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Related Concept Videos

Dimensional Analysis03:40

Dimensional Analysis

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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Dimensional Analysis01:27

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Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
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Dimensional Analysis01:23

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Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
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A strong acid is a compound that dissociates completely in an aqueous solution and produces a concentration of hydronium ions equal to the initial concentration of acid. For example, 0.20 M hydrobromic acid will dissociate completely in water and produces 0.20 M of hydronium ions and 0.20 M of bromide ions.
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Evolution of Staircase Structures in Diffusive Convection
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Semi-analytical solutions for two-dimensional convection-diffusion-reactive equations based on homotopy analysis

Chuang Yu1, Alin Deng1, Jianjun Ma2

  • 1College of Architecture and Civil Engineering, Wenzhou University, Wenzhou, 325035, China.

Environmental Science and Pollution Research International
|October 17, 2018
PubMed
Summary

This study introduces a new semi-analytical method to model contaminant transport in groundwater and landfills, accounting for real-world conditions. The approach accurately predicts contaminant fate in two-dimensional systems.

Keywords:
Convection–diffusion–reactiveHomology analysis methodSemi-analytical solutionsTwo-dimensional

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Area of Science:

  • Environmental Science
  • Geosciences
  • Applied Mathematics

Background:

  • Conventional models for contaminant transport in landfills and groundwater often use simplified geometries and boundary conditions.
  • These simplifications neglect complex real-world scenarios like lateral fluid transport, convection, and diffusion of contaminants such as landfill leachate.

Purpose of the Study:

  • To develop and present semi-analytical solutions for estimating contaminant fate in two-dimensional subsurface systems.
  • To address the limitations of traditional models by incorporating more general boundary conditions.

Main Methods:

  • Application of the Homotopy Analysis Method (HAM) to generate a series of deformation equations.
  • Ensuring accuracy by adapting equation series elements to satisfy the problem's partial differential equation.
  • Achieving convergence through proper control parameters for the HAM solution series.

Main Results:

  • The study presents novel semi-analytical solutions for two-dimensional contaminant transport problems.
  • Demonstrated good agreement between the Homotopy Analysis Method (HAM) solutions and existing numerical solutions from the literature.
  • Validated the capacity of HAM for accurately modeling contaminant fate under complex conditions.

Conclusions:

  • The developed semi-analytical solutions using HAM are effective for describing contaminant transport in two-dimensional systems.
  • HAM provides a robust and accurate alternative to traditional methods, especially for scenarios with complex boundary conditions.
  • The findings enhance the understanding and prediction of contaminant movement in environmental systems like landfills and groundwater.