Constant Heat Source Research Articles

Mixed convection and radiation studies on thermally developing laminar flow in a horizontal square channel with variable side heated wall

In this work presents the interaction of mixed convection and surface radiation heat transfer studies on thermally developing laminar airflow in a differentially heated horizontal channel with isothermal vertical walls and adiabatic top and bottom walls. The side heated isothermal wall incorporated a heater, and the opposite wall acts as a constant temperature heat source. The major thermal and geometric parameter includes variable wall temperatures, wall surface emissivity, Reynolds number, heat flux and air chosen as the working medium. Due to the wall surface emissivity of the channel, the internal wall surface radiation will significantly change the rate of total heat transfer inside the channel. Therefore, the current research focuses on the mixed convective and surface radiation heat transfer process happening in laminar flow over a horizontal channel. Radiative heat transfer is determined with the help of experimental results and the use of the numerical scheme. The results presented here show the rate of convection heat transfer and the distribution of surface temperature along the walls inside the channel. The flow configuration the channel inside is pictured by passing smoke at the bottom of the entrance section. The quantitative and qualitative results showed that the emissivity of walls and other thermal and geometric parameters significantly affected the overall heat transfer improvement from the square channel.

Heat-Transfer Enhancement Incorporating Fin-Like Structures Inside Droplet on Hydrophobic Surface

Enhancement of droplet heat transfer on a hydrophobic surface is examined via introducing the fin-like structures inside the droplet without altering the wetting state of the surface. A solution crystallization of polycarbonate surface is carried out and the functionalized silica particles are deposited onto the crystallized surface to create the hydrophobic surface characteristics. The ferrous particles (Fe2O3) are locally spread onto the hydrophobic surface and, later, manipulated by an external magneto-static force generating various configurations of fin-like structures inside the droplet. The droplet with fin-like structures is heated from the hydrophobic surface through introducing a constant temperature heat source. Flow and temperature fields inside the droplet are simulated in line with the experimental conditions. It is found that changing the configuration of the fin-like structures in the droplet modifies significantly the flow and temperature fields inside the droplet. The Bond number remains less than unity for all configurations of the fin-like structures while demonstrating the importance of the Marangoni current over the buoyancy current in the flow field. The presence of the fin-like structures lowers the difference between the fluid bulk and the minimum temperatures inside the droplet and improves considerably the heat transfer rates and the Nusselt number.

Thermal computational analysis of microclimates for optimal crop production in controlled atmosphere

This study aims to perform a thermal computational analysis of the indoor environment with a view to identifying a promising method to improve the level of harvest in a regulated indoor space or modified version of controlled environment agriculture (CEA) space. A modified closed cultivated greenhouse model is considered based on a customary model. The operational environment of the refined CEA space model is simulated in computational fluid dynamics environment. In the study, CEA space is assumed to be heated by a constant heat source from the same path for a limited time. The CEA space has two air inlets on one side and two outlets on the other side. A standard k-epsilon model was implemented in the simulation model to define the turbulent transport phenomena. On the virtual environment, the crop is defined using a porous medium approach that was proposed by Darcy-Forchheimer Law. The results are recorded in the form of temperature, velocity and pressure distribution.

Numerical study of magnetohydrodynamic mixed convective flow in a lid-driven enclosure filled with nanofluid saturated porous medium with center heater

This present numerical study explores the MHD mixed convective flow and heat transfer analysis in a square porous enclosure filled with nanofluid having center thin heater. The left and right walls of the enclosure are maintained at temperature T . The bottom wall is c considered with a constant heat source whereas the remaining part of bottom wall and top wall are kept adiabatic. The finite volume method based on SIMPLE algorithm is used to solve the governing equations in order to investigate the effect of heater length, Hartmann, Richardson, and Darcy numbers on the fluid-flow and heat transfer characteristics inside the enclosure. A set of graphical results are presented in terms of streamlines, isotherms, mid height velocity profiles and average Nusselt numbers. The results reveal that heat transfer rate increases as heater length increases for increasing Darcy and Richardson numbers. Among the two positions of heaters, larger enhancement of heat transfer is obtained for horizontal heater of maximum length. It is observed that, Hartmann number is a good control parameter for heat transfer in fluid-flow through porous medium in enclosure. Moreover, Ag-water nanofluid has greater merit to be used for heat transfer enhancement. This problem may be occurred in designing cooling system for electronic equipment to maximize the efficiency with active and secured operational conditions.

Effect of Richardson Number on Unsteady Mixed Convection in a Square Cavity Partially Heated From Below

Abstract: The objective of the present study is to analyze the laminar mixed convection in a square cavity with a side length L and moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall and all the other horizontal sides of the cavity are considered adiabatic. The numerical method used is based on a finite difference technique where the spatial partial derivatives and boundary conditions of the phenomenon governing equations are discretized using a high order scheme, and time advance is dealt with by the fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative importance of the natural and forced convection, is chosen as the bifurcation parameter. The effect of the Richardson number on the behavior of the fluid flow and the heat transfer has been analyzed. Although the geometry and boundary conditions concerning the velocity and the temperature are symmetrical relative to the vertical axis passing through the center of the cavity, analysis of the results allowed us to detect the existence of symmetric and asymmetric structures of the flow, completely different, depending on the value of the Richardson number.

A Study on AL2O3 – H2O Nano Fluid in the Presence of Constant Heat Source

A Study on AL2O3 – H2O Nano Fluid in the Presence of Constant Heat Source

Integral properties of temperature variance production in a turbulent channel flow with passive scalar transport

This paper investigates the integral properties of the mean temperature dissipation α(∂Θ/∂y)2 and the temperature variance production Pθ=Rvθ(∂Θ/∂y) in fully developed turbulent channel flow, and in particular the effects of Prandtl number Pr=ν/α and Reynolds number Reτ=δuτ/ν (and/or Peclet number Peτ=ReτPr). Here Θ is the mean temperature and Rvθ is the wall-normal turbulent heat flux. y is the wall-normal direction and δ is the channel half-height. ν and α are the fluid viscosity and thermal diffusivity, respectively. uτ is the friction velocity. The main findings of the present work include: (1) Identities are derived from the mean thermal energy equation for the global integral of the mean temperature dissipation and temperature variance production for four heating conditions: constant heat source (CHS), constant wall heat flux (CHF), constant temperature difference (CTD), and constant wall temperature (CTD). Identities for the CHS and CHF conditions are consistent with those derived by Pirozzoli et al. (2016) and Abe and Antonia (2017). The identities are verified using publicly available direct numerical simulation (DNS) data under three heating conditions CHS, CHF, and CTD. (2) The global integral of the mean temperature dissipation is found to depend strongly on the fluid Prandtl number, but it is largely independent of the Reynolds number of the flow. In inner-scaling, this global integral can be approximated as(1/Pr)∫0δ+(∂Θ+/∂y+)2dy+≈9.13Pr1-n where Θ+=Θ/θτ is the inner-scaled mean temperature and θτ is the friction temperature. y+=yuτ/ν is the inner-scaled wall-normal distance. n≈1/2 for Pr≲1 and n≈1/3 for Pr≳1. The strong dependence of (1/Pr)∫0δ+(∂Θ+/∂y+)2dy+ on the Prandtl number is directly rooted in the molecular thermal diffusion sub-layer. (3) The global integral of temperature variance production is found to strongly depend on both Prandtl number and Reynolds number. (3.1) At sufficiently high Reynolds number and Peclet number, the integral of temperature variance production is found to exhibit a logarithmic-like layer similar to that of the mean temperature profile. (3.2) The effect of Prandtl number is mainly caused by the molecular thermal diffusion sub-layer and buffer layer. (3.3) Between the peak wall-normal turbulent heat flux Rvθ location, ymt, and the channel centerline, δ, the integral of temperature variance production increases with Peclet number in a logarithmic-like fashion. (3.4) At low Prandtl number Pr≲1, the integral of temperature variance production is found to be equally partitioned around ymt.

Mean temperature calculations in a turbulent channel flow for air and mercury

Direct numerical simulations (DNSs) in a turbulent channel flow are used to examine the behavior of the turbulent Prandtl number Prt for air (Pr = 0.71) and mercury (Pr = 0.025), with a view to calculating the mean temperature. Constant time-averaged (surface) heat flux (CHF) is used as a thermal boundary condition. For each Pr, four values of the Kármán number (h+ = 180, 395, 640, 1020) are used. Datasets for the constant heating source (CHS) are also examined. For Pr = 0.71, Prt is approximately 1.1 at the wall, varies between 0.9 and 1.1 in the region y+ <100, and is approximated by 0.9–0.3(y/h)2 for y/h > 0.2. The latter relation, with a low Re correction term (i.e. 25/h+), yields an excellent prediction for the mean temperature up to h+ = 2000, whereas a calculation based on Prt = 0.85 underestimates the mean temperature. The calculated maximum wall-normal turbulent heat flux and Nusselt number also agree well with the empirical relations over a wide range of h+. For Pr = 0.025, Prt departs significantly from unity inside the inner region (y/h < 0.2) owing to the strong conductive effect, whilst the magnitude in the outer region (y/h > 0.2) tends to approach that corresponding to Pr = 0.71 as h+ increases due to the increase in the Peclet number. The h+ dependence of Prt in the logarithmic and outer regions is represented adequately by the turbulent Peclet number, i.e. Pet=Prνt/ν. The resulting Prt relation, which is an extension of the expression established by Kays (1994), leads to a correct calculation of the mean temperature not only for mercury (Pr = 0.025) but also for liquid sodium (Pr = 0.01). The mean temperature defect profile exhibits an outer-layer similarity when Pe(≡RebPr) ≥ 2000; the Nusselt number is represented by Nu=4.8+0.0147Pe0.84 reasonably well.

Investigation of Performance Enhancements for Air Brayton/ORC Combined Cycles for Small (~ 2 MWe) Power Systems and a Moderate Heat Source Temperature

Attractive power generation cycles from economic and sustainability considerations are highly efficient and require minimal cooling water. Air Brayton cycles (ABCs) require no cooling water; however, air Brayton combined cycles (ABCCs), which require a minimal water, are more efficient. Several ABCs and ABCCs designed to operate at 5 MWth (~ 2 MWe) were evaluated in temperate environments with a constant temperature heat source at 650°C. An Organic Rankine cycle (ORC) operating with r143a was selected for the bottoming cycle based on previous analyses. Efficiency can increase from 22.0% in the standard ABC to 39.8% in the ABCC. Various performance enhancements were explored, including air inlet cooling, ORC regeneration, and ORC reheat. For the recuperated ABCC with evaporative cooling, the capital cost is < US$17M and the payback period is < 13 years. The major exergy losses are 56.4% spent as work at the ABC turbine and 23.5% lost at the heat source.

Analytical Solution of Exothermic Reactions Model with Constant Heat Source and Porous Medium

The objective of this article is to present a modified analytical scheme, namely homotopy analysis transform method (HATM), to investigate the exothermic reactions model in the presence of constant heat source and porous medium. The heat flow patterns profiles are required for the heat transfer in each type of the thermal insulation. The driving force model to analyze the temperature gradient is studied. The governing equation of the model is restricted into an energy balance equation that gives the value of temperature in conduction state in the presence of constant heat source. By employing the HATM iterative process, we study the behavior of independent variable for the convergence series solution in admissible range. The HATM technique manipulates and controls the series solution, which quickly converges to the exact solution in large admissible domain in efficient way. The solution procedure and explanation show the flexible efficiency of HATM in comparison with other existing methods for handling different kinds of nonlinear differential equations occurring in fluid mechanics.

Numerical study of boiling around wires and influence of active or passive neighbours on vapour film dynamics

In the present study pool boiling around a heated wire has been simulated at atmospheric pressure, considering the wire to be at the constant temperature heat source. Film dynamics, bubble nucleation, growth, merging and pinch off has been observed in with perfectly smooth and uniform horizontal wire without any nucleation site. Effect of increase of the degree of superheat on boiling rate, measured in terms of vapour generation and bubble population has been studied next. Similar studies have been done by inclining the wire at different angles (10°, 45°, 60° and vertical), where axial and azimuthal bubble sliding and more efficient bubble merging have been observed. Bubble size and population distribution have been investigated along the length of the inclined wire to link up with corresponding enhancement in boiling rate. For understanding the effect of active and passive neighbour, horizontal boiling around two-wire system has been studied. First horizontal wires have been stacked at the same vertical plane and different active and passive combination have been simulated. Also boiling from two active wires placed at same horizontal plane has been studied for different wire spacings. For all these cases bubble life cycle has been investigated to understand the role of neighbouring wire. Effect of these neighbouring wires on boiling heat transfer and vapour generation rate has been reported.

Investigations on Material Loads during Grinding by Speckle Photography

The knowledge of the loads occurring during a manufacturing process (e.g., grinding) and of the modifications remaining in the material is used in the concept of process signatures to optimize the manufacturing process and compare it with others (e.g., laser processing). The prerequisite for creating a process signature is that the loads can be characterized during the running process. Due to the rough process conditions, until now there is no in-process technique to measure the loads in the form of displacements and strains in the machined boundary zone. For this reason, the suitability of speckle photography is demonstrated for in-process measurements of material loads in a grinding process without cooling lubricant and the measurement results are compared with finite element method (FEM) simulations. As working hypothesis for the simulation it is assumed, that dry grinding is a purely thermally driven process. Despite the approximation by a purely thermal model with a constant heat source, the measured displacements differ only by a maximum of approximately 20% from the simulations. In particular, the strain measurements in feed speed direction are in good agreement with the simulation and support the thesis, that the dry grinding conditions used here lead to a primarily thermally affecting process.

Analysis of thermal effect around an underground storage cavern with a combined three-dimensional indirect boundary element method

This paper combines a displacement discontinuity method (DDM) for elasticity and an indirect boundary element method (IBEM) for heat conduction to investigate three dimensional thermal displacements and stresses, such as those around an underground storage cavern. The thermal displacements and stresses due to temperature change are expressed in terms of a thermal displacement potential function. For a constant point heat source, we present a derivation for solution of the thermal displacement potential function and the solution is the same as found in literature. A hybrid scheme with semi-analytical integration and a direct numerical integration are used to integrate the thermal displacement potential function due to a constant heat source on a triangular region. The hybrid scheme is used to overcome a difficulty arising with the semi-analytical integration for points whose projection on the integration plane is close to the vertices of the triangle. The combined IBEM with the hybrid integration scheme is first verified with the analytical solution for an infinite elastic body with a spherical cavity. The results agree well, although differences are observed in the early stages of simulation. Then the method is used to simulate the deformation around a liquefied natural gas underground storage cavern.

Calculating the multi-domain transient heat conduction with heat source problem by virtual boundary meshfree Galerkin method

The virtual boundary meshfree Galerkin method (VBMGM) is given to calculate the multi-domain transient heat conduction with heat source problem. The radial basis function interpolation is used to obtain the virtual source function on the virtual boundary, the heat source, the particular solutions of the temperature, and the heat flux in the computational domain. The formula of the proposed method is gotten by the Galerkin method and the control equations of the multi-domain transient heat conduction with heat source. Therefore, there are the advantages of the Galerkin method, the boundary element method, and the meshfree method for the multi-domain transient heat conduction with heat source problem by VBMGM. The numerical meaning of the weighted values are definite for the multi-domain transient heat conduction with heat source problem through VBMGM, such as the partial derivatives of the temperature, the heat flux, the heat source, and the continuity conditions on the public boundary at time. The detailed calculation scheme of VBMGM is deducted for the multi-domain transient heat conduction with heat source problem. Two numerical examples, four subdomains with the time-dependent heat source problem and two subdomains with the constant heat source and mixed boundary condition problem, are computed. The accuracy and the stability of VBMGM for the multi-domain transient heat conduction with heat source problem are verified.

Exploration of geothermal activity using time series analysis of subsurface gases data from Bakreswar hot springs area, eastern India

Geothermal power seems to be a potential source of green energy in India. But these renewable energy resources are still ignored in India even after having a lot of potential sources as seen in more than 300 hot springs scattered throughout different geothermal areas of the country. Many of them could be utilized for power generation using the earth’s internal heat. More hours are needed to explore these geothermal areas using geochemical, geophysical techniques, and statistical analysis to qualitatively estimate power harnessing capabilities and sustainability of the areas for generation of geothermal power. In the present paper, attention has been focused to investigate Bakreswar geothermal field of India by continuous (24*7) and online monitoring of terrestrial gases such as He and radioactive gases (222Rn) in hot spring emanations of the geothermal area for more than 5 years along with discrete measurement of some other geochemical and geophysical parameters. The discrete measures imply that the seven hot spring vents at the study area are linked to the aquifer through different ways covering non-uniform rock assemblies and ascertain the presence of high amount of radioactive minerals at the underneath terrains. Stable activities with a high-out flux of 222Rn and He for a prolonged time period is expected within the reservoir present at the study area as consequence of analysis of the temporal variations and statistical measures of the continuous data sets. Seasonal variation of time series data also recommends that the high amount of radioactive sources present at the crust of the reservoir is able to produce enough quantity of heat irrespective of meteorological effects. The investigation on the power spectra interferes that the geothermal system is still in quite active phase on the influence of tectonic activities. Therefore, the geothermal reservoir present at the Bakreswar geothermal area may be utilized as a constant and continuous heat source for a long time period to run a geothermal power plant.

MHD mixed convective heat transfer in a lid-driven enclosure filled with Ag-water nanofluid with center heater

The MHD mixed convection inside enclosure with center heater is numerically investigated. The oppositely moving side walls of the enclosure are maintained at constant cold temperature whereas a constant heat source is considered in the bottom wall. The remaining parts of the bottom and top walls are kept adiabatic. The finite volume method and SIMPLE algorithm with power-law scheme is used to solve the governing equations. The present study is concerned with effect of pertinent parameters such as length of heater (Γ = 0.25, 0.50 and 0.75), Richardson number (Ri = 0.01, 1.0 and 100), Hartmann number (Ha = 0, 25 and 50) and solid volume fraction of nanoparticles on the fluid flow and heat transfer performance of the enclosure. Results are presented with streamlines, isotherms, velocity profiles and average Nusselt numbers. It is observed that heat transfer rate increases as heater length and Grashof number increases whereas heat transfer decrease is found for increasing magnetic field effect. The enhancement rate in heat transfer by increasing the solid volume fraction of nanoparticles is also obtained.

Melting and viscous dissipation effects on MHD flow over a moving surface with constant heat source

The effects of viscous dissipation and heat source on MHD flow and heat transfer from a warm, electrically conducting fluid to melting surface parallel to a constant free stream are investigated numerically. This model constitutes highly non-linear governing equations which are transformed using similarity variables and are then solved by fourth order Runge–Kutta scheme along with shooting method. The influence of the various interesting parameters on the velocity and temperature fields within the boundary layer is discussed and explained graphically. It is noticed that the melting phenomenon rises the skin friction coefficient and declines the Nusselt number at the solid interface.

Analysis of 2D anisotropic thermoelasticity involving constant volume heat source by directly transformed boundary integral equation

For treating 2D anisotropic thermoelasticity without heat sources, a new volume-to-surface integral transformation has been reported, where no coordinate transformation is involved. In that approach, it is still inevitable to add an extra line integral in the boundary integral equation (BIE) to validate the transformation. Obviously, evaluation of the extra line integral shall require determination of all thermal data along the integration path inside domain. As a result, this process will partially destroy the nature of boundary solution when internal thermal data need to be first determined by the BIE for potential problems. In this paper, this new approach to directly transform the domain integral without coordinate transformation is followed to further treat the problem when uniform hear sources are presented inside domain. Another new treatment is the reformulation of all kernel functions, by which no more extra line integral is needed as in the previous work. A few benchmark examples are presented at last to illustrate the veracity of all formulations derived.

Prediction of temperature distribution over cutting tool with alumina-MWCNT hybrid nanofluid using computational fluid dynamics (CFD) analysis

The accurate measurement of tool tip temperature in turning has been a challenging task for researchers. The present study covers the computational fluid dynamics (CFD) analysis of a single point carbide cutting tool dissipating heat and subjected to streams of nanofluid mist. This study is an attempt to numerically analyze the thermal behavior of the cutting tool having constant temperature heat source at its tip. To determine the optimized experimental value of nodal temperature, machining of AISI 304 steel has been carried out using alumina and alumina-MWCNT hybrid nanofluid mist with minimum quantity lubrication (MQL) system. Furthermore, the conjugate heat transfer (CHT) analysis has been performed to investigate the temperature distribution over the rake and flank face of carbide cutting insert. An overview of the mathematical model, complete geometry, and mesh generation of the carbide cutting tool is presented. Additionally, the CHT simulation results for the mist of alumina and alumina-MWCNT hybrid nanofluids were compared and validated successfully with the experimental data. The maximum variation of 5.79% has been observed between experimental and simulation data, which in turn proves the proposed conjugate heat transfer-based CFD model as an alternative approach to investigate the influence of cooling media on cutting tool under MQL technique.

Direct transformation of the volume integral in the boundary integral equation for treating three-dimensional steady-state anisotropic thermoelasticity involving volume heat source

In the direct formulation of boundary integral equation (BIE), thermal effect is present as extra integral, destroying the advantage of boundary modeling feature. The most appealing approach is to analytically transform the domain integral onto boundary such that the boundary modeling feature can be restored. Recently, the leading author has presented a direct transformation for two-dimensional anisotropic thermoelasticity, not relying on any domain distortion. However, due to mathematical complexity, such direct transformation has not been achieved for three-dimensional generally anisotropic thermoelasticity. Despite the importance of this topic in the BEM, the direct transformation has remained unexplored so far. As the first successful work, this paper presents the complete process to make this direct transformation for treating three-dimensional anisotropic thermoelasticity with implementation in an existing code. Additionally, this work also takes into account the presence of constant volume heat sources.