scholarly journals Temperature Distribution to Fluid Transport in a Vertical Porous Tube under the Action of Peristalsis

2019 ◽  
Vol 9 (1S5) ◽  
pp. 302-305
Keyword(s):  
Heat Transfer ◽  
Fluid Transport ◽  
Amplitude Ratio ◽  
Wave Length ◽  
Closed Form Solution ◽  
Form Solution ◽  
Boundary Wall ◽  
Long Wave ◽  
The Mean ◽  
Axisymmetric Tube

Peristaltic transport of a Newtonian fluid, with heat transfer, in a vertical porous axisymmetric tube under long wave length approximation is considered. Closed form solution is obtained as an asymptotic expansion in terms of porosity and free convection parameters. Expressions for temperature, coefficient of heat transfer and pressure -flow relationship at the boundary wall of the tube are derived. It is observed that pressure drop increases as amplitude ratio increases. Further, it has been observed that for some specific values of otherparameters under consideration the mean flux significantly increases by about 8 to 10 percent as Grashof number increasesfrom 1 to 2.

A comparative study of MHD fluid-particle suspension induced by metachronal wave under the effects of lubricated walls

2021 ◽  
pp. 2150204
Author(s):  
Mubbashar Nazeer ◽  
Farooq Hussain ◽  
Laiba Shabbir ◽  
Adila Saleem ◽  
M. Ijaz Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Magnetic Fields ◽  
Multiphase Flow ◽  
Thermal Radiation ◽  
Newtonian Fluid ◽  
Closed Form Solution ◽  
Casson Fluid ◽  
Form Solution ◽  
Phase Flow ◽  
Two Phase

In this paper, the two-phase flow of non-Newtonian fluid is investigated. The main source of the flow is metachronal waves which are caused by the back and forth motion of cilia attached to the opposite walls of the channel. Magnetohydrodynamics (MHD) of Casson fluid experience the effects of transverse magnetic fields incorporated with the slippery walls of the channel. Thermal effects are examined by taking Roseland’s approximation and application of thermal radiation into account. The heat transfer through the multiphase flow of non-Newtonian fluid is further, compared with Newtonian bi-phase flow. Since the main objective of the current study is to analyze heat transfer through an MHD multiphase flow of Casson fluid. The two-phase heated flow of non-Newtonian fluid is driven by cilia motion results in nonlinear and coupled differential equations which are transformed and subsequently, integrated subject to slip boundary conditions. A closed-form solution is eventually obtained form that effectively describes the flow dynamics of multiphase flow. A comprehensive parametric study is carried out which highlights the significant contribution of pertinent parameters of the heat transfer of Casson multiphase flow. It is inferred that lubricated walls and magnetic fields hamper the movement of multiphase flow. It is noted that a sufficient amount of additional thermal energy moves into the system, due to the Eckert number and Prandtl number. While thermal radiation acts differently by expunging the heat transfer. Moreover, Casson multiphase flow is a more suitable source of heat transfer than Newtonian multiphase flow.

scholarly journals Studying heat conduction in a sphere considering hybrid fractional derivative operator

2021 ◽  
pp. 332-332
Author(s):  
Abass Kader ◽  
Mohamed Latif ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Fractional Derivative ◽  
Dirichlet Boundary ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heat Absorption ◽  
Derivative Operator ◽  
Numerical Examples ◽  
Fractional Heat Equation

In this paper, the fractional heat equation in a sphere with hybrid fractional derivative operator is investigated. The heat conduction is considered in the case of central symmetry with heat absorption. The closed form solution in the form of three parameter Mittag-Leffler function is obtained for two Dirichlet boundary value problems. The joint finite sine Fourier-Laplace transform is used for solving these two problems. The dynamics of the heat transfer in the sphere is illustrated through some numerical examples and figures.

Natural Convection in a Vertical Annulus Containing Water Near the Density Maximum

1987 ◽  
Vol 109 (4) ◽  
pp. 899-905 ◽  
Author(s):  
D. S. Lin ◽  
M. W. Nansteel
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Density Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vertical Flow ◽  
Density Maximum ◽  
Vertical Annulus

Steady natural convection of water near the density extremum in a vertical annulus is studied numerically. Results for flow in annuli with aspect ratio 1≤A≤8 and varying degrees of curvature are given for 103≤Ra≤105. It is shown that both the density distribution parameter R and the annulus curvature K have a strong effect on the steady flow structure and heat transfer in the annulus. A closed-form solution for the vertical flow in a very tall annulus is compared with numerical results for finite-aspect-ratio annuli.

Analytical Solutions for Heat Transfer During Cyclic Melting and Freezing of a Phase Change Material Used in Electronic or Electrical Packaging

2003 ◽  
Vol 125 (1) ◽  
pp. 126-133 ◽  
Author(s):  
Suman Chakraborty ◽  
Pradip Dutta
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Phase Change Material ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Electronics Cooling ◽  
Form Solution ◽  
Transfer Model ◽  
Change Material

In this paper, we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each sub-domain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.

Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Mahdi Anbarloei ◽  
Elyas Shivanian
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Temperature Dependent Thermal Conductivity

In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.

The low frequency sound from multipole sources in axisymmetric shear flows, with applications to jet noise

1975 ◽  
Vol 70 (3) ◽  
pp. 595-604 ◽  
Author(s):  
M. E. Goldstein
Keyword(s):  
Closed Form Solution ◽  
Low Frequency ◽  
Form Solution ◽  
Point Sources ◽  
Mean Flow ◽  
Doppler Factor ◽  
The Mean ◽  
Axisymmetric Shear ◽  
Arbitrary Velocity ◽  
Multipole Sources

We have obtained a closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponentnof the Doppler factor (1 -Mcosθ)−nmultiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.

Linear theory of optimum hot air balloon performance – application to Titan

2008 ◽  
Vol 112 (1132) ◽  
pp. 353-355 ◽  
Author(s):  
R. D. Lorenz
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Low Temperature ◽  
Thermal Power ◽  
Closed Form Solution ◽  
Form Solution ◽  
Specific Mass ◽  
Hot Air ◽  
Maximum Payload ◽  
Payload Mass

Abstract We develop a simple theory for hot air balloon performance with fixed thermal power and linear heat transfer to the environment, applicable to low-temperature situations such as Titan’s atmosphere. The theory results in a closed-form solution and it is shown that an optimum balloon diameter exists – the maximum payload is achieved when the envelope mass and payload mass are equal. It is also shown simply that the floating mass for a given power has a stronger sensitivity to heat transfer coefficient than to the envelope specific mass. A hot air balloon on Titan with a ~2kW heat source could loft a theoretical maximum payload of ~195kg or ~100kg with appropriate margins.

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