Solution of the Heat and Mass Transfer Problem for Soil Radiant Heating Conditions Using the Error Function

Abstract

Achieving high yields of agricultural crops requires the ability to predict soil temperature and moisture regimes, taking into account soil heating technology. The object of study is soil heated by a ceiling infrared emitter. The subject of study is one-dimensional non-stationary fields of soil moisture content and temperature. The objective of the study is to predict soil temperature and moisture regimes under radiant heating conditions. Research methods: analytical methods for solving differential equations of heat and mass transfer using the error function. Research results: the top 5 mm layer of milled peat with an initial moisture content of 3.7 kg/kg will reach a final moisture content of 1.0 kg/kg in about 6 hours during infrared drying. As a result of radiant heating, the soil will heat up from an initial temperature of 5 ℃ to a final temperature of 20 ℃ in approximately 3 hours. The analytical solution of the mass transfer differential equation can be used for theoretical studies of drying of capillary-porous materials, for example, to determine the drying period or the thickness of the material layer that will dry to a given final moisture content. The analytical solution of the heat transfer differential equation can be used to control the operating mode of the infrared radiation source, for example, to determine the periods of its operation and switching off in case the soil surface temperature reaches the maximum (critical) value. The mathematical solutions considered in the article do not take into account the cross processes of heat and mass transfer, which is a promising direction for further scientific research.

Keywords

• soil moisture content
• soil temperature
• heat and mass transfer differential equations; one-dimensional non-stationary field
• soil
• radiant heating
• error function