Heat transfer with laminar forced convection in a porous channel exposed to a thermal asymmetry

The effect of thermal asymmetry on laminar forced convection heat transfer in a plane porous channel with Darcy dissipation has been investigated numerically. The parallel plates making the channel boundaries were kept at constant, but different temperatures. The thermal asymmetry thus imposed on the system, results in an asymmetric temperature field and different heat fluxes across the channel boundaries. Depending on Darcy, Peclét and Reynolds number, the thermal asymmetry may lead to a reversal of the heat flux at a certain position along the flow at least at one of the channel walls. The corresponding Nusselt numbers become zero and might experience discontinuities thereby jumping from infinite positive to infinite negative, or vice versa. This feature is observed not only in the region of thermal development, but also in the fully developed region. In the fully developed region, an analytical expressions for the Nusselt numbers were obtained. From these expressions, analytical equations were deduced for the calculations of the axial positions along the channel where the Nusselt numbers become zero, or experiences discontinuity.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall temperature

The exergy transfer characteristics of fluid flow and heat transfer inside a circular duct under fully developed laminar and turbulent forced convection are presented. Temperature is kept constant at the duct wall. The exergy transfer Nusselt number is put forward and the analytical expressions for exergy transfer Nusselt number are obtained as functions of heat transfer Nusselt number, Reynolds number, Prandtl number, etc. The variations of the local and mean convective exergy transfer coefficient, non-dimensional exergy flux, exergy transfer rate, etc. with operating parameters are presented graphically. By reference to a smooth duct and taking air as working fluid, a numerical analysis of the influence of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics has been conducted. The results show that the process parameters and configuration in the fluid flow and heat transfer inside a duct should be properly selected so that the forced convection process could have the best exergy utilization. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation

Abstract

Analytical expressions for the velocity and temperature profiles, bulk temperature and Nusselt numbers, in a fully-developed laminar Couette–Poiseuille flow between parallel plates of a power-law fluid with constant, and distinct, wall heat fluxes, in the presence of viscous dissipation are deduced and presented. Both favorable and adverse pressure gradient cases were analyzed. The walls’ shear stresses ratio, which arises naturally when the dimensionless hydrodynamic solution is obtained, together with the fluid power-law index Brinkman number and the walls’ heat fluxes ratio are the independent variables in the heat transfer solutions. With the exception of Newtonian fluids, there are in general two distinct analytical solutions, one for positive and another for negative values of the walls’ shear stresses ratio. The existence of singular points are also observed, where for a given value of the power-law index, there are values of the walls’ shear stresses ratio for which the Nusselt number becomes independent of the Brinkman number. It was also found that in a Couette–Poiseuille flow, for each value of the power-law index there exists a certain negative value of the walls’ shear stresses ratio that makes the Nusselt numbers at both walls identically zero.     

Limiting Nusselt numbers for viscous dissipative flow between parallel plates kept at unequal temperatures

The limiting Nusselt number value of 4 for laminar convection through parallel plates kept at unequal temperatures in the absence of viscous dissipation is independent of the degree of asymmetry. Similarly, when the parallel plates are kept at equal temperatures, the limiting Nusselt number value of 17.5 when viscous dissipation is included is independent of the Brinkman number, which characterizes the viscous dissipation. This paper examines the dependence of limiting Nusselt numbers on the Brinkman number and the degree of asymmetry when the parallel plates are kept at unequal temperatures and viscous dissipation is included.     

Local and average heat transfer in the thermally developing region of an asymmetrically heated channel

Forced convection heat transfer between parallel plates kept at unequal wall temperatures has been studied assuming laminar, incompressible, steady flow of a Newtonian fluid of constant thermophysical properties. Unequal wall temperatures have been characterized by an asymmetry parameter. It has been shown that the heat transferred from the walls monotonically varies with the axial distance even though the Nusselt number (at one of the walls) does not vary continuously due to asymmetry. It has been found that a modified Nusselt number varies continuously with the asymmetry parameter. Plots to obtain heat transferred from each wall have been presented which serve the purpose of mean Nusselt number. Non-dimensional heat transferred from the two walls is independent of the asymmetry parameter. The down stream boundary condition applicable for the thermal field when the walls are kept at unequal temperatures has been brought out which becomes necessary when solving elliptic form of conservation of thermal energy equation, say, when axial conduction is included.     

Towards the Investigation of Heat Transfer Characteristics in a Viscous Dissipative Shear Driven Flow Through an Annulus: An Analytical Study

In the present study, the laminar forced convective heat transfer of a shear‐driven flow through an annulus in a viscous dissipative environment is investigated. The temperature distribution for different constant heat flux boundary conditions is studied, and so are the heat transfer characteristics of a Newtonian fluid under consideration. Following an analytical methodology, closed‐form expressions of the Nusselt number on both walls of the annulus have been devised. It is shown that the effect of viscous dissipation significantly alters the temperature profile, and the consequential effect is reflected in the variation of the Nusselt number. In most of the cases, variation of the Nusselt number exhibits a discontinuity in behavior at different locations within the annulus where an equilibrium state between the energy is attained due to shear heating and the heat supplied by the wall. However, it has been observed that the greater viscous dissipative heat causes a rise in the temperature and consequently a fall in the rate of heat transfer. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 569–588, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21057     

Fully-developed heat transfer in annuli with viscous dissipation

For Newtonian concentric annular flows analytical solutions are obtained under imposed asymmetric constant wall heat fluxes as well as under imposed asymmetric constant wall temperatures, taking into account viscous dissipation and for fluid dynamic and thermally fully-developed conditions. Results for the special case of the heat flux ratio for identical wall temperatures and the critical Brinkman numbers marking changes of sign in wall heat fluxes are also derived.Equations are presented for the Nusselt numbers at the inner and outer walls, bulk temperature and normalised temperature distribution as a function of all relevant non-dimensional numbers. Given the complexity of the derived equations, simpler exact expressions are presented for the Nusselt numbers for ease of use, with their coefficients given in tables as a function of the radius ratio.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall heat flux

The examination of exergy transfer characteristics caused by forced convective heat transfer through a duct with constant wall heat flux for thermally and hydrodynamic fully developed laminar and turbulent flows has been presented. The exergy transfer Nusselt number is put forward and the dependence relationships of the exergy transfer Nusselt number on the heat transfer Nusselt number, Reynolds number and Prandtl number are obtained. Expressions involving relevant variables for the local and mean convective exergy transfer coefficient, non-dimensional exergy flux and exergy transfer rate, etc. have been derived. By reference to a smooth duct, the numerical results of exergy transfer characteristics for fluids with different Prandtl number are obtained and the effect of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics is analyzed. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

First and Second Law Analysis for the MHD Flow of Two Immiscible Couple Stress Fluids between Two Parallel Plates

This paper aims to analyze the heat transfer by the first and second laws of thermodynamics for the flow of two immiscible couple stress fluids inside a horizontal channel under the action of an imposed transverse magnetic field. The plates of the channel are maintained at constant and different temperatures higher than that of the fluid. The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. No slip condition is taken on the plates and continuity of velocity, vorticity, shear stress, couple stress, temperature, and heat flux are imposed at the interface. The velocity and temperature distributions are derived analytically and these are used to compute the dimensionless expressions for the entropy generation number and Bejan number. The results are presented graphically. It is observed that the imposed magnetic field reduces the entropy production rate near the plates.     

Jet impingement cooling and optimization study for a partly curved isothermal surface with CuO-water nanofluid

Numerical and optimization study of jet impingement cooling of a partly curved surface with CuO-water nanofluid was performed with Galerkin weighted residual finite element method and COBYLA (constrained optimization by linear approximation) optimization algorithm. Target surface was partly curved which has a semi-elliptic shape and kept at constant hot temperature. Simulations were performed for various values of Reynolds number and solid particle volume fraction. It was observed that effects of curved wall on the distribution of fluid flow and heat transfer characteristics are more pronounced for higher values of Reynolds number as compared to a flat wall configuration. Highest heat transfer is obtained with curved wall and significant differences are observed between the peak values of Nusselt number between a flat wall and curved wall case. The average Nusselt number is a linear increasing function of nanoparticle volume fraction and the trends in local and average heat transfer are similar for curved wall and flat wall configurations when nanoparticles are added. Average Nusselt number enhances by about 20% at the highest particle volume fraction as compared to water. A polynomial type correlation for the average Nusselt number was derived which depends on the Reynolds number and solid particle volume fraction for both configurations.     

Combined forced and free-convection over thin needlesConvection mixte autour d'aiguilles finesTeплooбмeH пpи выHyждeHHoй и cвoбoдHoй кoHвeкции y тoHкич cтepжHeй

The problem of laminar combined forced and free-convection heat transfer from a vertical thin needle in a variable external stream is considered. The similarity solutions for needles with isothermal walls and needles with uniform wall heat fluxes have been obtained. For a given value of the needle size, the flow and heat transfer behaviours are similar to those encountered with flat plates. The Nusselt number and the skin-friction coefficients increase with decreasing needle sizes for assigned values of Prandtl number, local Reynolds number, and local Grashof number.     

Magnetohydrodynamic mixed convection in a non-Newtonian third-grade fluid flowing through vertical parallel plates: A semianalytical study of flow and heat transfer

Buoyancy assisted and buoyancy opposed mixed convection of a third-grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third-grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non-Newtonian third-grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing.     

A new method for heat transfer and fluid flow performance simulation of plate heat exchangers

Successful numerical simulation on heat transfer and fluid flow performances of plate heat exchangers is vital. Their complex structures often make the numerical calculation quite difficult and time-consuming. Conclusions drawn by the present work are promising for greatly simplifying the simulation. Different types of plates consisting of different numbers of periods are analyzed and it is concluded that the Nusselt number remains constant for different periods of different plates under different inlet velocities. The central friction coefficients behave the same as Nusselt number. For the first and last periods, the respective friction coefficient also remains for different plates. A small plate fraction with four periods is enough for performance prediction of any-sized plates.     

Soret effects on the mixed convection flow using Robin boundary conditions

An investigation has been undertaken as Soret and Schmidt outcomes on the mixed convection flow using Robin boundary conditions. The results use a vertical channel being kept at constant cold temperature and concentration at the left wall and hot temperature and concentration at the right wall. The exchange of heat is done by help of plates with a fluid. We consider the external fluid with equal and different temperatures. This physical problem is solved by using nondimensional parameters with the corresponding boundary conditions. To find analytical solution, the regular perturbation series method is used, and for finding the numerical solution, the well‐known Runge–Kutta method with shooting technique is employed. Comparison of the current study is favorable with the previous published results. The obtained results depend on the governing parameters such as thermal Grashof number, solutal Grashof number, Biot numbers, symmetric and asymmetric wall temperatures, Schmidt number, Soret number, and Brinkman number. An influence of these parameters on the fields of velocity, temperature, and concentration is reported. Further, the numerical results for the Nusselt number, mean value of the velocity, dimensionless bulk temperature, skin friction, and molecular diffusion coefficient are tabulated for different parametric conditions and explained. For small value of Brinkman number, the obtained values agree with other published results for all considered cases.     

Analytical modeling of electrokinetic effects on flow and heat transfer in microchannels

A fundamental understanding of electrolytic flow in microchannels is essential for the design of microfluidic devices. Hence, an analytic investigation is presented on the effects of electrostatic potential in microchannels. Solving the Navier–Stokes equations, an expression for the C_fRe product is presented. Solving the energy equation the Nusselt number for constant wall heat flux and constant wall temperature boundary conditions are presented with analytic expressions over a wide range of operating conditions.     

Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid

This paper presents a numerical study of natural convection cooling of a heat source horizontally attached to the left vertical wall of a cavity filled with copper-water nanofluid. The left vertical wall is kept at the constant temperature, while the other ones are kept adiabatic. The numerical approach is based on the finite volume method with a collocated grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. In this study, the influence of some effective parameters such as: Rayleigh number, location and geometry of heat source and solid concentration are studied and discussed. Results are presented in the form of streamlines, isotherms, and average Nusselt number. The results show that dimension of the heat source is an important parameter affecting the flow pattern and temperature field, so that the average Nusselt number decreases with an increase in the length of the heater. It is also observed that at a given Rayleigh number and definite heat source geometry, the average Nusselt number increases linearly with the increase in the solid volume fraction of nanofluid. The increase of Rayleigh numbers strengthens the natural convection flows which leads to the decrease in heat source temperature. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.     

Experimental study of laminar flow forced-convection heat transfer in air flowing through offset plates heated by radiation heat flux

An experimental study of the steady state laminar flow forced-convection heat transfer of air flowing through offset plates located between two parallel plates and heated by radiation heat flux was carried out. The ranges of parameters tested were incident radiation heat fluxes of 500, 700, and 1000 W/m² . With Re ranging from 650 to 2560. the inlet air bulk temperatures changed from 18.2 to 70 °C and the tilting angel of the unit with the horizontal ranged from 0 to 90° respectively. The results show that the rate of the increase in the local Nusselt number was observed to be proportional with Re up to 1900, while it became less sensitive over Re range of 1900–2500. Also. in this range of Re, with the inlet air temperature of 20 °C, the angel of inclination of the unit has no effect on the local Nusselt number. Increasing the incident radiation heat flux in the case of higher values of Re leads to a slight decrease in the value of the local Nusselt number. The effect of the inlet air bulk temperature on the forced-convection heat transfer coefficient shows. in the case of the horizontal position. an increase in the inlet air bulk temperature leads to slight decreases in the value of the average Nusselt number. while it leads to a significant decreases in the value of the average Nusselt number as the tilting angle increases up to the vertical position. This effect is clearer in the case of Re = 650 rather than Re = 2550.     

Similarity solutions for flows and heat transfer in microchannels between two parallel plates

In this paper we give analytical similarity solutions of the Navier–Stokes equations coupled with energy equation of Newtonian fluid in a microchannel between two parallel plates taking into account the effects of viscous dissipation, the velocity slip and the temperature jump at the wall. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). We provide new similarity transformations for the governing equations and derive the expressions of Poiseuille number (Po) and Nusselt number (Nu). Then, the homotopy analysis method (HAM) is employed to solve the nonlinear differential equations with related boundary conditions. Both the dimensionless analytical expressions of velocity and temperature are obtained. The rarefaction effects on velocity distribution and flow friction are exhibited. The interactive effects of the Brinkman number (Br) and the Knudsen number (Kn) on Nu are analytically studied for both the CHF and CWT cases.     

Heat transfer inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths

The heat transfer phenomena inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths was investigated numerically in the present work. The heat source is considered as a local heating element of varying length, which is embedded at the bottom wall of the enclosure and maintained at a constant temperature. The air flow enters the channel horizontally at a constant cold temperature and a fixed velocity. The other walls of the enclosure and the channel are kept thermally insulated. The flow is assumed laminar, incompressible, and two‐dimensional, whereas the fluid is considered Newtonian. The results are presented in the form of the contours of velocity, isotherms, and Nusselt numbers profiles for various values of the dimensionless heat source lengths (0.16 ≤ ε ≤ 1). while, both Prandtl and Reynolds numbers are kept constant at (Pr = 0.71) and (Re = 100), respectively. The results indicated that the distribution of the isotherms depends significantly on the length of the heat source. Also, it was noted that both the local and the average Nusselt numbers increase as the local heat source length increases. Moreover, the maximum temperature is located near the heat source location.     

Analysis of laminar heat transfer in micro-Poiseuille flow

The present study examines laminar forced convective heat transfer of a Newtonian fluid in a microchannel between two parallel plates analytically. The viscous dissipation effect, the velocity slip and the temperature jump at the wall are included in the analysis. Both hydrodynamically and thermally fully developed flow case is examined. Either the hot wall or the cold wall case is considered for the two different thermal boundary conditions, namely the constant heat flux (CHF) and the constant wall temperature (CWT). The interactive effects of the Brinkman number and the Knudsen number on the Nusselt numbers are analytically determined. Different definitions of the Brinkman number based on the definition of the dimensionless temperature are discussed. It is disclosed that for the cases studied here, singularities for the Brinkman number-dependence of the Nusselt number are observed and they are discussed in view of the energy balance.