Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
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Ryoichi Chiba
Abstract
The transient natural convection of a viscous fluid in a heated vertical tube is studied using the two-dimensional differential transform method (DTM). A time-dependent Dirichlet boundary condition is imposed for tube wall temperature. The partial differential equations for the velocity and temperature fields within the tube are solved by the DTM while considering temperature-dependent viscosity and thermal conductivity of the fluid. As a result, tractable solutions in double-series form are derived for the temperature and flow velocity. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results illustrate the effects of temperature-dependent properties on transient temperature and flow behaviour, including the Nusselt number and volumetric flow rate. The DTM gives accurate series solutions without any special functions for nonlinear transient heat transfer problems which are advantageous in finding the derivative or integral.
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Articles in the same Issue
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- Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials
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- Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models
- Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals
- Investigation of Thermal Expansion and Physical Properties of Carbon Nanotube Reinforced Nanocrystalline Aluminum Nanocomposite
- Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions
- Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
Articles in the same Issue
- Frontmatter
- Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
- The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations
- Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials
- Rational Solutions for Lattice Potential KdV Equation and Two Semi-discrete Lattice Potential KdV Equations
- Structural, Electronic, Magnetic and Optical Properties of Ni,Ti/Al-based Heusler Alloys: A First-Principles Approach
- Ab Initio Calculations on the Structural, Mechanical, Electronic, Dynamic, and Optical Properties of Semiconductor Half-Heusler Compound ZrPdSn
- Qualitative Behaviour of Generalised Beddington Model
- Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models
- Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals
- Investigation of Thermal Expansion and Physical Properties of Carbon Nanotube Reinforced Nanocrystalline Aluminum Nanocomposite
- Bistable Bright Optical Spatial Solitons due to Charge Drift and Diffusion of Various Orders in Photovoltaic Photorefractive Media Under Closed-Circuit Conditions
- Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties
