Analysis of the 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient: Part I – Extended inverse and direct solutions

A closed-form inverse solution of the 1-D heat conduction problem for a single fin or spine of constant cross section with an insulated tip is generalized to account for the effect of the tip heat loss. The heat transfer coefficient (HTC) is assumed to exhibit the power-law type dependence on the local excess temperature with arbitrary value of the exponent n in the range of ?0.5 ? n ? 5. The form of the obtained inverse solution is the same as the one for a fin with an insulated tip. However, in addition to the dimensionless fin tip temperature T_e and n, the fin parameter N also depends on the complex parameter ω²Bi. Using the inversion of this solution and a linearization procedure, the recurrent direct solution with a high convergence rate is derived. Based on the latter, the explicit direct closed-form solution for the accurate determination of the temperature distribution along a fin height at the given values of N, n, and ω²Bi is obtained. This allows one to determine the base thermal conductance G of the straight plate fin (SPF) and cylindrical pin fin (CPF). The relations between the fin parameters are systematized and collected in two tables for the SPF and CPF. They permit one to determine the arbitrary dimensionless geometrical or thermal fin parameter at given value of any other of its parameters and prescribed or calculated values of the main fin parameter(s) N or (and) G.     

Pressure corrections for the potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer

Pressure corrections for the viscous potential flow analysis of Kelvin–Helmholtz instability at the interface of two viscous fluids have been carried out when there is heat and mass transfer across the interface. Both fluids are taken as incompressible and viscous with different kinematic viscosities. In viscous potential flow theory, viscosity enters through normal stress balance and effect of shearing stresses is completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface for two fluids. It has been observed that heat and mass transfer has destabilizing effect on the stability of the system. A comparison between viscous potential flow (VPF) solution and viscous contribution to the pressure for potential flow (VCVPF) solution has been made and it is found that the effect of irrotational shearing stresses stabilizes the system.     

Mass and heat transport impact on the peristaltic flow of a Ree–Eyring liquid through variable properties for hemodynamic flow

Variable properties play a prominent role in analyzing the blood flow in narrow arteries. Specifically, considering the variation of thermal conductivity and viscosity helps in the understanding of the rheological behavior of blood and other biological fluids, such as urine, spermatozoa, and eye drops. Inspired by these applications, the current study incorporates the impact of variable thermal conductivity and viscosity for modeling the peristaltic flow of a Ree–Eyring liquid through a uniform compliant channel. The governing equations are nondimensionalized with the assistance of similarity transformations. The long-wavelength and small Reynolds wide variety approximation are utilized for solving the governing differential equations. Furthermore, the series solution method (perturbation technique) is utilized for solving the nonlinear temperature equation. The obtained results show that the velocity is greater in the case of the Newtonian liquid than that of the non-Newtonian liquid.     

Calculation of the glass cover temperature and the top heat loss coefficient for 60° vee corrugated solar collectors with single glazing

In this paper, the top heat losses from a 60° vee corrugated solar collector with single glazing have been investigated. An approximate method for computation of glass cover temperature and top heat loss coefficient has been followed. A modified equation from Akhtar and Mullick’s relation was proposed. The predicted values of the glass cover temperature and the top heat loss coefficient were compared with the results obtained by iterative solution of the energy balance equations over a wide range of operating conditions. A good accuracy is provided by the proposed equation which is recommended to be used in the energy analysis of the present configuration.     

Comments on “Mechanism of Soret-Dufour,magnetohydrodynamics, heat and mass transfer flow with buoyancy force,and viscous dissipation effects‏‏”

This commentary shows that the correct units of mass expansion coefficient (β_c) must be m³/mol (ie, the inverse of the concentration [C] units) so that the product β_c(C − C_∞) is dimensionless in the momentum equation. Also, the correct units of magnetic field strength (B₀) must be Tesla so that the last term in RHS of the momentum equation has the units of m/s². In addition, the correct units of dynamic viscosity (μ) must be kg/m·s so that the last term in RHS of the energy equation has the units of K·s. These correct units must be used too in the converted momentum and energy equations after introducing the stream function Ψ(x, y). Using these wrong units will cause some dimensionless parameters such as Grashof number (Gb) and magnetic parameter (M) will be dimensional.     

“Blind test” calculations of the performance and wake development for a model wind turbine

This is a summary of the results from the “Blind test” Workshop on wind turbine wake modeling organized jointly by Nowitech and Norcowe in Bergen, October, 2011. A number of researchers were invited to predict the performance and the wake development for a model wind turbine that has been developed by and extensively tested at the Department of Energy and Process Engineering, NTNU. In the end, contributions were received from eight different groups using a wide range of methods, from standard Blade Element Momentum (BEM) methods to advanced fully resolved Computational Fluid Dynamics (CFD) and Large Eddy Simulation (LES) models. The range of results submitted was large, but the overall trend is that the current methods predict the power generation as well as the thrust force reasonably well, at least near the design operating conditions. But there is considerable uncertainty in the prediction of the wake velocity defect and turbulent kinetic energy distribution in the wake.     

Multilayered Plate Model with “Adaptive” Representation of Displacements and Temperature Across the Thickness and Fixed D.O.F.

A new multilayered zig-zag plate model for analysis of thermo-elastic problems is developed. It a priori fulfils the boundary conditions and the stress contact conditions on interlaminar shear and normal stresses and the continuity of the heat flux and temperature at the layer interfaces, as prescribed by the elasticity theory and heat conduction equation. The functional d.o.f. are the mid-plane displacements and shear rotations, like for classical plate models, and the temperature at the upper and lower bounding faces. A non-classical feature, a high-order piecewise variation of the transverse displacement is assumed across the thickness aimed at accurately describing the transverse normal stress, as it has a significant bearing for keeping equilibrium in thermo-elastic problems. Also non classical feature, the representation of displacements and temperature can be different from point to point across the thickness, to adapt to the variation of solutions. This refinement is obtained by keeping the number of functional d.o.f. unchanged, since the coefficients of the hierarchic contributions are determined enforcing the fulfillment of the equilibrium and heat conduction equation at selected points across the thickness. As shown by the comparison with exact solutions of benchmark test cases, the present model accurately predicts displacement, stress and temperature variations across the thickness from constitutive equations, even when thickness is extreme and the thermo-elastic properties of layers are distinctly different. Its basic advantage over existing models is a lower computational effort under the same accuracy.     

A “special” anhydrous system for the preparation of alloyed Pd1Ce0.5 nanonetworks catalyst supported on carbon nanotubes with high electrochemical oxidation activity for formic acid

Herein, Pd₁Ce_0.5 alloy nanonetworks (ANNs) on multi-walled carbon nanotubes (MWCNTs) supported bimetallic catalyst (referred to Pd₁Ce_0.5/MWCNTs-D) was prepared in deep eutectic solvents (DESs). The Pd₁Ce_0.5/MWCNTs-D catalyst shows remarkable catalytic performance toward formic acid oxidation (FAO) (1968.5 mA mg_Pd^?1) and better CO anti-poisoning capability compare with Pd/MWCNTs-D, Pd/MWCNTs-W (prepared in water) and commercial Pd/C catalysts. The excellent network structure and synergistic effect are the main reasons for the improvement of electrochemical activity of Pd₁Ce_0.5/MWCNTs-D catalyst. This study provides a new method for preparation of high performance Pd-based electrocatalysts for direct formic acid fuel cell (DFAFC) applications.