Chi-Chang Wang

FORCED CONVECTION IN A WAVY-WALL CHANNEL

Abstract The rates of heat transfer for flow through a sinusoidally curved converging–diverging channel has been analyzed using a simple coordinate transformation method and the spline alternating-direction implicit method. The effects of the wavy geometry, Reynolds number and Prandtl number on the skin-friction and Nusselt number have been studied. Results show that the amplitudes of the Nusselt number and the skin-friction coefficient increase with an increase in the Reynolds number and the amplitude–wavelength ratio. The heat transfer enhancement is not significant at smaller amplitude wavelength ratio, however, at a sufficiently larger value of amplitude wavelength ratio the corrugated channel will be seen to be an effective heat transfer device, especially at higher Reynolds numbers.

Transient force and free convection along a vertical wavy surface in micropolar fluids

Abstract This work studies the transient behavior of the laminar mixed convection in micropolar fluid flow over a vertical wavy surface. Effects of micropolar parameters and wavy geometry on the transient skin friction coefficient and Nusselt number are examined. Results show that the transient skin-friction coefficient and heat transfer rate show a mixture of two harmonics. Forced convection dominates the first harmonic at smaller time or near the leading edge, while free convection dominates the second harmonic as the time increases and fluid moves downstream. As the vortex viscosity increases the Nusselt number decreases, thus micropolar fluids have smaller heat transfer rates.

Mixed convection boundary layer flow of non-Newtonian fluids along vertical wavy plates

Abstract Mixed convection boundary layer flows of non-Newtonian fluids over the wavy surfaces are studied by the coordinate transformation and the cubic spline collocation numerical method. The effects of the wavy geometry, the buoyancy parameter and the generalized Prandtl number for pseudoplastic fluids, Newtonian fluids and dilatant fluids on the skin-friction coefficient, local and mean Nusselt numbers have been graphically studied. Results show that both higher generalized Prandtl numbers and buoyancy parameters are seen to enhance the influence of wavy surfaces on the local Nusselt number, irrespective of whether the fluids are Newtonian fluids or non-Newtonian fluids. Moreover, the irregular surfaces have higher total heat flux than that of corresponding flats plate for any fluid.

Use of New Residual Correction Method to Calculate Upper and Lower Solutions of Natural Convection

This article uses the concept of differential equation maximum principle as well as the technique of virtual time to establish a solutions monotonic relation with the residual of a differential equation for a natural-convection problem. To obtain solutions, the article first uses cubic spline approximation to discretize the equation, then applies a new “residual correction method” to convert the once complex inequality constraint mathematical programming problem into a simple problem of equation iteration. The numerical results validate the correctness of this method. Moreover, when there are a very limited number of grid points, the accuracy of mean approximate solutions is still rather satisfying.

Three-dimensional inverse heat transfer analysis during the grinding process

Abstract A three-dimensional inverse analysis is adopted to estimate the unknown conditions on the workpiece surface during a grinding process. The numerical method (linear least-squares error method) requires just one iteration and can solve the inverse problems given only the temperature information at a finite number of locations beneath the working surface within a specified time domain. Results show that the heat source into the grinding zone and the heat transfer coefficient in the cooling region can be obtained by the proposed method even when under the influence of measured errors. Furthermore, it is found that the estimated heat transfer coefficient is more sensitive than the heat source to different measured errors and depths. Analyses of the temperature, heat distribution and heat transfer coefficient of the workpiece will help prevent the occurrence of thermal damage to the workpiece, which are caused by the high temperatures generated during the grinding process.

Use residual correction method to calculate the upper and lower solutions of initial value problem

Abstract This article attempts to establish solutions’ monotonic relation with residuals of initial value problem through the concept of maximum principle for differential equations, then discretizes the equation by the simple spline approximation for initial value problem, converts the once complex inequation constraint mathematical programming problem into a simple problem of equation iteration by applying the new “residual correction method for initial value problem” put forth by this article, and obtains the upper and lower solutions of initial value problem. Results from numerical validation indicate this method is accurate, simple and fast, the approximate solutions obtained can correctly analyze error range and the new method put forth hereby helps increase the accuracy of mean approximate solutions.

Natural convection between two horizontal cylinders inside a circular enclosure subjected to external convection

Abstract This paper presents a numerical study, supplemented with experiments of flow visualization and holographic interferometric measurement, concerning the buoyancy-induced fluid flow and heat transfer between two horizontal, differentially heated cylinders inside a circular, air-filled enclosure subjected to external convection. Numerical simulations via a finite-difference method have been conducted mainly to investigate the effect of insulation (namely, the external convection boundary condition) at the circular enclosure wall on the buoyant air flow structure and heat transfer characteristics among the horizontal cylinders and the circular enclosure wall. The results are displayed graphically to emphasize the effects of the Rayleigh number (Ra = 104∼107), the inclination angle of the enclosure with respect to gravity (φg = 30, 60, 90°) and the gap width between the horizontal cylinders (s/d = 0.7, 0.8333, 1.0) in the presence of external convection. The external convection at the circular enclosure wall was found to further promote buoyant convection flow and a markedly enhanced heat transfer between the cylinders accordingly results. In addition, the simulation taking account for the external convection at the enclosure wall was found to compare favorably with the experimental results of flow visualization and temperature distribution in a test cell with imperfect thermal insulation.

Mixed convection of micropolar fluids along a vertical wavy surface

SummaryThis paper presents numerical results for the steady-state mixed convection in micropolar fluids along a vertical wavy surface. The problem has been formulated by a simple trnasposition theorem, and the spline alternating-direction implicit method has been applied to solve the governing momentum, angular momentum and energy equations. The influence of the micropolar parameters (R and λ), the amplitude-wave length ratio and the Gr/Re2 number on the skin-friction coefficient and Nusselt number have been studied. Results demonstrate that the skin friction coefficient and local Nusselt number consist of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases but the skin friction increases. In addition, when the spin gradient viscosity parameter (λ) increases, the heat transfer rate and the skin friction decreases. However, the heat transfer rate of a micropolar fluid is smaller than a Newtonian fluid, but the skin friction of a micropolar fluid is larger than a Newtonian fluid under all circumstances.

Study on monotonicity of boundary value problems of differential equations

This article presents two new test methods to decide monotonic increasing or decreasing properties of differential equations. For simple problems, the eigenfunction test method can be applied to obtain their exact monotonicity or their loosest conditional expression, and can contribute to probes into accumulated effect of various terms in equations on their monotonicity. Secondly, the trial function test method sets relatively strict conditions for discrimination of monotonicity, but it can verify complex non-linear problems in a simple and rapid way. Therefore, these two similar test methods will help to further understand theories on monotonicity, thus making it possible to apply monotonic equations more widely to other problems.

Forced Convection in Micropolar Fluid Flow through a Wavy-Wall Channel

ABSTRACT Forced convection of micropolar fluids through a periodic array of wavy-wall channels has been analyzed by using a simple coordinate transformation method and the spline alternating- direction implicit method. The effects of the wavy amplitude, the micropolar parameter, and the Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging-diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and larger wavy amplitudes. For the micropolar fluids, increasing the vortex viscosity causes an increase in the total viscosity of the fluid, thus the skin friction coefficient increases while the Nusselt number decreases. Also, the influence of vortex viscosity on the minimum cross section of the wavy-wall channel and on a tiny change of the maximum cross section is manifest. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, regardless of whether the fluids are Newtonian or micropolar fluids.