles, Darcy-Forchheimer, particle shape effect and viscous dissipation are also incorporated for the present mechanism. The resulting system of nonlinear equations is solved numerically by using the RKF-45 method. Expressions for the velocity and temperature profile are derived and plotted under the assumption of a flow parameter. The influence of various parameters on surface drag force and heat transfer rates have been discussed with the help of tables and plots.

Radiative Flow of Third Grade Non-Newtonian Fluid From A Horizontal Circular Cylinder

Abstract In this article, we study the nonlinear steady thermal convection of an incompressible third-grade non-Newtonian fluid from a horizontal circular cylinder. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-differences Keller Box technique. The influence of a number of emerging non-dimensional parameters, namely the third-grade fluid parameter (ϕ), the material fluid parameters (ϵ1, ϵ2), Prandtl number (Pr), Biot number (y), thermal radiation (F) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation is achieved. It is found that the velocity, skin friction and Nusselt number (heat transfer rate) reduce with increasing third grade fluid parameter (ϕ), whereas the temperature is enhanced. Increasing material fluid parameter (ϵ1) reduces the velocity and heat transfer rate but enhances the temperature and skin friction. The study is relevant to chemical materials processing applications and low density polymer materials processing.

Assessment of the inclination surface on the microlayer behavior during nucleate boiling, a numerical study

Nucleate boiling is an important part of pool boiling process. Heat transfer from the microlayer plays a considerable role in heat transfer to the fluid. The axisymmetric assumption of the microlayer for a horizontal surface needs to be evaluated for an inclined one. In this study, the effect of surface orientation on the microlayer thickness and the heat transfer rate are investigated numerically. The governing equations are simplified employing scaling analysis. The results for the microlayer thickness, the heat flux and the total heat transfer rate for the heated surface are obtained and presented. The asymmetry of the microlayer increases as the surface inclination angle varies from horizontal to vertical. Even though, the driving force due to gravity in the microlayer is negligible, however its effect on the macro region changes the microlayer parameters. The results show that the maximum microlayer heat transfer rate for the vertical surface increases by 28.8% compared to that for a horizontal surface. The proposed model, which is capable of evaluating the microlayer thickness and its surface heat transfer rate, can be employed as a surface boundary condition in the macro region simulations of the nucleate boiling.

New transient simplified model for radiant heating slab surface temperature and heat transfer rate calculation

A new simplified model based on a semi-analytical correlation is proposed in this paper to evaluate the heating radiant slab surface temperature and to examine its thermal behavior under dynamic solicitations. In fact, the surface temperature is a normative design parameter and shall be kept under an upper limit whatever are the running conditions. Experimental measurements and a two-dimensional finite difference model (2D FDM) were carried out to validate the developed simplified model based on two characteristic parameters that are the time constant and the delay time. A Design of Experiments (DoE) method is employed to derive meta-models for the time constant and the delay time in order to compute the surface temperature. The sensitivity analysis shows that the specific heat capacity of the slab material and the heating water flow rate affect significantly the time constant compared to the thermal conductivity and the heating water pipe inner diameter. Moreover, it was found that all these parameters, except the heating water flow rate, have a substantial impact on the delay time. Compared to the experimental results, the maximum relative deviations from the computed surface temperature are within 2.4% for the numerical model and 1.75% for the simplified semi-analytical model. Consequently, the proposed simplified model may be utilized by engineers and designers to quickly estimate the radiant slab surface temperature and heat flux as well as to study its thermal behavior under dynamic running conditions. This model may also be integrated in the thermal building simulation software.

Thermal properties and time-dependent flow behavior of a viscous fluid

Our goal in this attempt is to model a nonlinear stretchable flow of a radiative viscous liquid with magnetohydrodynamics. Flow caused is due to a unsteady stretching surface with variable thickness. Consideration of thermal radiation effect characterizes the heat transfer process. Induced electric and magnetic fields are not accounted for. Appropriate transformations gave nonlinear systems. Modern methodology, i.e., НAM, is implemented for the computational process. Velocity and temperature are plotted for influential variables which are important in this problem. Moreover, surface drag force and heat transfer rate are computed and discussed. Velocity field is noted to decay the function of the larger Hartman number whereas opposite situation for temperature is examined via larger radiation parameter.

Finite element analysis on transient magnetohydrodynamic (MHD) free convective chemically reacting micropolar fluid flow past a vertical porous plate with Hall current and viscous dissipation

This article deals with boundary layer analysis of magnetohydrodynamics on an unsteady chemically reactive micropolar rotating fluid flow past a semi-infinite vertical plate with the impact of Hall current and viscous dissipation. The relevant equations on the fluid flow have been developed under Boussinesq approximation. The governing partial differential equations are transformed into a set of coupled partial differential equations using suitable dimensionless quantities. The resultant equations are solved numerically using variational finite element method. A parametric study illustrating the influence of different pertinent parameters is performed and the numerical results for translational velocity, microrotation velocity, temperature and concentration distributions near the boundary layers are discussed and presented graphically for the parametric variations. Finally, the skin-friction, wall couple stress, surface heat transfer and mass transfer rate dependency on the emerging thermo-physical parameters are also tabulated. The finite element code is benchmarked with the results reported in the literature to check the validity and accuracy under some limiting cases and excellent agreement with published solutions is achieved.

Cattaneo-Christov model for electrical magnetite micropoler Casson ferrofluid over a stretching/shrinking sheet using effective thermal conductivity model

Nanofluids are the key building block of nanoparticles. So in particular, the researchers got attention in the development of nanotechnology. The knowledge of heat transmission in magnetohydrodynamic nanofluid flows through diverse geometries is significant for heat exchangers design, transpiration, fiber coating, etc. Currently, the nanomaterial's are among the well-known tackles for refining the low thermal conductivity of working liquids. Naturally, magnetite (Fe3O4) nanoparticles move randomly within the base fluid. When transverse magnetic force is applied, the motion of nanofluid becomes uniform. With this instigation, a mathematical model is developed to examine the heat transmission performance of electrically conducting MHD flow of a Casson ferrofluid over a stretching sheet. Moreover, we have considered water as a base fluid in this work. The formulated model has been solved with homotopy analysis method (HAM) by using similarity variables. The impact of embedded parameters on velocity, micro-rotation velocity, and temperature profiles have been shown graphically and discussed in detail. Also the impact of embedded parameters on surface drag force and heat transfer rate have been shown through tables and discussed as well.

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

AbstractNonlinear, steady‐state, viscous flow, and heat transfer between two stretchable rotating disks spinning at dissimilar velocities are studied with a non‐Fourier heat flux model. A nondeformable porous medium is intercalated between the disks and the Darcy model is used to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless parameters, that is, Prandtl number, upper disk stretching, lower disk stretching, permeability, non‐Fourier thermal relaxation, and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial, and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to rotating disk bioreactors in chemical engineering.

Significance of Darcy-Forchheimer Porous Medium in Nanofluid Through Carbon Nanotubes

This article manages Darcy-Forchheimer 3D flow of water based carbon nanomaterial (CNTs). A bidirectional nonlinear stretchable surface has been utilized to make the flow. Disturbance in permeable space has been represented by Darcy Forchheimer (DF) expression. Heat transfer mechanism is explored through convective heating. Outcomes for SWCNT and MWCNT have been displayed and compared. The reduction of partial differential framework into nonlinear common differential framework is made through reasonable variables. Optimal series scheme is utilized for arrangements advancement of associated flow issue. Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables. Moreover surface drag coefficients and heat transfer rate are analyzed through plots.

Darcy–Forchheimer 3D flow of carbon nanotubes with homogeneous and heterogeneous reactions

This article deals with Darcy–Forchheimer three dimensional (3D) flow of water-based carbon nanotubes (CNTs) with heterogeneous–homogeneous reactions. A bidirectional nonlinear extendable surface has been employed to create the flow. Flow in porous space is represented by Darcy–Forchheimer expression. Heat transfer mechanism is explored through convective heating. Equal diffusion coefficients are considered for both auto catalyst and reactants. Results for single-wall (SWCNT) and multi-wall (MWCNT) carbon nanotubes have been presented and compared. The diminishment of partial differential framework into nonlinear ordinary differential framework is made through suitable transformations. Optimal homotopy scheme is used for arrangements development of governing flow problem. Optimal homotopic solution expressions for velocities and temperature are studied through plots by considering various estimations of physical variables. Moreover the surface drag coefficients and heat transfer rate are analyzed through plots.

Entropy generation minimization (EGM) of nanofluid flow by a thin moving needle with nonlinear thermal radiation

Entropy generation minimization (EGM) and heat transport in nonlinear radiative flow of nanomaterials over a thin moving needle has been discussed. Nonlinear thermal radiation and viscous dissipation terms are merged in the energy expression. Water is treated as ordinary fluid while nanomaterials comprise titanium dioxide, copper and aluminum oxide. The nonlinear governing expressions of flow problems are transferred to ordinary ones and then tackled for numerical results by Built-in-shooting technique. In first section of this investigation, the entropy expression is derived as a function of temperature and velocity gradients. Geometrical and physical flow field variables are utilized to make it nondimensionalized. An entropy generation analysis is utilized through second law of thermodynamics. The results of temperature, velocity, concentration, surface drag force and heat transfer rate are explored. Our outcomes reveal that surface drag force and Nusselt number (heat transfer) enhanced linearly for higher nanoparticle volume fraction. Furthermore drag force decays for aluminum oxide and it enhances for copper nanoparticles. In addition, the lowest heat transfer rate is achieved for higher radiative parameter. Temperature field is enhanced with increase in temperature ratio parameter.

Rheology of Burgers’ model with Cattaneo-Christov heat flux in the presence of heat source/sink and magnetic field

This investigation presents the characteristics of Cattaneo-Christov heat flux model for the boundary layer flow of Burgers’ fluid model. Instead of simple Fourier’s law of heat conduction, we presented the Cattaneo-Christov model to analyze the thermal relaxation properties when the heat source/sink is present in the system. Mathematical modeling the laws of momentum and energy are presented under the order analysis approach. It is revealed that the term “” is for the hydro-magnetic rheology of the Newtonian model whereas the generalized magnetic field term (as mentioned in Eq. 2) is for the Burgers’ model which is incorporated in the current analysis. Suitable transformations are utilized for the conversion of partial differential system into coupled nonlinear set of ordinary differential equations which are tackled analytically through homotopy analysis technique. The plots of various physical quantities are presented showing the dynamics of the considered analysis. Streamlines for Burgers’ and Newtonian model are presented which show a difference of rheology. Numerical values for skin friction and surface heat transfer rate are presented in the form of tables.

Numerical simulation for homogeneous–heterogeneous reactions in flow of Sisko fluid

Magnetohydrodynamic flow of Sisko liquid over a stretching surface is addressed. Stretching property of sheet is the main agent for fluid flow. Heat transfer is modelled by convective condition. Homogeneous–heterogeneous reactions are also attended. Ordinary differential systems are acquired by using proper transformations. The resulting non-linear system is solved via ND solve shooting technique. Graphs are interpreted to examine the behavior of sundry embedded parameters on temperature and concentration profiles. Also surface drag forces and heat transfer rate are inspected for the impact of numerous pertinent variables. It is revealed that increasing magnetic parameter diminishes the temperature profile. Further for higher values of homogeneous reaction parameter the surface concentration reduces. In addition the verification of present results is achieved by developing comparison with already existing work. The results are found in an excellent agreement.

Effect of surface roughness on the heating rates of large-angled hypersonic blunt cones

Surface-roughness caused by the residue of an ablative Thermal Protection System (TPS) can alter the turbulence level and surface heating rates on a hypersonic re-entry capsule. Large-scale surface-roughness that could represent an ablated TPS, was introduced over the forebody of a 120° apex angle blunt cone, in order to test for its influence on surface heating rates in a hypersonic freestream of Mach 8.8. The surface heat transfer rates measured on smooth and roughened models under the same freestream conditions were compared. The hypersonic flow-fields of the smooth and rough-surfaced models were visualized to analyse the flow physics. Qualitative numerical simulations and pressure measurements were carried out to have an insight into the high-speed flow physics. Experimental observations under moderate Reynolds numbers indicated a delayed transition and an overall reduction of 17–46% in surface heating rates on the roughened model.

Partial slip and thermal radiation effects on hydromagnetic flow over an exponentially stretching surface with suction or blowing

This paper is devoted to analyze computational simulation to study the partial slip and thermal radiation effects on the flow of a viscous incompressible electrically conducting fluid through an exponentially stretching surface with suction or blowing in presence of magnetic field. Using suitable similarity variables, the non-linear boundary-layer PDE are converted to ODE and solved numerically by Runge-Kutta fourth order method in association with shooting technique. Effects of suction or blowing parameter, velocity slip parameter, magnetic parameter, thermal slip parameter, thermal radiation parameter, Prandtl number, and Eckert number are demonstrated graphically on velocity and temperature profiles while skin friction coefficient and surface heat transfer rate are presented numerically. Moreover, comparison of numerical results for non-magnetic case is made with previously published work under limiting cases.

ROTATING UNSTEADY MULTI-PHYSICO-CHEMICAL MAGNETO-MICROPOLAR TRANSPORT IN POROUS MEDIA: GALERKIN FINITE ELEMENT STUDY

In this paper, a mathematical model is developed for magnetohydrodynamic (MHD), incompressible, dissipative and chemically reacting micropolar fluid flow, heat and mass transfer through a porous medium from a vertical plate with Hall current, Soret and Dufour effects. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations for momentum, heat, angular momentum and species conservation are transformed into dimensionless form under the assumption of low Reynolds number with appropriate dimensionless quantities. The emerging boundary value problem is then solved numerically with a Galerkin finite element method employing the weighted residual approach. The evolution of translational velocity, micro-rotation (angular velocity), temperature and concentration are studied in detail. The influence of many multi-physical parameters in these variables is illustrated graphically. Finally, the friction factor, surface heat transfer and mass transfer rate dependency on the emerging thermo-physical parameters are also tabulated. The finite element code is benchmarked with the results reported in the literature to check the validity and accuracy under some limiting cases and an excellent agreement with published solutions is achieved. The study is relevant to rotating MHD energy generators utilizing non-Newtonian working fluids and also magnetic rheo-dynamic materials processing systems.

Heat transfer analysis in the time-dependent axisymmetric stagnation point flow over a lubricated surface

In this paper time-dependent, 2-D, axisymmetric flow and heat transfer of a viscous incompressible fluid impinging orthogonally on a disc is examined. The disc is lubricated with a thin layer of power-law fluid of variable thickness. It is assumed that surface temperature of the disc is time-dependent. Continuity of velocity and shear stress at the interface layer between the fluid and the lubricant has been imposed to obtain the solution of the governing partial differential equations. The set of partial differential equations is reduced into ordinary differential equations by suitable transformations and are solved numerically by using Keller-Box method. Solutions are presented in the form of graphs and tables in order to examine the influence of pertinent parameters on the flow and heat transfer characteristics. An increase in lubrication results in the reduction of surface shear stress and consequently viscous boundary layer becomes thin. However, the thermal boundary layer thickness increases by increasing lubrication. It is further observed that surface shear stress and heat transfer rate at the wall enhance due to unsteadiness. The results for the steady case are deduced from the present solutions and are found in good agreement with the existing results in the literature.

Nose-Tip Transition Control by Surface Roughness on a Hypersonic Sphere

The surface heat flux on a 100 mm diameter hypersonic sphere was reduced through surface roughness on its forebody. The test model was subjected to a hypersonic freestream of Mach 8.8 and Reynolds number 1.98 million/m, in a shock tunnel. Forebody surface heat transfer rates measured on smooth and rough spheres, under the same free-stream conditions, were compared. The comparison of heat flux indicated an overall reduction in surface heating rates on the rough model, which could be attributed to the delayed nose tip transition. The surface roughness on the forebody of the model generated miniature cavities. Stability of the free shear layer over the miniature cavities and entrapment of the destabilizing vortices in the cavities, make the flow over the rough test model more stable than the attached boundary layer over the smooth model, under transitional conditions.

Exploring magnetic dipole contribution on radiative flow of ferromagnetic Williamson fluid

Abstract The purpose of present article is to analyze the impacts of thermal radiation and magnetic dipole in flow of ferromagnetic Williamson liquid over a stretched surface. Appropriate transformations are utilized to obtain the relevant nonlinear differential system. The obtained differential system is tackled numerically with the help of built-in-shooting method. Influence of viscous dissipation, ferromagnetic interaction parameter, cure temperature, Prandtl number, Weissenberg number (material parameter) and thermal radiation are observed on temperature and velocity fields. Further velocity and temperature gradients are discussed and analyzed graphically. The obtained outcomes declare that surface drag force and heat transfer rate enhance for higher estimation of thermal radiation and Prandtl number. Moreover velocity field decays verses Weissenberg number.

Double dispersion effects on non-Darcy free convective boundary layer flow of a nanofluid over vertical frustum of a cone with convective boundary condition

AbstractIn this paper, a numerical analysis is performed to investigate the effects of double dispersion and convective boundary condition on natural convection flow over vertical frustum of a cone in a nanofluid saturated non-Darcy porous medium. In addition, Brownian motion and thermophoresis effects have taken into consideration, and the uniform wall nanoparticle condition is replaced with the zero nanoparticle mass flux boundary condition to execute physically applicable results. For this complex problem, the similarity solution does not exist and hence suitable non-similarity transformations are used to transform the governing equations along with the boundary conditions into non-dimensional form. The Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM) is used to solve the reduced non-similar, coupled partial differential equations. To test the accuracy of proposed method, the error analysis and convergence tests are conducted. The effect of flow influenced parameters on non-dimensional velocity, temperature, nanoparticle volume fraction, regular concentration field as well as on the surface drag, heat transfer, nanoparticle and regular mass transfer rates are analyzed.