An efficient adaptive moving grid algorithm for time-fractional integrodifferential equations governing viscoelastic nanofluid dynamics

In this paper, a numerical study of space-dependent fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness is investigated. The governing momentum and energy equations are formulated using left and right Riemann–Liouville fractional derivatives. Numerical solutions of the governing fractional differential equations are acquired utilizing finite difference method after approximating the space fractional derivative by shifted Grünwald formulae. The impact of included parameters such as the exponent parameter, fractional parameter, and weight coefficient on the temperature and velocity distributions are demonstrated graphically. The obtained numerical results indicate that for a larger fractional parameter temperature and velocity boundary layers are thicker. The velocity and temperature boundary layers are thicker at a larger y while thinner at a smaller y for higher values of weight coefficient. The larger values of the exponent parameter enhance the thickness of velocity boundary layer while the thermal boundary layer is thicker at the smaller y and thinner at the larger y.

The flow and heat transfer for an electrically conducting fluid with a porous substrate and a flat plate under the influence of magnetic field is considered. The magnetic field is assumed to be uniform and also along normal to the surface. The momentum and energy equations are transformed to ordinary differential equations by using suitable similarity transformation and are solved by standard techniques. But the energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. Numerical results are presented through graphs with various values of magnetic parameter for both velocity and thermal boundary layers along with Nusselt number and for various values of Prandtl number and Eckert number in thermal boundary layer.

DNS, LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

Laminar flow and heat transfer near rotating axisymmetric surface

Direct numerical simulation of the compression stroke under engine-relevant conditions: Evolution of the velocity and thermal boundary layers

Numerical modeling of fractional viscoelastic non-Newtonian fluids over a backward facing step – Buoyancy driven flow and heat transfer

A compressible viscous two-phase flow of SF6 and Ar with condensation in a supersonic nozzle is calculated. The flow field is solved with a 3rd-order MUSCL type TVD scheme. The calculation of condensate mass fraction and nucleation rate was based on Becker-Doring's condensation theory. The development of velocity and thermal boundary layer is discussed in detail from the point of view of the interaction between the boundary layer and condensation. Distribution of pressure along the nozzle axis obtained from the numerical calculation is in good accordance with the experimental one in the case of the stagnation pressure region from 20 kPa to 100 kPa. It was found from the result that the condensation takes place in a limited region under relatively high stagnation pressure, which spreads downstream as the stagnation pressure decreases. The temperature and velocity gradients in the boundary layer increase due to the latent heat release of condensation. Consequently, development of the velocity and thermal boundary layers was suppressed by the condensation.

This piece of work provides an in‐depth analysis of magnetohydrodynamics (MHD) fluid flow and heat transport near a continuously moving vertical plate in the presence of nonlinear thermal radiation with convective boundary condition. A nonlinear dependence of thermal radiation on temperature enhances thermal transport, while convective boundary conditions govern heat transfer at the plate surface. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) through the application of a similarity transformation. To numerically solve these ODEs, we have used bvp4c method in MATLAB. The influences of dimensionless parameters on heat transfer and fluid flow are presented using tables and graphs. The key novelty of this study lies in analyzing the impact of nonlinear thermal radiation on MHD flow over a constantly moving vertical plate using the bvp4c method. When the fluid flows in the positive x‐direction and the plate moves in the opposite direction, the coefficient of skin friction decreases. Moreover, when the direction of the fluid and the plate is the same, both the velocity and the temperature profiles increase with greater nonlinear thermal radiation. Near the wall, the temperature gradient decreases as nonlinear thermal radiation intensifies, while it increases in the free stream. The thickness of the thermal boundary layer decreases, while the thickness of the velocity boundary layer increases with increasing magnetic parameter. Similarly, when the Grashof number increases, the velocity boundary layer becomes thicker, while the thermal boundary layer tends to become thinner. However, when the Prandtl number increases, the thermal boundary layer becomes thicker, whereas the velocity boundary layer tends to become thinner. Practically, these findings aid in optimizing heat transfer in engineering applications such as cooling systems, heat exchangers, aerospace thermal protection, and biomedical devices.

Thermally developed unsteady viscoelastic micropolar nanofluid with modified heat/mass fluxes: A generalized model

Dynamic heat flux analysis in a high-pressure turbine

In this article, the fully developed steady state flow of an incompressible fluid pertained to as viscoelastic nanofluid model with radiation effects through a penetrable plate is studied. Continuity, momentum and energy equations are elaborated to comprehend the nature of the fluid flow. By using similarity transformations, the solution of arising governing equations is obtained numerically with the assistance of a shooting technique. Furthermore, the consequences of different parameters, that is, Brownian motion parameter, Weissenberg number, thermophoresis parameter, permeability parameter, non-Newtonian parameter and radiation parameter on concentration, velocity and temperature fields, are canvassed with the help of graphs. The effects of Pr and [Formula: see text] on Nusselt number and [Formula: see text] and [Formula: see text] on Sherwood number are also discussed with the assistance of graphs and tables for different values of dimensionless parameters.

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh numberRavarying from 109to 1010and the Prandtl numberPrfixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυfollows the classical Blasius-like laminar boundary layer in the present range ofRa, and it scales with the Reynolds numberReas δυ/H= 0.64Re−0.50±0.03(whereHis the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar forRa< 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent atRa~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend onRaand varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw~Re1.55, the viscous sublayer δw~Re−0.91, the friction velocityuτ~Re0.80, and the skin-friction coefficientcf~Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that ofcf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (atz+=z/δw≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

An approximate solution is obtained for the heat transfer to an incompressible turbulent boundary layer with arbitrary freestream-velocity and surface-temperature distributions. The analysis is based on the simultaneous solution of the boundarylayer momentum and energy integral equations and employs several simplifying assumptions, the most important of which is the approximation that the boundary-layer velocity and totaltemperature profiles and the skin-friction coefficient are independent of pressure gradient. Solutions are given for twodimensional and axisymmetric flows. Although the flow in supersonic nozzles is not incompressible, an adaptation of the aforementioned result, termed the quasiincompressible solution, is suggested for calculating the heat transfer to such nozzles. In order to estimate rapidly the maximum rate of heat transfer which occurs near the throat of a supersonic nozzle, a throat approximation is developed which involves only the nozzle supply conditions, throat opening, and throat radius of curvature. The application of these solutions to a sample nozzle gave the following results using the quasi-incompressible analysis: (1) The heat-transfer coefficients based on solution of both the momentum and energy equations were between 0 and 15 per cent lower than the values based on a solution of the momentum equation alone, and (2) the heat-transfer coefficients that included the effects of variable wall temperature were between 0 and 15 per cent lower than the values obtained assuming constant wall temperature. The throat-approximation, heat-transfer coefficients were within 10 per cent of the corresponding quasiincompressible values.

A study of the velocity and thermal boundary layers on a semi-infinite inclined plate with temperature oscillations is presented in this work. The non-linear, coupled parabolic integro-partial differential equations governing flow and heat transfer have been solved numerically using an implicit finite difference scheme of Crank-Nicolson type. The numerical values for the flow field, temperature, shearing stress, and heat transfer coefficients are presented in a graphical form. It is observed that the velocity and temperature profiles decrease as the frequency parameter increases.

Three-dimensional numerical investigation on flow and heat transfer characteristics and multi-objective optimization of interconnected microchannels