Dimensionless Temperature Research Articles

Method for calculation of ground temperature in scenario involving multiple ground heat exchangers considering groundwater advection

The calculation of the ground temperature considering groundwater advection is one of the most noteworthy challenges for the simulation and design of a shallow geothermal system. This paper proposes a new method to calculate the temperature considering the groundwater advection in a scenario involving multiple ground heat exchangers and the time-variable heat flux condition. The superposition principle of the moving infinite cylindrical source solution and the moving infinite line source solution was applied in combination. Furthermore, a regression analysis was performed for various numerical calculation results obtained using a moving infinite cylindrical source model, and a simple and fast calculation solution for the problem was established. The proposed method demonstrated a maximum error of 0.0879 for the dimensionless temperature compared with the numerical calculation result.

Features of Cattaneo‐Christov heat flux model for Stagnation point flow of a Jeffrey fluid impinging over a stretching sheet: A numerical study

AbstractThe present work focuses on a two‐dimensional steady incompressible stagnation point flow of a Jeffery fluid over a stretching sheet. The Cattaneo‐Christov heat flux model is incorporated into this study. Simulation is conducted via the Runge‐Kutta fourth‐order cum shooting method for the transformed system of nonlinear equations. The influence of the governing parameters on the dimensionless velocity, temperature, skin friction, streamlines, and isotherms is incorporated. A significant outcome of the current investigation is that an increase in the relaxation time parameter uplifts temperature; however, a gradual decrease is observed in the velocity field. Another important outcome of the present analysis is that the momentum boundary layer augments due to an increase in the Deborah number; however, a decrease is observed in the temperature. Furthermore, it is also observed that the skin friction coefficient escalates with an increase in the relaxation time parameter for the assisting flow, but a reverse trend is observed for the opposing flow.

Similarity Solution and Numerical Analysis of the Steady Nanofluid Layer Induced by Gyrotactic Microorganisms Containing Wall Temperature Variations

The problem of free convective steady boundary layer flows over a solid horizontal flat plate nested in a porous medium filled with a nanofluid containing gyrotactic microorganisms is considered. The exponent of the temperature, the nanoparticle volume fraction and the density of motile microorganisms are introduced to make the quantities dimensionless. The impacts of the considered exponent and bioconvection parameters on the dimensionless temperature, velocity, nanoparticle concentration and density of motile microorganisms along with Nusselt, Sherwood and motile microorganism numbers are tabulated and shown graphically. For a regular fluid and also for the isothermal case, the results are compared with the existing data and excellent compatibility is found.

Mixed convection of single-walled carbon nanotubes in a triangular cavity containing a pentagonal impediment

Mixed convection of nanofluid (a homogeneous mixture of water and single-walled carbon nanotubes) is investigated numerically in a triangular cavity containing an adiabatic pentagonal obstacle close to the top surface. Analytical models are employed for effective thermophysical properties of nanofluid regarding carbon nanotubes and water. The top wall of the cavity is kept at a higher temperature, while the inclined sidewalls are kept at a lower temperature. A constant magnetic field of intensity B0 is introduced in the momentum equation. The effects of radiation and viscous heating on heat transfer are neglected. The impacts of Richardson number on the dimensionless velocity and temperature are presented graphically in terms of streamlines and isotherms. The Galerkin finite element method with a penalty function is employed to obtain the solution of dimensionless partial differential equations. The numerical results are examined for governing parameters, including volume fraction of carbon nanotubes, Richardson, and Hartmann numbers. It is concluded that the Nusselt number increases with increasing the governing parameters in the presence of an adiabatic pentagonal obstacle.

Computation of spatio-temporal temperatures in simple bodies with thermal radiation cooling by means of the numerical method of lines (NMOL)

Abstract The objective of the present study is to examine an approximate numerical solution of unsteady heat conduction in simple bodies (wall, cylinder and sphere) with thermal radiation cooling to a nearby sink environment. The finite difference method to be employed is the N umerical M ethod O f L ines (NMOL), instead of the traditional finite difference methods. One component of NMOL discretizes the spatial derivatives of first and second order in the one–dimensional heat conduction equation using two-point and three-point central finite-difference approximations; both involve truncation errors of second order. This step generates an adjoint system of n ordinary differential equations of first order, which consists in n−1 ordinary differential equations of first order at the interior lines and one nonlinear ordinary differential equation of first order at the surface line. Another component of NMOL deals with the numerical solution of the adjoint system of n ordinary differential equations of first order along with the initial condition with the potent fourth order Runge-Kutta algorithm. The two controlling parameters are the radiation-conduction parameter NRC and the dimensionless sink temperature ϕs. The numerically-computed temperature distributions are channeled through the center, surface and mean temperature distributions for suitable combinations of NRC and ϕs.

Investigation of the impact of the reactants temperature and equivalence ratio on the outlet mixture temperature, velocity and mole fraction for the combustion of the carbon monoxide and nitrous

In the present study, a numerical code is used for three-dimensional simulation of non-premixed form of the combustion of nitrous-carbon monoxide mixture. This code includes standard K-ε as turbulent model and Probability Density Function (PDF) as thermo-chemistry approach. Ten species i.e. nitrous, carbon monoxide, carbon dioxide, nitrogen, nitrogen monoxide, atomic oxygen, oxygen, ozone, cyanate and atomic carbon are assumed contributing in this reaction. For the validation of model, experimental measurement of previous studies are applied. The influence of equivalence ratio and inlet gases temperature, on outlet mixture velocity, temperature and outlet species mole fraction are obtained in the form of charts for wide ranges, which was not clearly obtained in previous works. These charts are useful for designer of these systems. Results indicate, when Ø ≥ 0.15 N2O is decomposed completely and the maximum mole fractions for O2(approximately 0.27), N2 (approximately 0.77) and O3 (depending on the temperature) are obtained. Furthermore, it was found the mole fraction of the outlet carbon dioxide and dimensionless temperature of the outlet mixture are maximum at equivalence ratio equal to unity and if the temperature of the inlet gases is kept constant and the equivalence ratio reduces, the outlet carbon monoxide mole fraction decreases.

Generalized Non-dimensional Wind and Temperature Gradients in the Surface Layer

We propose a single generalized function for dimensionless wind and temperature gradients in stable and unstable conditions based on Monin–Obukhov similarity theory. The proposed function may be matched with the currently accepted universal functions for the dimensionless wind-speed and temperature gradients using the empirical coefficients a and b to yield differences within ± 14% for both wind and temperature gradients in the interval of $$-2$$ < z/L < 0.5 (z is height and L is the Obukhov length). In neutral conditions, wind and temperature profiles are the same as the standard log-law profile. Under unstable conditions, the differences are smaller than 1.5%; conversely, under stable conditions, the differences reach up to $$-~5.2$$%. The coefficients a and b are analyzed here to evaluate the limits of this proposed semi-empirical function and possible physical characteristics are discussed. Although we use the same theoretical assumptions and limitations of Monin–Obukhov similarity theory in the surface layer, the proposed function has the flexibility of adjusting the wind and temperature gradients for specific sites using the empirical coefficients a and b within the range 0–1, with stable and unstable conditions able to be described by a single general function.

Curing Kinetics and Thermal Stability of Epoxy Composites Containing Newly Obtained Nano-Scale Aluminum Hypophosphite (AlPO2).

For the first time, nano-scale aluminum hypophosphite (AlPO2) was simply obtained in a two-step milling process and applied in preparation of epoxy nanocomposites varying concentration (0.1, 0.3, and 0.5 wt.% based on resin weight). Studying the cure kinetics and thermal stability of these nanocomposites would pave the way toward the design of high-performance nanocomposites for special applications. Scanning electron microscopy (SEM) and transmittance electron microscopy (TEM) revealed AlPO2 particles having domains less than 60 nm with high potential for agglomeration. Excellent (at heating rate of 5 °C/min) and Good (at heating rates of 10, 15 and 20 °C/min) cure states were detected for nanocomposites under nonisothermal differential scanning calorimetry (DSC). While the dimensionless curing temperature interval (ΔT*) was almost equal for epoxy/AlPO2 nanocomposites, dimensionless heat release (ΔH*) changed by densification of polymeric network. Quantitative cure analysis based on isoconversional Friedman and Kissinger methods gave rise to the kinetic parameters such as activation energy and the order of reaction as well as frequency factor. Variation of glass transition temperature (Tg) was monitored to explain the molecular interaction in the system, where Tg increased from 73.2 °C for neat epoxy to just 79.5 °C for the system containing 0.1 wt.% AlPO2. Moreover, thermogravimetric analysis (TGA) showed that nanocomposites were thermally stable.

Fluid-structure interaction of a hot flexible thin plate inside an enclosure

This study aims to assess the natural convection heat transfer in a square cavity wherein the buoyancy-induced flow is generated by a thin flexible heater-plate inside the cavity. The vertical walls of the cavity are cold and the horizontal walls are adiabatic. The thin hot plate is assumed to be isothermal and fixed at an alterable point in the middle of the cavity with different inclination angles. To analysis the fluid-structure interaction (FSI), the finite element method along with the Arbitrary Lagrangian-Eulerian (ALE) technique is employed. Isotherms and streamlines, as well as the average Nusselt number, the dimensionless temperature in the cavity, and the maximum applied stress on the flexible plate, are studied. The results are presented as a function of Rayleigh number, Prandtl number, inclination angle, and different positions of the fixed point. The outcomes indicate the importance of the inclination angle and the position of the fixed point of the hot plate. The plate experiences significantly large values of stress when it is mounted horizontally. In the case of a plate fixed at its top, the highest stress occurs with an inclination angle of 40°. In contrast, the lowest stress is associated with the plate when it is positioned vertically.

Performance of a liquid cooling‐based battery thermal management system with a composite phase change material

This article reports a recent study on a liquid cooling-based battery thermal management system (BTMS) with a composite phase change material (CPCM). Both copper foam and expanded graphite were considered as the structural materials for the CPCM. The thermal behaviour of a lithium-ion battery was experimental investigated first under different charge/discharge rates. A two-dimensional model was then developed to examine the performance of the BTMS. For the copper foam-based CPCM modelling, an enthalpy-porosity approach was applied. The numerical modelling aimed to study the impacts of CPCM types and inlet velocity of heat transfer fluid on both the maximum battery temperature and temperature distribution under different current rates. Dimensional analyses of the results were performed, leading to the establishment of relationships of the Nusselt numbers and dimensionless temperature against the Fourier and Stefan numbers.

Non-Linear Radiation, Chemical Reaction, and Soret/Dufour Effects on Magnetohydrodynamic Natural Convection About a Permeable Horizontal Circular Cylinder in Non-Darcy Porous Media With Heat Source/Sink

Abstract In this paper, the nonlinear radiation, chemical reaction, and Soret/Dufour effects on magnetohydrodynamic (MHD) natural convection about a permeable horizontal circular cylinder in non-Darcy porous media with heat source/sink are numerically analyzed. The surface of the horizontal circular cylinder is subjected to uniform wall temperature and uniform wall concentration (UWT/UWC). The governing equations are transformed into dimensionless, non-similar forms using suitable non-dimensional variables and then solved using Keller box method (KBM). Comparisons with previously published work are performed, and the results are found to be in an excellent agreement. Numerical data of the dimensionless temperature profile, the dimensionless concentration profile, the Nusselt number, and the Sherwood number are presented in graphic and tabular forms for the main parameters. The physical aspects of the problem are discussed in detail. The Nusselt number increases with increasing the Soret parameter, radiation parameter, and surface temperature ratio. Increasing the Dufour parameter, radiation parameter, surface temperature ratio, coefficient of space-dependent internal heat generation/absorption, and dimensionless chemical reaction parameter enhances the Sherwood number.

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article, three-dimensional mixed convection flow over an exponentially stretching sheet is investigated. Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity. Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations. Resulting nonlinear ordinary differential equations are solved numerically employing the Runge–Kutta shooting method. In order to check the accuracy of the method, these equations are also solved using bvp4c built-in routine in Matlab. Both solutions are in excellent agreement. The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs. The novelty of this analysis is the self-similar solution of the three-dimensional boundary layer flow in the presence of mixed convection, viscous dissipation and variable thermal conductivity.

Analysis of a Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

Abstract In this article, the differential transform method (DTM) is used to solve the nonlinear boundary value problems describing heat transfer in continuously moving fins undergoing convective-radiative heat dissipation. The thermal conductivity is variable and temperature dependent. The surface of the moving fin is assumed to be gray with a constant emissivity ɛ. The flow in the surrounding medium provides a constant heat transfer coefficient h over the entire surface of the moving fins. The effects of some physical parameters such as the Peclet number, Pe, thermal conductivity parameter, β, convection-conduction parameter, N c , radiation-conduction parameter, N r , and dimensionless convection-radiation sink temperature, θ a , on the temperature distribution are illustrated and explained.

Quasi-1D model for exhaust gas and pipe with convective and temperature dependent emissivity based radiative heat losses

Knowledge of accurate exhaust gas and pipe temperatures are critical for efficient design of automotive underbody components and exhaust systems. Prediction of these temperatures requires precise evaluation of the flow, and radiative and convective heat transfer rates inside and around the pipe. In this work, a quasi one-dimensional (quasi-1D) thermal framework is developed by modeling the energy balance for the exhaust gas and the pipe wall, accounting for both forced convection and radiation heat transfer, and effects of temperature dependent emissivity. The dimensionless governing equations for the quasi-1D model are solved iteratively at steady state using finite difference. The flow inside the pipe is assumed to be hydrodynamically fully developed and thermally developing, while that outside is assumed to be simultaneously developing. The predicted Nusselt numbers as well as gas and pipe temperatures under both laminar and turbulent internal or external flows are validated using conjugate computational fluid dynamics (CFD) simulations carried out using OpenFOAM and in conjunction with experimental or theoretical data available in literature. The convective heat transfer coefficients on the inner or outer pipe walls required to close the quasi-1D formulation are evaluated from skin-friction correlations developed from separate CFD simulations carried out in this work and by applying the Chilton-Colburn analogy, or from literature. It is found that surface radiation on the outer wall plays a critical role in the overall heat transfer characteristics of the exhaust pipe and can result in the reduction of dimensionless pipe temperatures by over 40% for a variation in emissivity from 0 to 1. It is also found that the influence of temperature dependence of emissivity can be important in cases where surface radiation is the dominating mode of heat loss from the pipe. A reduction in the dimensionless pipe temperature of up to 12% was found for an increase in the temperature coefficient of emissivity from 0 to 1, for the representative cases studied.

Analytical study for MHD flow of Williamson nanofluid with the effects of variable thickness, nonlinear thermal radiation and improved Fourier’s and Fick’s Laws

The key aim of the present work is to analyze the magnetohydrodynamic 2D flow of Williamson type nanofluid. Heat and mass transfer impacts are carried out in the manifestation of nonlinear thermal radiation, Cattaneo–Christov heat and mass flux models and varying thicker surface. By applying the appropriate similarity transformations, the mathematical equations of velocity, temperature and volume fraction transform to NODEs. An analytical scheme is pragmatic to estimate the convergence solutions in terms of power series. The dimensionless velocity profile, temperature profile and nanoparticle volume fraction with the administrative physical aspects are depicted through graphs. It is evidently ostensible that the dimensionless velocity declines for the augmented index parameter and wall thickness while cumulative values of M and $$ \beta $$ , the horizontal fluid velocity decreases. Temperature specie upsurges with rising of Nb, Nt, $$ n,\;\beta ,\;R_{d} ,\theta_{w} $$ and M. Consequently demotes with the higher values of Pr and $$ De_{1} . $$ Nanoparticle volumetric specie escalates with the growing effects of Nt, while it diminishes with Nb, Sc and $$ De_{2} . $$ Comparison is the key procedure for validation our results with the earlier literature.

Mathematical modelling of conjugate laminar and turbulent heat transfer in a cavity: Effect of a vertical glazed wall

A numerical analysis of the laminar and turbulent natural convection combined with surface thermal radiation in a square cavity with a glazed wall is presented. The enclosure is composed of one left vertical isothermal wall, two horizontal adiabatic walls, and one right vertical partially semitransparent wall (clear glass sheet). Different values of the aspect ratio of the right vertical glazed wall (A=0.15,0.25,0.5,0.75,1.0) are analyzed, and the incoming solar irradiation (G) over the glass is varied from 0 to 750 W/m2 at intervals of 150 W/m2. Three different case studies were considered based on the position of the clear glass sheet on the right wall: (a) located at bottom side/Case 1 (C1), (b) located at the middle side/Case 2 (C2), and (c) located at the upper side/Case 3 (C3). The numerical solution was carried out using an in-house code based on the finite volume method. The numerical code was validated against experimental data for the turbulent natural convection problem. A comparison between the predicted and measured dimensionless vertical velocity, temperature profiles and local and average Nusselt numbers are presented, obtaining good agreement. Results show that convective heat transfer increases from about 70 to 250 as the aspect ratio increases from 0.15 to 1.0, for all solar radiation intensities, and all cases of turbulent flow. Also, radiative heat transfer decreases as the aspect ratio and solar radiation increase, which implies that it could become lower than convective heat transfer for some aspect ratio values set. When a laminar flow regime is considered, lower average convective and radiative heat transfer rates are obtained regarding the case of turbulent flow. In general, they are between 2.0<Nuconv<7.5 and 2.0<Nurad<13.5 for all cases under analysis. Finally, a set of correlations for the total Nusselt number were obtained for turbulent conjugate heat transfer.

Experimental study on vertical temperature profile of buoyant window spill plume from intermediate‐scale compartments

SummaryThe correlation between dimensionless temperature and vertical position z were discussed by conducting a series of intermediate‐scale tests performed a 1.35 m (L) × 1.35 m (H) × 1.35 m (W) fire compartment, whose window‐opening size varied from 0.91 m (H) × 0.41 m (W) to 0.91 m (H) × 0.91 m (W) and heat release rate (HRR) differed from 200 to 1000 kW. The effects of fire plume reattaching‐to‐wall behaviors, the varied neutral plane positions, and window‐opening aspect n on Yokoi's correlation is analyzed according to the comparison of theoretical analysis and experimental results. Finally, an attempt to increase the rationality and continuity of Yokoi's plots is conducted. The new correlation consists of two different types of plots regarding the plume region and flame region. The reattaching‐to‐wall behavior of flame region showed a heavy effect on the new correlation plot. Chamber dimension imposes little influence on the new correlation plot.

Unsteady Bioconvection in a Squeezing Flow of a Couple-Stress Fluid Through Horizontal Channel

The bioconvection in an unsteady flow of an incompressible couple-stress fluid consists of microorganisms between two parallel plates is considered. A model containing coupled non-linear system of partial differential equations for the mass, momentum, energy, mass diffusion, and microorganisms is reduced to a set of non-linear ordinary differential equations with the help of suitable transformations. The resulting non-linear ordinary differential equations are linearized using successive linearization method and then Chebyshev collocation method is used to solve resulting system of linearized ordinary differential equations. The comprehensive investigation demonstrating the impacts of various fluid flow governing physical parameters such as the couple-stress parameter, squeezing parameter, the bioconvection Schmidt number, Prandtl numbers, Lewis number and bioconvection Peclet number on the distributions of dimensionless velocity, temperature, concentration and motile microorganism is graphically presented.

Electrothermal transport of third-order fluids regulated by peristaltic pumping.

The study of heat and electroosmotic characteristics in the flow of a third-order fluid regulated by peristaltic pumping is examined by using governing equations, i.e., the continuity equation, momentum equation, energy equation, and concentration equation. The wavelength is considered long compared to its height and a low Reynolds number is assumed. The velocity slip condition is employed. Analytical solutions are performed through the perturbation technique. The expressions for the dimensionless velocity components, temperature, concentration, and heat transfer rate are obtained. Pumping features were computed numerically for discussion of results. Trapping and heat transfer coefficient distributions were also studied graphically. The findings of the present study can be applied to design biomicrofluidic devices like tumor-on-a-chip and organ-on-a-chip.

Performance of heat transfer in MHD mixed convection flow using nanofluids in the presence of viscous dissipation: Local non-similarity solution

In this study, an investigation has been carried out to examine the effects of thermal radiation, heat generation/absorption, viscous dissipation and suction parameter on MHD flow of water-base nanofluid (Ag, Cu, Al2O3, CuO and TiO2). This study also focused on the mixed convective flow of water-base nanofluid due to a vertical permeable plate in the presence of convective boundary condition. Further, heat transfer has been inspected for water-base fluid influenced by heat generation/absorption and viscous dissipation. Moreover, the governing equations are reduced to nonlinear ordinary differential equations via Sparrow–Quack–Boerner local non-similarity method. These nonlinear ODEs are simulated numerically by means of Runge–Kutta–Fehlberg method (RKF-45). The impact of pertinent parameters on the dimensionless velocity, nanofluid temperature, skin friction and local Nusselt number are discussed and displayed. The results match with a special case of formerly available work. The present exploration exhibits that nanoparticle volume fraction increases the velocity and temperature of Cu-water nanofluid. It is also shown that magnetic parameter reduces the heat transfer rate.