Ambient Fluid Temperature Research Articles

Nonsimilar stagnation flow of Williamson fluid over an isothermal linearly stretched sheet

The objective of this work is to analyze the boundary layer flow in the vicinity of a stagnation point on a linearly stretched isothermal flat surface. The ambient fluid temperature is considered different than that of the sheet. The streaming fluid rheological behavior is approximated via the Williamson fluid model. The normalized partial differential equations based on the balances of mass, momentum, and energy are simulated numerically via the symbolic and numeric computing software Maple for two entirely different scenarios. In the first scenario, the outer potential flow velocity dominates the sheet velocity whilst it is the other way round for the second scenario. The plots showing the behaviors of velocity and temperature are presented at various streamwise locations. The skin friction and Nusselt number are also visualized graphically and listed in tabular forms. The analysis reveals that all quantities including velocity and temperature show a strong dependence on the streamwise co-ordinate. In general, velocity distribution and temperature rise with a gradual march along the streamwise direction. The heat transfer coefficient also elevates upon an increase in the streamwise co-ordinate. This contradicts several previously published results on the boundary layer flow of Williamson fluid where no such dependence is seen.

Numerical simulation for thermally stratified Powell–Eyring fluid due to the Riga plate: application of the Cattaneo–Christov theory

The present study demonstrates the behavior of Powell–Eyring fluid flow deformed by a linearly stretchable Riga plate. The analysis of heat characteristics is scrutinized with the thermal stratification phenomenon conducted through generalized Fourier’s law (i.e. the Cattaneo–Christov theory). Heat generation/absorption is assumed to disclose the features of thermal transport phenomena. The temperature of the plate is higher than the ambient fluid temperature. It is noted that the Cattaneo–Christov model is responsible to generate some extra terms of heat absorption or generation in the energy conservation law. Appropriate transformations are implemented to achieve nonlinear governing equations in the form of an ordinary differential equation. Numerical solutions are computed for the governing equations through the Range–Kutta Fehlberg technique. In summary, the modified Hartman number is responsible to grow up velocity distribution while the opposite trend is noted for the variable thickness parameter. Heat transport phenomenon can be minimized by incorporating higher thermal relaxation parameters (i.e. it can be used as a cooling phenomenon).

The unsteady nonlinear convective flow of a nanofluid due to impulsive motion: Triple diffusion and magnetic effects

• The unsteady nonlinear convection due to impulsive motion is investigated. • Governing equations have been transformed using Mangler's transformations. • Quasi-linearization technique is utilized for solution of the problem. • The surface drag coefficient increases with magnetic parameter. • Heat transport rate rises only when the Eckert number is positive. By a semi-similar approach, the paper aims to study the unsteady nonlinear convection due to impulsive motion with triple diffusion and magnetic effects. Since the mainstream has been set into impulsive motion, the fluid motion is unsteady. Simultaneously, the temperature of the surface is abruptly changed from its ambient fluid temperature. The influence of chemical reactions and convective boundary constraints are also considered in this investigation. The nonlinear coupled partial differential equations (PDEs) with appropriate boundary conditions that govern the given problem are transformed into dimensionless equations by using Mangler's transformations. For mathematical computations, the technique of Quasi-linearization and second order implicit finite difference method are utilized, and so obtained results are semi-similar solutions that are discussed with the aid of graphs. The results reveal that for the case of aiding buoyancy, the surface drag coefficient increases about 5% when the nonlinear convection parameter increases from 0 to 3 and about 61% when the magnetic parameter increases from 0 to 0.5. The heat transfer rate enhances about 65% for variation of the magnetic parameter from 0 to 0.3 for a positive Eckert number. The mass transfer rate is pronounced more for linear chemical reaction than the nonlinear chemical reaction for the constructive chemical reaction parameter. It is found at about 7% for Schmidt number 240. The current findings are compared to previously reported literature and are found to be in good agreement.

Integral properties of turbulent natural convection over a vertical flat plate

This paper investigates global integrals of the volumetric, momentum and temperature fluxes for turbulent natural convection over a vertical plate (TNCVP). The global integral of the mean continuity equation gives a relation for the mean wall-normal velocity outside the boundary layer as W∞ = − d(∫0∞Udz)/dx where U is the mean velocity in the streamwise x direction and z is the wall-normal direction. The global integral of the mean momentum equation gives a relation for the specific wall momentum flux as uτ2 = gβ∫0∞(Θ∞ − Θ)dz − d(∫0∞U2dz)/dx where uτ is the friction velocity, g is the gravitational acceleration and β is the thermal expansion coefficient. Θ = Tw − T is the difference between the wall temperature Tw and the fluid temperature, and Θ∞ = Tw − T∞ is the difference between the wall temperature and the ambient fluid temperature. Finally, the global integral of the mean heat equation gives a relation for the wall temperature flux as uτθτ = − W∞Θ∞ − d(∫0∞UΘdz)/dx where θτ is the frictional temperature. Based on the global integrals of the momentum and heat fluxes, we propose an indirect determination of uτ and θτ. Given the extreme challenge in direct measurement of uτ and θτ in wall-bounded turbulent flows, the indirect determination proposed here offers a powerful tool to subsequent experimental studies of TNCVP.

Scaling patch analysis of turbulent planar plume

Proper scaling in turbulent planar plumes is investigated here using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity Uref=Uctr, and a proper temperature scale for the temperature excess is Θref=Tctr−T∞, where Tctr is the plume centerline temperature and T∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is Vref=(dδ/dx)Uctr, where dδ/dx is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is Rvu,ref=UctrVref=(dδ/dx)Uctr2, a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is Rvθ,ref=VrefΘctr, a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri=defgβΘctrδt/(UctrVref)≈1/2, where g is the gravitational acceleration, β is the thermal expansion coefficient, and δt is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

Unsteady heat transfer in non-axisymmetric Homann stagnation-point flows towards a stretching /shrinking sheet

Abstract We have studied the unsteady non-axisymmetric Homann’s stagnation point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet in the presence of time dependent free stream. In a very recent paper Mahapatra and Sidui (2017) show a modification of Homann’s stagnation point flow over a rigid plate. Now if the plate is not rigid but linearly stretched as well as shrunk with velocities in x and y -directions, then there is a new family of asymmetric viscous stagnation-point flows depending on the unsteadiness parameter δ ( = σ ∕ | c | ) and the ratios of shear to the rate of linear stretching/shrinking of the sheet γ ( = b ∕ | c | ) , the strain-rate to the rate of linear stretching/shrinking of the sheet λ ( = a ∕ | c | ) in the range − ∞ γ , λ ∞ . Here a and b are the strain rate and shear rate of the stagnation-point flow respectively, σ is a positive constant whose dimension is t i m e − 1 and c is the rate of linear stretching/shrinking of the sheet along x - and y -axes at unit distance from origin when time, t = 0 . We have also studied the heat transfer in the flow. The temperature of the sheet is assumed to be higher than the ambient fluid temperature. The governing momentum equations are solved numerically using fourth order Runge–Kutta method with shooting technique. The effect of the various parameters on wall shear stress parameters, dimensionless velocities, displacement thicknesses and temperature distributions are analysed. A good agreement is found when we compare our numerical results of wall shear stress, displacement thickness and temperature distributions with their corresponding asymptotic value behaviours. For the flow past a shrinking sheet dual solutions are found to exist. Here we have made a stability analysis in the case of non-unique solutions to identify the stable solution.

Unsteady heat transfer in non-axisymmetric Homann stagnation-point flows

An analysis is carried out to study the unsteady non-axisymmetric Homann’s stagnation-point flow and heat transfer of an incompressible viscous fluid over a rigid plate in the presence of time-dependent free stream. The temperature of the plate is assumed to be higher than the ambient fluid temperature. Using similarity variables, the governing partial differential equations are transformed into nonlinear ordinary differential equations. These equations are then solved numerically using fourth-order Runge–Kutta method with shooting technique. The effects of the shear-to-strain rate ratio parameter \(\gamma \) (\(\gamma =b/a\) where a and b are the strain rate and shear rate of the stagnation-point flow, respectively) and the unsteadiness parameter \(\lambda \) on wall shear stress parameters, dimensionless velocities, rate of heat transfer at the wall and dimensionless temperature are analysed. It is found that the large-\(\gamma \) asymptotes do not depend on the parameter \(\lambda \).

Application of Collocation Spectral Method for Irregular Convective–Radiative Fins with Temperature-Dependent Internal Heat Generation and Thermal Properties

A collocation spectral method (CSM) is developed to solve the fin heat transfer in triangular, trapezoidal, exponential, concave parabolic, and convex geometries. In the thermal process of fin heat transfer, fin dissipates heat to environment by convection and radiation; internal heat generation, thermal conductivity, heat transfer coefficient, and surface emissivity are functions of temperature; ambient fluid temperature and radiative sink temperature are considered to be nonzero. The temperature in the fin is approximated by Chebyshev polynomials and spectral collocation points. Thus, the differential form of energy equation is transformed into the matrix form of algebraic equation. In order to test efficiency and accuracy of the developed method, five types of convective–radiative fins are examined. Results obtained by the CSM are assessed by comparing available results in references. These comparisons indicate that the CSM can be recommended as a good option to simulate and predict thermal performance of the convective–radiative fins.

The Effect of Radiofrequency Energy on Ambient Fluid Temperature in an Enclosed Compartment: An in Vitro Model of the Subacromial Space

Background Radiofrequency (RF) devices are widely used in arthroscopic shoulder surgery for tissue ablation and other effects. They have heating effect during tissue application. It is known that chondrocyte death occurs with temperatures above 45 °C. The present study aimed to investigate the effect of various factors on the heating effect of RF probes in a controlled in vitro model. Methods A perspex model was used, in which volume, flow, outflow position, duration of RF probe use and inflow temperature could be closely controlled. Results Temperature rises in the bathing fluid sufficient to cause cell death were seen. The temperature rise was most noticeable when there was no fluid flow through the compartment, at smaller fluid volumes, if the fluid inflow temperature is elevated, and if the outflow is distant from the RF device. Of note, 30 seconds of use in a volume of 20 mL with no flow led to temperatures above 50 °C. Discussion Most of the factors affecting temperature rises using RF devices are directly under the surgeon's control. Further work is needed in this area to define the potential clinical effects of the use of these devices.

Buoyancy‐driven flow of a viscous incompressible fluid in an open‐ended rectangular cavity with permeable horizontal surfaces

PurposeThe purpose of this paper is to consider the unsteady natural convection flow of a viscous incompressible fluid, which is induced by differential heating on the solid vertical boundary of an open‐ended rectangular cavity with the two horizontal surfaces which are permeable and maintained at the temperature of ambient fluid. Attention is focused on how the flow and heat transfer is affected by variations of the buoyancy force, as well as by the permeability of the surfaces.Design/methodology/approachAn upwind finite‐difference method in conjunction with a successive over‐relaxation iteration technique is used to solve the governing boundary layer equations. To do this, the first and second derivatives were approximated by central differences and were used in the vorticity, energy and Poisson equations. To preserve the conservative property, the finite‐difference forms of the vorticity and energy equations were written in conservative form for the convective terms.FindingsLocal rate of heat transfer from the heated surface increases owing to an increase in the value of Ra. In the region near the bottom surface, the heat transfer from the left vertical surface decreases, but that increases in the region near the upper surface. Due to blowing of fluid through the permeable surfaces, the rate of heat transfer is higher than the situation where fluid is being withdrawn. This difference was found to be higher in the case of larger value of Ra.Research limitations/implicationsThe analysis is valid for unsteady, two‐dimensional natural convection flow of a viscous fluid filled in an open‐ended rectangular enclosure. An extension to three‐dimensional flow case is left for future work.Practical implicationsThe method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes.Originality/valueThe results of this study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures.

Temperature corrections for constant temperature and constant current hot-wire anemometers

Changes in the ambient fluid temperature change the calibration curve for velocity measurements taken using hot-wire anemometry. New correction methods are proposed to account for the effects of relatively large temperature changes in the heat-transfer process and on the fluid properties. The corrections do not assume any particular heat-transfer correlation, and they do not require multiple calibrations over a range of temperatures. The corrections are derived for the constant temperature and constant current modes of operation.

Transient conjugated heat transfer in thick walled pipes with convective boundary conditions

Transient conjugated heat transfer for laminar flow in the thermal entrance region of pipes is investigated by considering two dimensional wall and axial fluid conduction. The problem is handled for an initially isothermal, infinitely long, thick-walled and two-regional pipe for which the upstream region is insulated and solved numerically by a finite difference method for hydrodynamically developed flow with a step change in the ambient fluid temperature in the heated downstream region. A parametric study is done to analyse the effects of five defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and the Biot number.

Constant voltage anemometer operated hot wire at subsonic speeds over wide overheats in unsteady flows

The constant voltage anemometer (CVA) was used to calibrate a hot wire over a wide overheat range. Instead of the output voltage (E) of the anemometer which is normally used, at each test point a quantity represented by “pdr” equal to the ratio of power dissipated in the hot wire (Pw) and the associated difference in the heated resistance of the hot wire (Rw) and its resistance (Ra) at the ambient fluid temperature is calculated. It is shown that the calibration curves so obtained with pdr=Pw/(Rw−Ra) as the output variable instead of E can be represented by a single calibration equation covering the wide overheat range. Overheat variation is equivalent to allowing an ambient temperature change of the fluid at a given setting. It demonstrates that this approach can be used to cover measurements using the hot wire with fluid temperature drifts without using a second hot wire for temperature corrections and without any temperature calibration. The calibration data was then applied to measure the unsteady flow in the near orifice region of synthetic jets with very good results. The measurements confirm the computational predictions that show that although there is flow reversal, over a cycle of oscillation, the synthetic jet actuator spends most of the cycle ejecting rather than ingesting fluid.

The effect of steady streamwise surface temperature variations on vertical free convection

We examine how the steady free convective boundary-layer flow induced by a vertical heated surface is affected by the presence of sinusoidal surface temperature variations about a constant mean value which is above the ambient fluid temperature. The problem is studied using fully numerical techniques and an asymptotic analysis which is valid at large distances from the leading edge. The surface rate of heat transfer eventually alternates in sign with distance from the leading edge, but no separation occurs unless the amplitude of the thermal modulation is sufficiently high. The agreement between the numerical results and a two-term asymptotic analysis is excellent.

Unsteady mixed convection boundary-layer flow on a vertical surface in a porous medium

An analysis is made of the unsteady mixed convection from a vertical flat plate embedded in a fluid-saturated porous medium. For time t < 0 a uniform free stream velocity U exists parallel to the plate surface and the temperature T ∞ throughout the porous medium is uniform. Then at time t = 0 the temperature on the surface is instantaneously changed from the ambient fluid temperature T ∞ to T w . At small times the transport effects are confined within a narrow layer adjacent to the plate. As this inner boundary layer evolves, a steady boundary layer is approached but far from the plate the ambient conditions remain. A complete analysis is made of the governing equations at t = 0, the steady state at large times and a series solution valid at small times is derived. A numerical solution of the full boundary-layer equations is then obtained for the whole transient from t = 0 to the steady state. Results are presented to illustrate the occurrence of transients when the buoyancy parameter is positive (buoyancy and free stream forces in the same direction) and negative (buoyancy and free stream forces in opposing directions) . The uniqueness of this problem lies in the fact that we have been able to match significantly different profiles at the time when the forward integration approach breaks down and the solution at large times and establish a smooth evolution around the transition time.

Solution numérique généralisée du problème de la conduction thermique dans les solides de diverse configuration lors d'un refroidissement convectif

A numerical solution has been obtained for a very general thermophysical problem including a large number of heat conduction cases. An inhomogeneous partial differential equation of thermal conduction has been integrated by means of the finite-difference method. Inhomogeneous third-kind boundary conditions and an initial condition expressing a spatial unevenness of the temperature are applied to different geometries of the body. A mathematical model has been developed for determining the unsteady-state temperature field and the duration of the cooling (or heating) of solids of different configurations by using a universal approach. The three classical one- dimensional bodies (infinite slab, infinite cylinder and sphere) are studied, as well as various complicated multidimensional solids by using a rational approach for reducing the multidimensional problem to a one- dimensional one. (As has been accepted in heat-transfer theory, an m-dimensional solid ( m = 1,2,3) means a body with an m-dimensional temperature field.) The initial temperature distribution and the ambient fluid temperature have been considered as arbitrary functions of the variable of space and time, respectively. Moreover, the volumetric specific power of the internal heat source is an arbitrary function of the spatial coordinate and time. An effective algorithm intended for numerical simulation software has been proposed. The model can also be applied to other physical transfer processes having mathematical descriptions analogous to that of heat conduction (molecular diffusion, etc.).

Free convection flow over an uniform-heat-flux surface with temperature-dependent viscosity

The role of temperature-dependent viscosity is studied in laminar free convection flow adjacent to a vertical surface with uniform heat flux. The resulting non-similar equations are solved by using a suitable variable transformation and employing an implicit finite difference method. It is shown that the constant viscosity results evaluated at the ambient fluid temperature underestimate the Nusselt number and overestimate the drag coefficient. The heat transfer predictions for large values of the viscosity parameter may be two times the constant viscosity parameter prediction. The present analysis is in good agreement with the corresponding correlation of previous experimental investigation.

Empirical expression for hot wire with corrections for temperature drift

In using the empirical expression of King's law,E 2 =E 0 2 + BU″, to correlate the data obtained from constant temperature hot wire in real low turbulence flow, the value of exponentn can assume widely differing values and is never a universal constant. Also corrections must be employed for varying ambient fluid temperature from the temperature at which calibration was carried out. This paper discuss the possibility of replacing King's law by another empirical expression,E 2=E 0 2 + BU 0.5 + CU, in which the exponentn will be fixed at a value 0.5 and the termCU is regarded as a correction factor for changing the exponentn in King's law as well as for the effect of ambient temperature drift. The advantages of using the new expression, beside incorporating the required corrections, are reflected on reducing the errors in local sensitivity resulted from using approximated exponent in King's law, and its validity for very low mean velocities.

A NUMERICAL METHOD IN SOLVING A COUPLED THERMOELASTICITY EQUATION AND SOME RESULTS

Abstract This paper discusses a numerical method for solving a coupled dynamical ther-moelasticity problem in a long hollow cylinder. The inner boundary conditions are the traction and the fluid temperature imposed on the inner surface of the cylinder, whereas the outer boundary is subjected to the ambient fluid temperature and is free of traction. This problem is solved by a finite element method in which the spatial and the time variables are discretized by several schemes. The study shows that the central explicit scheme for space discretization combined with a time marching scheme, which incorporates moderate damping, is suitable for this particular problem. Numerical results of the temperature and stress responses due to a modified step or single pulse are presented and discussed. One interesting observation is that, under high rate of stress loading, the coupling in the energy equation could generate temperature variations of significant magnitude.

An Annular Contact Friction and Boundary Lubrication Tester

A simple, inexpensive, easy to use, and very accurate annular contact friction and boundary lubrication tester is described. Data are presented to show excellent reproducibility and extremely low experimental scatter. The system allows the accurate simultaneous measurement of normal load, friction force, ambient fluid temperature, and mean surface contact temperature. Analyses are presented, which are applicable to other testers in addition to the present one, for determining the true mean surface contact temperature from a measured near surface temperature (determined with a thermocouple), and for calculating the viscous drag component of the measured friction (thereby allowing its separation). The tester is particularly well suited for simulating and studying the surface contact phenomena which arise in multiple disc brakes and clutches.