English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We use an approximation method to study the solution to a nonlinearheat conduction equation in a semi-infinite domain. By expanding an energy densityfunction (defined as the internal energy per unit volume) as a Taylor polynomial ina spatial domain, we reduce the partial differential equation to a set of first-orderordinary differential equations in time. We describe a systematic approach to deriveapproximate solutions using Taylor polynomials of a different degree. For a special case,we derive an analytical solution and compare it with the result of a self-similar analysis.A comparison with the numerically integrated results demonstrates good accuracy of ourapproximate solutions. We also show that our approximation method can be appliedto cases where boundary energy density and the corresponding effective conductivityare more general than those that are suitable for the self-similar method. Propagationof nonlinear heat waves is studied for different boundary energy density and theconductivity functions

Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain