Solution Of Convective Heat Transfer Research Articles

An analytical solution for convective heat transfer in conical gaps with either cone or disk rotating

This study is devoted to solving two problems of laminar fluid flow in a conical gap with small conicity angles up to 4°: cone rotation with a fixed disk, and disk rotation with a fixed cone. A new improved asymptotic expansion method for energy equation was used to obtain an approximate analytical solution to the convective heat transfer equation. The characteristic Reynolds number ranged from 0.001 to 1.0, the Prandtl number took values 0.71, 1, 5, and 10, and the exponent n* in the power-law for the disk temperature was 0 (constant disk temperature) or 2 (strongly radially increasing disk temperature). A novel model for the asymptotic expansion of the temperature profile and a novel expansion parameter Sv = Re2Pr, which is a new dimensionless number proposed for the first time in the known scientific literature, was developed. For the first time, new approximate analytical solutions were obtained for temperature profiles and Nusselt numbers on the disk and cone for both problems that agree well with the self-similar solution, if the Re and Pr numbers do not exceed threshold values. These analytical solutions are advantageous in analysis of experimental data and further development of one-dimensional models for gases, water, and aqueous solutions (Pr = 0.71–10).

Erratum: “An asymptotic expansion method vs a self-similar solution for convective heat transfer in rotating cone-disk systems” [Phys. Fluids 34, 103610 (2022)

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An asymptotic expansion method vs a self-similar solution for convective heat transfer in rotating cone-disk systems

This paper compares an asymptotic expansion method and a self-similar solution for modeling Couette flow and convective heat transfer in a conical gap at small conicity angles up to 4°. The cases of rotation of a cone with a stationary disk and rotation of a disk with a stationary cone are considered. The self-similar system of equations provides the best agreement with experiments compared to the asymptotic expansion method. In any case, both methods are applicable only to conicity taper angles up to 4°, while at large conicity angles, the calculation results become significantly inaccurate. Calculations also showed that, at small conicity angles, convective heat transfer can be modeled using the self-similar energy equation in the boundary-layer approximation without considering radial heat conduction. In this study, analytical solutions were also obtained for limiting cases of a stationary fluid in a gap at small conicity angles without and with allowance for radial heat conduction.

Simultaneous solutions for convective heat transfer in dusty-nano- and dusty-hybrid nanoliquids

The present study investigates the heat transfer and flow behaviour of magnetohydrodynamic dusty-nano- and dusty-hybrid nanoliquids caused by the stretched surface. We considered the copper oxide (CuO) and magnesium oxide (MgO) nanoparticle suspension in water (H2O) as the base liquid. Similarity transformations are used to transform the partial differential equations to ordinary differential equations and solved by the Runge-Kutta Fehlberg 45 method with a shooting procedure. Outcomes of the velocity and thermal gradients for diverse physical impacts are depicted via plots and the skin friction factor and heat transfer rate are illustrated via tabulated values. Results reveal that dusty-hybrid nanoliquids and their conductive properties play an important role throughout the study. A growth in the mass concentration of dust particles augments the temperature and the Nusselt number, but the reverse reaction to the friction factor and velocity profile has been seen. The Eckert number has a propensity to magnify the temperature of the fluid phase and dust phase. The interaction of dust and nanoparticles extends to the greater heat transmission in the dust phase associated with the fluid phase. Hybridization showed a positive response in the heat transmission of the nanoliquid. The dusty hybrid-nano liquid shows higher heat dispersion compared to the dusty nanoliquid.

An analytical solution of convective heat transfer in microchannel or nanochannel

The two-dimensional energy equation with a first-order velocity slip model and a temperature jump model is studied analytically and a solution consisting of an infinite series is obtained. Impacts of viscous dissipation, axial conduction and rarefied effect on the local Nusselt number, the asymptotic Nusselt number and the bulk temperature profile of fluid are investigated. Results show that the cooling effect of the fluid benefits from the higher rarefied effect and axial conduction effect, as well as the lower viscous dissipation. The asymptotic dimensionless bulk temperature of fluid converges to a constant value that is higher than the wall temperature at a given set of Brinkman number, Péclet number and Knudsen number regardless of the inlet conditions. When neglecting axial conduction and the rarefied effect, the asymptotic Nusselt number with or without viscous dissipation is 17.5 or 7.54, respectively. Effects of axial conduction on the asymptotic Nusselt number are negligible when the Péclet number is greater than 10, while its influence on the non-dimensional bulk temperature of fluid and local Nusselt number can be neglected only when Pe > 100.

Comparison of Convection Models for Hot Blast Stove Regenerative Chamber

Low error numerical solutions of convective heat transfer in high-temperature air regenerative heat exchangers in the convective regime rely on the correct determination of the wall heat transfer coefficient. Presented are results of simulations computed using a similarity theory-based numerical model. They imply that the current empirical formulas based on the theory of similarity, derived for analogous model cases of convective heat transfer do not allow to achieve satisfactory accuracy. Actual dependencies of parameters and criteria yielding more representative heat transfer coefficient values might be obtained through the means of experimental research in thermodynamics of an experimental device.

Exact Analytical and Numerical Solutions for Convective Heat Transfer in a Semi-Spherical Extended Surface with Regular Singular Points

In this study, an exact analytical solution for the convective heat transfer equation from a semi-spherical fin was presented. To obtain a mathematical model, the system was assumed to be a lump in the vertical direction and the governing equation in the Cartesian coordinate was transferred to the Mathieu equation. The exact solution was compared with numerical results such as the finite difference method and midpoint method with Richardson extrapolation (Midrich). Not surprisingly, the exact solution prevailed over the numerical solutions in terms of accuracy and ease of use. Furthermore, the effect of Biot number on the heat transfer of the fin and the fine performance was investigated. The relative error of the results obtained from the analytical and numerical solutions at the base, center, and tip of the fin was 0, 7.72, and 40.25 percent, respectively. The results showed that the relative error between the analytical and numerical solutions depends on the Biot number and varies as a function of the fin length. The obtained analytical solution could be encouraging from different mathematical and industrial applications' points of view.

Analytical solution of convective heat transfer of a quiescent fluid over a nonlinearly stretching surface using Homotopy Analysis Method

Abstract In this article, an analytical solution of the boundary layer fluid flow and heat transfer of a quiescent viscous fluid over a non-linearly stretching surface is presented. The thermal radiation effects are included in the energy governing equation. Surface velocity and temperature conditions are assumed to be of the power-law form with an exponent of 1/3 for velocity and arbitrary exponent m for surface temperature or heat flux conditions. The system of nonlinear differential equations is solved by Homotopy Analysis Method (HAM) for two cases of Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF). The results of this method appear in the form of series expansions, the convergence of which is analyzed carefully. Graphical results are finally presented in order to investigate the influence of Prandtl number (Pr) and thermal radiation on heat transfer phenomena.

An Exact Analytical Solution for Convective Heat Transfer in Elliptical Pipes

In this paper, an analytical solution for convective heat transfer in straight pipes withthe elliptical cross section is presented. The solution is obtained for steady-state fluid flow and heattransfer under the constant heat flux at walls using the finite series expansion method. Here, the exactsolution of Nusselt number as well as temperature distribution in terms of aspect ratio is presented as thecorrelation in the Cartesian coordinate system and validated with the previous investigations. It is shownthat the minimum amount of Nusselt number, as well as the maximum absolute value of dimensionlesstemperature at the center of the cross section, are related to the aspect ratio equal to 1 (circular pipe). Thesolution indicated that the amount of Nusselt number is increased by changing the geometry of crosssection from circular to an elliptical shape and it finally tends to 4356/833 at large enough aspect ratios.Our results also show that 95% of the increase in Nusselt number to the circular cylinder is related toaspect ratio equal to 18.36. The present method of solution could be used to obtain the exact solution ofconvective heat transfer in elliptical pipes for other thermal boundary conditions and fluid rheologicalbehaviors.

A New Exact-Analytical Solution for Convective Heat Transfer of Nanofluids Flow in Isothermal Pipes

ABSTRACTThis study presents a new exact-analytical solution for convective heat transfer of thermally fully-developed laminar nanofluid flows in a circular tube for the first time. In this problem, the pipe wall is exposed to a constant temperature. The solution is based on the Whittaker function and perturbation technique. In the nanofluid model, it is assumed that nanoparticles and base-fluid behave as a single-phase with average properties. In this study, the effects of Reynolds number, volume fraction of the particles, Peclet number, and particle diameter are investigated on the average heat transfer coefficient, surface mass transfer, and Nusselt number.

Analytical solution for the convection of Phan-Thien-Tanner fluids in isothermal pipes

In this paper, EXACT analytical solutions for convective heat transfer of both linear and exponential Phan-Thien Tanner fluids (LPTT and EPTT) through an isothermal pipe are presented. The previous studies are limited to the successive approximations or guessing method for just LPTT fluid (simplified PTT). Here, due to the eigenvalue form of heat convection equation, the temperature distribution and Nusselt number are calculated based on the modal analysis technique. The non-singular Taylor series of temperature distributions of LPTT and EPTT viscoelastic flows are obtained using the Frobenius method. The accurate correlations for the Nusselt number and core temperature are derived. The solutions are validated in three ways and the effect of the Weissenberg number and extensional parameter of PTT model on heat convection in isothermal pipes are investigated in detail. The proposed method of solution could be generalized to solve the other non-Newtonian flows in isothermal pipes.

Analytical Solution of Convective Heat Transfer of Oscillating Flow Subject to a Triangular Pressure Waveform

Analytical Solution of Convective Heat Transfer of Oscillating Flow Subject to a Triangular Pressure Waveform

An analytical solution for convective heat transfer of viscoelastic flows in rotating curved pipes

This research reports an analytical solution for flow and convective heat transfer of an Oldroyd-B viscoelastic fluid in rotating curved pipes with viscous dissipation effects. In order to solve the momentum and energy conservation equations, a perturbation method is employed. Fully-developed hydrodynamic and thermal boundary conditions are considered with a constant heat flux imposed at the pipe wall. A physical solution based on the H2 boundary condition is presented and it is shown that the results of the present study are more physically realistic than those reported in previous studies utilizing only the H1 assumption. The computations have shown that due to the large gradient of velocity field and rheological properties of viscoelastic fluids, the internal heat generated by viscous dissipation exerts a significant role on both flow and heat transfer characteristics in the present regime. Furthermore, the interesting phenomenon of dissipation of mechanical energy is also investigated. Therefore, the current study emphasizes the substantial effects of viscous dissipation on the heat transfer in non-symmetric temperature distributions. The present analysis evaluates in detail the collective effects of Coriolis force, inertia forces, elastic force and dissipation effects, via the Rossby, Reynolds, Weissenberg and Brinkman numbers, respectively. An increase in Rossby number for the co-rotation case is observed to displace the minimum temperature location toward the outer side of the pipe and additionally enhances the sensitivity of the flow to Reynolds, Weissenberg, Prandtl numbers, viscosity ratios and curvature ratios. Visualization of the main and secondary flows is also presented. The study is relevant to thermal polymeric flow processing.

An exact analytical solution for convective heat transfer in rectangular ducts

An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time. This solution is valid for both H1 and H2 boundary conditions, which are related to fully developed convective heat transfer under constant heat flux at the duct walls. The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution. The local and mean Nusselt numbers are also obtained as functions of the aspect ratio. A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions. This is one of the major innovations of the current study. The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.

An explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream

An analytic technique, namely the homotopy analysis method, is applied to study the flow and heat transfer characteristics in an electrically conducting fluid near an isothermal sheet. The sheet is linearly stretched in the presence of a uniform free stream of constant velocity and temperature. The effects of free convection and internal heat generation or absorption are also considered. Within the framework of boundary layer approximations, the explicit, totally analytic and uniformly valid solutions governed by a set of three fully coupled, highly non-linear equations are obtained, which agree well with numerical results.

Natural convection heat transfer from complex surface

The analytical solution of convective heat transfer from an isothermal complex surface in an unlimited space has been presented. The complex surface is represented by a horizontal ring of diameters D and d with hemispherical segment of diameter d in the centre. The shape of the complex surface was expressed by factor p = d/ D. The presented solution has been verified experimentally on a set-up of diameter of 0.4 m and height of 0.5 m with surfaces of constant external diameter D = 0.06 m and various shape factor p = 0—round plate, 0.183, 0.233, 0.40, 0.483, 0.554, 0.650, 0.817 and 1.0—hemisphere. The tested fluid was glycerine. The comparison of theoretical and experimental results gives good agreement.

On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects

AbstractThe integral transform method is employed in the analytical solution of the non‐classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.

Shear Flow Over a Wall With Variable Temperature

The Leveque solution for forced convection due to shear flow over a plate is one of the basic solutions of convective heat transfer. The solution is exact if the fluid velocity is linear, such as that generated by the movement of parallel plates. The solution is asymptotic if the thermal boundary layer is much thinner than the velocity boundary layer, such that the local velocity profile is approximately linear. This occurs for developing thermal boundary layers. Although the author discussed the general case, Leveque originally considered shear flow over a plate with a sudden constant temperature change. The problem was subsequently extended to the constant heat flux case by Worsoe-Schmidt. In both instances exact similarity boundary layer solutions are obtained. In this note he considers the variable wall temperature case. Both analytic and numerical methods will be used.

Computational modeling of stationary gastungsten-arc weld pools and comparison to stainless steel 304 experimental results

A systematic study was carried out to verify the predictions of a transient multidimensional computational model by comparing the numerical results with the results of an experimental study. The welding parameters were chosen such that the predictions of the model could be correlated with the results of an earlier experimental investigation of the weld pool surface temperatures during spot gas-tungsten-arc (GTA) welding of Type 304 stainless steel (SS). This study represents the first time that such a comprehensive attempt has been made to experimentally verify the predictions of a numerical study of weld pool fluid flow and heat flow. The computational model considers buoyancy and electromagnetic and surface tension forces in the solution of convective heat transfer in the weld pool. In addition, the model treats the weld pool surface as a truly deformable surface. Theoretical predictions of the weld pool surface temperature distributions, the cross-sectional weld pool size and shape, and the weld pool surface topology were compared with corresponding experimental measurements. Comparison of the theoretically predicted and the experimentally obtained surface temperature profiles indicated agreement within ±8 pct for the best theoretical models. The predicted surface profiles were found to agree within ±20 pct on dome height and ±8 pct on weld pool diameter for the best theoretical models. The predicted weld cross-sectional profiles were overlaid on macrographs of the actual weld cross sections, and they were found to agree very well for the best theoretical models.

An analytical/numerical solution of convective heat transfer in the thermal entrance region of irregular ducts

This study presents an analytical/numerical solution to convective heat transfer in the thermal entrance region of irregular ducts (i.e., square, rectangular and equilateral triangular ducts) that are subjected to a constant wall temperature accounting for fully developed velocity. The developing temperature field in these ducts is obtained analytical from solution of the energy equation employing the method of lines (MOL). The resulting system of first order differential equations is readily solved analytically or numerically on a personal computer. Furthermore, the paper discusses in detail the proposed methodology where all calculations are based on a coarse grid with sixteen lines or, a fine grid with twenty-five lines, in the cross-stream direction of the duct. Based on the temperature fields, the representative curves illustrating variations of the bulk temperature and the Nusselt numbers with pertinent parameters are plotted. The computed results are compared against some limited analytical and numerical findings reported in the literature. In all cases, satisfactory comparison is obtained.