Effect of viscous dissipation on forced convection for laminar flow through a straight regular polygonal duct using BEM method

2018 ◽  
Vol 28 (1) ◽  
pp. 220-238 ◽  
Author(s):  
Tomasz Janusz Teleszewski ◽  
Slawomir Adam Sorko
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Wall Temperature ◽  
Bulk Temperature ◽  
Brinkman Number ◽  
Content Type ◽  
Flow Through

Purpose The purpose of this paper is to investigate the effect of the viscous dissipation of laminar flow through a straight regular polygonal duct on forced convection with constant axial wall heat flux with constant peripheral wall temperature using the boundary element method (BEM). Design/methodology/approach Both the wall heating case and the wall cooling case are considered. Applying the velocity profile obtained for the duct laminar flow and the energy equation with the viscous dissipation term is solved exactly for the constant wall heat flux using the BEM. The numerical values are obtained by means of a computer program, written by the authors in Fortran. The results of the BEM approach are verified by analytic models. Nusselt numbers are obtained for flows with a different number of sides of a regular polygonal duct and Brinkman numbers. Findings When the difference in temperature between the wall temperature and the fluid bulk temperature changes the sign, then the functions of the Nusselt number with the Brinkman number generated some singularities (BrqLs). For the Brinkman number referring to the total wall linear power, with the increasing value of the number of sides of a regular polygonal duct, BrqLs decreases in the range of 3 ≤ n < ∞. If the BrqL < BrqLs, it is possible to note that, in general, the Nusselt number is higher for cross-sections having a lower value of the number of sides of a regular polygonal duct. For BrqL > BrqLs, this rule is reversed. Originality/value This paper illustrates the effects of viscous dissipation on laminar forced convective flow in regular polygon ducts with a different number n of sides. A compact relationship for the Nusselt number vs the Brinkman number referring to the temperature difference between the wall temperature and the fluid bulk temperature and the Brinkman number, which is based on the total wall linear power, have been proposed.

Fluid-to-Fluid Conjugate Heat Transfer for a Vertical Pipe—Internal Forced Convection and External Natural Convection

1980 ◽  
Vol 102 (3) ◽  
pp. 402-407 ◽  
Author(s):  
E. M. Sparrow ◽  
M. Faghri
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Forced Convection ◽  
Wall Temperature ◽  
Bulk Temperature ◽  
Vertical Pipe ◽  
Uniform Wall Temperature ◽  
Uniform Wall

An analysis is made of the interactive heat transfer problem involving forced convection flow in a vertical pipe and natural convection boundary layer flow external to the pipe. Both flows are laminar. Solutions of the conservation equations for mass, momentum, and energy were obtained numerically by an iterative scheme which deals successively with the internal and external flows. Remarkably rapid convergence was achieved by adopting a procedure whereby information is transferred between the two flows via heat transfer coefficients rather than via the wall or bulk temperatures or the heat flux. Results are presented for the axial distributions of the internal and external Nusselt numbers, of the wall temperature, and of the bulk temperature of the internal flow—all as a function of three parameters. It was found that at any (dimensionless) axial station, the pipe Nusselt number is insensitive to the parameters and is bounded between the values for uniform wall temperature and uniform wall heat flux. On the other hand, the external natural convection Nusselt number is highly sensitive to the parameters and departs substantially from the standard uniform wall temperature results.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

MHD micropolar nanofluid flow through an inclined channel with entropy generation subjected to radiative heat flux, viscous dissipation and multiple slip effects

2020 ◽  
Vol 16 (6) ◽  
pp. 1475-1496
Author(s):  
A. Roja ◽  
B.J. Gireesha ◽  
B.C. Prasannakumara
Keyword(s):  
Heat Flux ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Radiative Heat ◽  
Radiative Heat Flux ◽  
Nanofluid Flow ◽  
Content Type ◽  
Inclined Channel ◽  
Micropolar Nanofluid ◽  
Flow Through

PurposeMiniaturization with high thermal performance and lower cost is one of the advanced developments in industrial science chemical and engineering fields including microheat exchangers, micro mixers, micropumps, cooling microelectro mechanical devices, etc. In addition to this, the minimization of the entropy is the utilization of the energy of thermal devices. Based on this, in the present investigation, micropolar nanofluid flow through an inclined channel under the impacts of viscous dissipation and mixed convection with velocity slip and temperature jump has been numerically studied. Also the influence of magnetism and radiative heat flux is used.Design/methodology/approachThe nonlinear system of ordinary differential equations are obtained by applying suitable dimensionless variables to the governing equations, and then the Runge–Kutta–Felhberg integration scheme is used to find the solution of velocity and temperature. Entropy generation and Bejan number are calculated via using these solutions.FindingsIt is established to notice that the entropy generation can be improved with the aspects of viscous dissipation, magnetism and radiative heat flux. The roles of angle of inclination (α), Eckert number (Ec), Reynolds number (Re), thermal radiation (Rd), material parameter (K),  slip parameter (δ), microinertial parameter (aj), magnetic parameter (M), Grashof number (Gr) and pressure gradient parameter (A) are demonstrated. It is found that the angle of inclination and Grashof number enhances the entropy production while it is diminished with material parameter and magnetic parameter.Originality/valueElectrically conducting micropolar nanofluid flow through an inclined channel subjected to the friction irreversibility with temperature jump and velocity slip under the influence of radiative heat flux has been numerically investigated.

Laminar Forced Convection in Transversely Corrugated Microtubes

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Forced Convection ◽  
Wall Temperature ◽  
Wall Heat Flux ◽  
Bulk Temperature ◽  
Straight Tube ◽  
Computational Domain ◽  
Constant Wall Temperature ◽  
Constant Wall Heat Flux

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

Viscous dissipation effects on the limiting value of Nusselt numbers for a shear-driven flow through an asymmetrically heated annulus

2012 ◽  
Vol 226 (12) ◽  
pp. 2941-2949 ◽  
Author(s):  
Pranab Kumar Mondal ◽  
Sanchayan Mukherjee
Keyword(s):  
Nusselt Number ◽  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Axial Direction ◽  
Analytical Framework ◽  
Analytical Investigation ◽  
Interactive Effects ◽  
Brinkman Number ◽  
Nusselt Numbers ◽  
Flow Through

In this study, an analytical investigation for analyzing the effects of viscous dissipation on the limiting Nusselt number for a hydro-dynamically fully developed laminar shear-driven flow through an asymmetrically heated annulus of two infinitely long concentric cylinders has been made, where the inner cylindrical rod is moving in an axial direction at a constant speed. On the basis of some common assumptions, an analytical framework has been devised to explore the effects of viscous dissipation on the heat transfer characteristics for the flow of Newtonian fluid, and, consequently, closed-form expressions for the limiting Nusselt numbers are evaluated. In the analysis, focus has been given on the viscous dissipative effect due to the shear produced by the movable inner cylindrical rod apart from the viscous dissipation due to internal fluid friction for the flow of a Newtonian fluid. The interactive effects of the Brinkman number and degree of asymmetry on the limiting Nusselt number are analytically investigated. It is observed from this study that the limiting Nusselt number becomes independent of Brinkman number when both the walls of the annulus are kept at an equal temperature. Moreover, the temperature profile in the conduction limit obtained with the consideration of viscous dissipation effect provides a boundary condition required for solving energy equation including the axial conduction in the fluid.

Transient Internal Forced Convection Under Step Wall Heat Flux Condition

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
Majid Bahrami
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Steady State ◽  
Forced Convection ◽  
Analytical Model ◽  
Fluid Velocity ◽  
Wall Heat Flux ◽  
Bulk Temperature ◽  
Steady State Condition ◽  
Long Time

A new closed-form analytical model is developed to predict transient laminar forced convection inside a circular tube following a time-wise step change in the wall heat flux. The proposed all-time model is based on a blending of two asymptotes; i) short-time asymptote: transient pure conduction in an infinite cylinder and ii) long-time asymptote: steady-state convective heat transfer inside a circular duct. Different fluid velocity profiles are taken into consideration and the model covers: i) Slug Flow (SF); ii) Hydrodynamically Fully Developed Flow (HFDF); and iii) Simultaneously Developing Flow (SDF) conditions. The present model is developed for the entire range of the Fourier and Prandtl numbers. As such, short- and long-time asymptotes for the fluid bulk temperature are obtained. The Nusselt number is defined based on the local temperature difference between the tube wall temperature and the fluid bulk temperature. It is shown that irrespective of the velocity profile, at the initial times the Nusselt number is only a function of time. However, at the steady state condition it depends solely upon the axial location. In addition, during the transient period, the Nusselt number is much higher than that of the long-time response. We also performed an independent numerical simulation using COMSOL Multiphysics to validate the present analytical model. The comparison between the numerical and the present analytical model shows good agreement; a maximum relative difference less than 9.1%.

scholarly journals Viscous dissipation effect on laminar forced convection in a circular duct with adiabatic walls - preliminary numerical investigation

2018 ◽  
Vol 240 ◽  
pp. 03016
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Heat Flux ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Heat Flux Density ◽  
Energy Equation ◽  
Brinkman Number ◽  
Circular Duct ◽  
Nusselt Numbers ◽  
Axial Heat ◽  
Laminar Forced Convection

In this work, an analysis of laminar forced convection in a pipe with heated and adiabatic walls for a Newtonian fluid with constant properties is performed by taking the viscous dissipation into account when the axial heat conduction in the fluid is neglected. The Nusselt number versus the Brinkmann, which is based on the total wall heat flux density, have been investigated. In order to determine the temperature field, an analytical solution describing the velocity field in the pipe was used, while the energy equation was determined by the boundary element method (BEM). The results of the calculations of Nusselt numbers as a function of the Brinkman number for different thermal insulation heights to the diameter of the circular duct were presented in the form of diagrams.

Pressure Loss of Water Flow and Flow Boiling Heat Transfer in Microtubes

2015 ◽  
Author(s):  
Takeya Okamoto ◽  
Hiroyasu Ohtake ◽  
Koji Hasegawa
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Laminar Flow ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Flow Boiling ◽  
Bulk Temperature ◽  
Internal Diameter ◽  
Flow Boiling Heat Transfer ◽  
Phase Change Heat Transfer

The phase change heat transfer is one of the most effective cooling methods. Therefore, investigations for the phase change heat transfer and the two-phase flow have been performed by many researchers in the past. This study provided the frictional drop of single-phase flow and flow boiling heat transfer in microchannels. An internal diameter of the present micro pipes for our research was 161 μm, 86 μm and 54 μm, respectively. Test liquid was commercial pure water. A range of Reynolds number was 20 < Re < 2.7×103: the range of liquid velocity was 0.21 < u < 12 m/s. The correlation between a heat flux and a temperature difference between the wall temperature and the bulk temperature with a 161 μm internal diameter was higher than the conventional correlations for turbulent flow about single phase heat transfer. The correlation between a heat flux and a temperature difference between the wall temperature and the bulk temperature with an 86 μm internal diameter was also higher than the conventional correlations for laminar flow. However, the correlation between a heat flux and a temperature difference between the wall temperature and the bulk temperature with a 54 μm internal diameter was in good agreement with the conventional correlations for laminar flow. CHF was increased with increasing the internal diameter. Moreover, critical heat flux depends on velocity of flow. The CHF in the case of a 161 μm internal diameter in turbulent flow was approximately 20 MW/m2; the CHF in the case of an 86 μm internal diameter in laminar flow was approximately 6.9 MW/m2 and a 54 μm internal diameter in laminar flow was approximately 3.1 MW/m2. As a result, the CHF in case of an 86 μm internal diameter in laminer flow was in good agreement with conventional value calculated by Ivey-Morris equation.

Effect of Viscous Dissipation on Forced Convection Heat Transfer in Parallel Plate Channels With Asymmetric Boundary Conditions

2013 ◽  
Author(s):  
Ramjee Repaka ◽  
V. V. Satyamurty
Keyword(s):  
Nusselt Number ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Convection Heat Transfer ◽  
Axial Position ◽  
Inlet Temperature ◽  
Parallel Plates ◽  
Brinkman Number ◽  
Heating And Cooling ◽  
Limiting Condition

Effect of viscous dissipation on steady two-dimensional laminar forced convection in hydrodynamically developed and thermally developing flow between asymmetrically heated parallel plates (the plates have been kept at unequal temperatures) has been studied. The asymmetric heating is characterized by an asymmetry parameter, A, defined as the ratio of wall temperatures in excess of the fluid inlet temperature. Viscous dissipation is characterized by the Brinkman number, Br. Br <0, when the fluid is being heated and Br >0 when the fluid is being cooled. Heating and cooling have been, defined on the basis of average the wall temperatures. When the walls are subjected to equal wall temperature (i.e., A = 1), it may be recalled that the limiting value for the Nusselt number is 17.5 when viscous dissipation is included (Br ≠ 0), and is independent of the Brinkman number, Br. Similarly, when viscous dissipation is not included, for the case of unequal wall temperatures, (i.e., A ≠ 1), the Nusselt number in the conduction limit is 4, and is independent of the value of A, not equal to one. In the present investigation, it has been shown that the local Nusselt number values in the thermally developing region as well as in the limiting condition, do vary continuously with Brinkman number when the plates are kept at unequal temperatures. The axial location where the Nusselt number displays an unbounded swing depends on the Brinkman number for a given A, and vice versa. The axial position where the Nusselt number displays an unbounded swing depends on the combination of Br and A values and differs from the position for A = 1, Br < 0, or A > 0, Br = 0.

Sign in / Sign up

Export Citation Format

Share Document