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IT has been stated above that the rate of heat transfer is closely proportional to the temperature difference between the plate and the free air stream, and over the laminar portion it will also be proportional to the conductivity of the air. It remains to consider to what extent the actual temperature of the air in the boundary layer will influence the rate of heat transfer. The conductivity of air increases with temperature by reason of the increased molecular velocities, and we might expect, therefore, that the hotter the surface the greater will be the rate of heat transfer per unit of temperature difference above that of the air. This is, in fact, found to be the case.

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).

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.

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 (Br_qLs). 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, Br_qLs decreases in the range of 3 ≤ n < ∞. If the Br_qL < Br_qLs, 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 Br_qL > Br_qLs, this rule is reversed.

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.

This paper aims to present a high-order algorithm implemented with the modal spectral element method and simulations of three-dimensional thermal convective flows by using the full viscous dissipation function in the energy equation. Three benchmark problems were solved to validate the algorithm with exact or theoretical solutions. The heated rotating sphere at different temperatures inside a cold planar Poiseuille flow was simulated parametrically at varied angular velocities with positive and negative rotations.

The fourth-order stiffly stable schemes were implemented and tested for time integration. To provide the hp-refinement and spatial resolution enhancement, a modal spectral element method using hierarchical basis functions was used to solve governing equations in a three-dimensional space.

It was found that the direction of rotation of the heated sphere has totally different effects on drag, lateral force and torque evaluated on surfaces of the sphere and walls. It was further concluded that the angular velocity of the heated sphere has more influence on the wall normal velocity gradient than on the wall normal temperature gradients and therefore, more influence on the viscous dissipation than on the thermal dissipation.

This paper concerns incompressible fluid flow at constant properties with up to medium temperature variations in the absence of thermal radiation and ignoring the pressure work.

This paper contributes a viable high-order algorithm in time and space for modeling convective heat transfer involving an internal heated rotating sphere with the effect of viscous heating.

Results of this paper could provide reference for related topics such as enhanced heat transfer forced convection involving rotating spheres and viscous thermal effect.

The merits include resolving viscous dissipation and thermal diffusion in stationary and rotating boundary layers with both h- and p-type refinements, visualizing the viscous heating effect with the full viscous dissipation function in the energy equation and modeling the forced advection around a rotating sphere with varied positive and negative angular velocities subject to a shear flow.

This paper aims to present a numerical investigation into heat transfer and entropy generation resulting from magnetohydrodynamic laminar flow through a microchannel under asymmetric boundary conditions. Furthermore, the authors consider the effects of viscous dissipation and Joule heating.

The finite difference method is used to obtain the numerical solution. Simulations are conducted across a broad range of Hartmann (Ha = 0 ∼ 40) and Brinkman (Br = 0.01 ∼ 1) numbers, along with various asymmetric isothermal boundaries characterized by a heating ratio denoted as ϕ.

The findings indicate a significant increase in the Nusselt number with increasing Hartmann number, regardless of whether Br equals zero or not. In addition, it is demonstrated that temperature differences between the microchannel walls can lead to substantial distortions in fluid temperature distribution and heat transfer. The results reveal that the maximum entropy generation occurs at the highest values of Ha and η (a dimensionless parameter emerging from the formulation) obtained for ϕ = −1. Moreover, it is observed that local entropy generation rates are highest near the channel wall at the entrance region.

The study provides valuable insights into the complex interactions between magnetic fields, viscous dissipation and Joule heating in microchannel flows, particularly under asymmetric heating conditions. This contributes to a better understanding of heat transfer and entropy generation in advanced microfluidic systems, which is essential for optimizing their design and performance.

Efficient thermal management of central processing unit (CPU) cooling systems is vital in the context of advancing information technology and the demand for enhanced data processing speeds. This study aims to explore the thermal performance of a CPU cooling setup using a cylindrical porous metal foam heat sink.

Nanofluid flow through the metal foam is simulated using the Darcy–Brinkman–Forschheimer equation, accounting for magnetic field effects. The temperature distribution is modeled through the local thermal equilibrium equation, considering viscous dissipation. The problem’s governing partial differential equations are solved using the similarity method. The CPU’s hot surface serves as a solid wall, with nanofluid entering the heat sink as an impinging jet. Verification of the numerical results involves comparison with existing research, demonstrating strong agreement across numerical, analytical and experimental findings. Ansys Fluent® software is used to assess temperature, velocity and streamlines, yielding satisfactory results from an engineering standpoint.

Investigating critical parameters such as Darcy number (10⁻⁴ ≤ Da_D ≤ 10⁻²), aspect ratio (0.5 ≤ H/D ≤ 1.5), Reynolds number (5 ≤ Re_D,bf ≤ 3500), Eckert number (0 ≤ EC_bf ≤ 0.1) , porosity (0.85 ≤ ε ≤ 0.95), Hartmann number (0 ≤ Ha_D,bf ≤ 300) and the volume fraction of nanofluid (0 ≤ φ ≤ 0.1) reveals their impact on fluid flow and heat sink performance. Notably, Nusselt number will reduce 45%, rise 19.2%, decrease 14.1%, and decrease 0.15% for Reynolds numbers of 600, with rising porosity from 0.85 to 0.95, Darcy numbers from 10⁻⁴ to 10⁻², Eckert numbers from 0 to 0.1, and Hartman numbers from 0 to 300.

Despite notable progress in studying thermal management in CPU cooling systems using porous media and nanofluids, there are still significant gaps in the existing literature. First, few studies have considered the Darcy–Brinkman–Forchheimer equation, which accounts for non-Darcy effects and the flow and geometric interactions between coolant and porous medium. The influence of viscous dissipation on heat transfer in this specific geometry has also been largely overlooked. Additionally, while nanofluids and impinging jets have demonstrated potential in enhancing thermal performance, their utilization within porous media remains underexplored. Furthermore, the unique thermal and structural characteristics of porous media, along with the incorporation of a magnetic field, have not been fully investigated in this particular configuration. Consequently, this study aims to address these literature gaps and introduce novel advancements in analytical modeling, non-Darcy flow, viscous dissipation, nanofluid utilization, impinging jets, porous media characteristics and the impact of a magnetic field. These contributions hold promising prospects for improving CPU cooling system thermal management and have broader implications across various applications in the field.

This study aims to understand the difference between irreversibility in heat and work transfer processes. It also aims to explain that Helmholtz or Gibbs energy does not represent “free” energy but is a measure of loss of Carnot (reversible) work opportunity.

The entropy of mass is described as the net temperature-standardised heat transfer to mass under ideal conditions measured from a datum value. An expression for the “irreversibility” is derived in terms of work loss (W_loss) in a work transfer process, unaccounted heat dissipation (Q_loss) in a heat transfer process and loss of net Carnot work (CW_net) opportunity resulting from spontaneous heat transfer across a finite temperature difference during the process. The thermal irreversibility is attributed to not exploiting the capability for extracting work by interposing a combination of Carnot engine(s) and/or Carnot heat pump(s) that exchanges heat with the surrounding and operates across the finite temperature difference.

It is shown, with an example, how the contribution of thermal irreversibility, in estimating reversible input work, amounts to a loss of an opportunity to generate the net work output. The opportunity is created by exchanging heat with surroundings whilst transferring the same amount of heat across finite temperature difference. An entropy change is determined with a numerical simulation, including calculation of local entropy generation values, and results are compared with estimates based on an analytical expression.

A new interpretation of entropy combined with an enhanced mental image of a combination of Carnot engine(s) and/or Carnot heat pump(s) is used to quantify thermal irreversibility.

The unsteady natural convection flow of a viscous dissipative fluid along a semi‐infinite vertical plate subjected to periodic surface temperature oscillation is investigated.

An electrical‐network model based on the Network Simulation Method is developed to solve the governing equations. The accuracy and effectiveness of the method are demonstrated.

The increasing of the viscous dissipation and the decreasing in the Prandtl number lead to a decrease in Nusselt number and an increase in the local skin‐friction. Also, it is found that the oscillations of the Nusselt number and of the local skin‐friction depend on the frequency and amplitude of the oscillating surface temperature. For Pr = 1,000 and ε = 0.005 (realistic case) the effect of the viscous dissipation is appreciable at large distances from the leading edge.

The inclusion of viscous dissipation in the energy equation, except of the theoretical interest, has applications in very special cases, for example, gases at very low temperature and also for high Prandtl number liquids.

The influence of the non‐uniformity of wall temperature on the heat transfer by natural convection along of the plate together with the viscous dissipation of the fluid are analysed by means of a new numerical technique based on the electrical analogy.

By the use of ceramic ball grid array connections, the number of I/Os can be increased substantially in comparison with PGA (pin grid array) while maintaining an unchanged module size. In most cases, this also signifies a higher packing density and thus a higher power density, which must be dissipated as occurring heat. The fact that the dissipation of heat can also be improved considerably by the use of modules with CBGA (ceramic ball grid array) connections instead of PGA connections is demonstrated on a simulation model. Moreover, the use of chip carriers made of different ceramics (LTCC or Al₂O₃) has a substantial influence on the possible heat dissipation (LTCC= low temperature cofired ceramic).

The purpose of this paper is to consider unsteady free convection flow of a dissipative fluid past an exponentially accelerated infinite vertical porous plate in the presence of Newtonian heating and mass diffusion.

The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A Galerkin finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. It is a powerful, stable technique which provides excellent convergence and versatility in accommodating coupled systems of ordinary and partial differential equations.

It is found that the skin friction coefficient increases with increases in either of the Eckert number, thermal Grashof number, mass Grashof number or time whereas it decreases with increases in either of the suction parameter, Schmidt number or the acceleration parameter for both air and water. The skin friction coefficient is also found to decrease with increases in the values of the Prandtl number. In addition, it is found that the rate of heat transfer increases with an increase in the suction parameter and decreases with an increase in the Eckert number for both air and water. Lastly, it is found that the rate of heat transfer increases with increasing values of the Prandtl number and decreases with increasing time for all values of the Prandtl number.

The present study has considered only Newtonian fluids. Future studies will address non-Newtonian liquids.

A very useful source of information for researchers on the subject of free convective flow over the surface when the rate of heat transfer from the surface is proportional to the local surface temperature.

This paper is relatively original and illustrates the effects of viscous dissipation on free convective flow past an exponentially accelerated infinite vertical porous plate with Newtonian heating and mass diffusion.

The purpose of this paper is to investigate the thermal behaviour of thin- and thick-film resistor with different dimensions and contacts embedded into printed circuit board (PCB) and compare them to the similar constructions of discrete chip resistors assembled to standard PCBs.

In investigations the thin- and thick-film embedded resistors with the bar form in different dimensions and configurations of contacts as well as rectangular chip resistors in package 0603 and 0402 were used. In tests were carried out the measurements of dissipated power in temperature of resistor about 40°C, 70°C and 155°C. The power dissipation was calculated as a multiplying of electrical current flowing through the resistor with voltage across the resistor. The dissipation of heat generated by electrical current flowing through resistors was examined by means of the FLIR A320 thermographic camera with lens Closeup×2 and the power source.

The results show that, in case of chip resistors, the intensity of heat radiation strongly depends on dimensions of copper contact lands and also depends on the dimensions of the resistor. In case of embedded resistors, with comparable dimensions to chip resistors, they have lower ability to power dissipation, as well as the copper contact lands dimensions have lower influence. The thermal radiation through resin material is not as effective as it is in case of resistors assembled on PCB. However, the embedded thick-film resistors, especially made of paste Minico M2010, have already the similar parameters to 0402 chip resistors.

Research shows that embedded resistors can be used interchangeably with SMD resistors it allows to open up space on the surface of PCB, but it should be taken into account the lower energy dissipation capabilities. It is suggested that further studies are necessary for accurately determining the thermal effects and investigate the structures of embedded passive components that allow for better heat management.

Thermal stability of embedded resistors during operation is a critical factor of success of embedded resistor technology. The way of power dissipation and heat resistance are one of the important operating parameters of these components. The results provide information about the power and the energy dissipation of embedded thin- and thick-film resistors compared to the standard surface mount technology.