Analytical solution for the heat and mass transfer of spherical grains during drying

Wang, Chen; Wang, Shugang; Xu, Jian; Zhang, Tengfei; Li, Zhixiong

doi:10.1016/j.biosystemseng.2021.11.006

Cited by 8 publications

(11 citation statements)

References 34 publications

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“…For a nonhomogeneous boundary condition, an auxiliary function ω ( r , τ ) to satisfy the given boundary condition and express the solution to the problem as the sum of two functions: T ( r , τ ) = U ( r , τ ) + W ( r , τ ). The corresponding auxiliary function W ( r , τ ) is constructed for the third kind of boundary condition [22]. The function U ( r , τ ) represents heat conduction when heat sources presented within the kernel and boundary conditions are zero.…”

Section: A Developed Solutionmentioning

confidence: 99%

“…Moreover, the solution U ( r , τ ) can be expressed as the sum of two functions: U ( r , τ ) = U 1 ( r , τ ) + U 2 ( r , τ ), where U 1 ( r , τ ) is the solution of the homogeneous equation with the given initial conditions and zero boundary conditions, and U 2 ( r , τ ) is the solution of the nonhomogeneous equation with zero initial and boundary conditions. By using the variable separation approach, PDEs for U 1 ( r , τ ) and U 2 ( r , τ ) can be solved directly [22]. More details about the derivation are provided in the Appendix.…”

Section: A Developed Solutionmentioning

confidence: 99%

“…The variation of thermal conductivity of the grain kernel with time can be obtained by using equations ( 12) and (22). As a result, the thermal conductivity can be expressed as a piecewise constant function of time as the following:…”

Section: Case Studymentioning

confidence: 99%

“…An auxiliary function W(r,τ) was introduced to satisfy the given nonhomogeneous boundary condition of Equation ( 14) [22], and T(r,τ) was divided as follows T r τ W r τ U r τ ( , ) = ( , ) + ( , ).…”

Section: Appendix a Solving For Case (1) The Bulk Density As A Piecew...mentioning

confidence: 99%

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Integration of recent developments in transient heat conduction and mass transfer for solid sphere into teaching

Wang

Jiang

et al. 2022

Comp Applic In Engineering

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To bring research and teaching together in engineering education, the term scholarship can be categorized into four types: research scholarship, applied research scholarship, integrative research scholarship, and teaching scholarship. Linking traditional research and classroom-oriented teaching scholarship is a common and recurring challenge for many academics and active involvement in the latest research developments would directly improve the quality of teaching. In the case of research-teaching of a heat transfer course, the teaching methodologies integrating academic research offer a great experience for students to learn various heat transfer concepts in a limited time frame. From the view of the research-teaching nexus, analytical solving methods introduced in textbooks are reasonable ways to apply the integrated teaching strategies, which is highlighted by their fast results and versatility. Furthermore, a complete analytical solution to the subject matter could provide the fundamental knowledge necessary to comprehend the behavior of the associated thermal systems. This article demonstrates an analytical solution to the problem of heat and mass transfer for spherical particles in an airflow field. This investigation elucidates the basic principles in combination with advanced mathematical knowledge learned and its application to frontier research to improve the teaching of heat conduction and enhance the understanding of students at an undergraduate or graduate level. It greatly improves the engagement of students, promoting the theoretical concepts in engineering applications. The introduction of the latest developments in analytical solutions to teaching activities in the classroom will undoubtedly enhance the motivation and the horizon of students. K E Y W O R D Sheat and mass transfer, heat transfer course, integration of research into teaching, scholarship of teaching, solid sphere

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Section: A Developed Solutionmentioning

confidence: 99%

Section: A Developed Solutionmentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

Section: Appendix a Solving For Case (1) The Bulk Density As A Piecew...mentioning

confidence: 99%

See 2 more Smart Citations

Integration of recent developments in transient heat conduction and mass transfer for solid sphere into teaching

Wang

Jiang

et al. 2022

Comp Applic In Engineering

Self Cite

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“…Researchers have explored the diffusion mechanisms of moisture and heat within grains (Jiang et al, 2021; Thorpe et al, 1991), as well as the processes of convective heat and mass transfer at the surface (Mhimid et al, 2000). Numerical simulation methods can be employed to simulate the distribution of moisture and temperature within grain kernels and analyze the variations in heat and mass transfer coefficients (ElGamal et al, 2014; Wang et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Numerical study of heat and mass transfer during drying process of barley grain piles based on the pore scale

Li,

Wang,

Yang

et al. 2023

J Food Process Engineering

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Drying conditions greatly affect the quality of grains, and efforts should be made to minimize the loss of grains during the drying process. In this study, numerical simulations were conducted to investigate the drying behavior of barley at both the particle and grain pile scales by solving the coupled heat and moisture equation. The model was validated using thin‐layer drying experimental results from the literature, and it was found that the simulated values of average moisture content of the grain had a maximum relative error of 7.73% compared to the experimental values. Furthermore, the impact of air temperature and relative humidity on drying was analyzed. The results showed that the heat and mass transfer coefficients of barley grains varied along the surface, the irregularity of the barley grains resulted in an asymmetric distribution of the surface heat transfer coefficient. Regions with lower porosity in the grain pile exhibited lower rates of heat and moisture transfer, particularly in the central area. Moisture transfer within the grain pile dominated the drying time compared to heat transfer. It was also observed that air temperature and relative humidity were the main variables influencing the drying rate of the grains. As the inlet air temperature increased from 45 to 70°C, the drying rate of the grain pile increased from 0.068% to 0.085%(d.b.)/min. Similarly, reducing the relative humidity from 40% to 18% resulted in an increase in the drying rate from 0.062% to 0.075%(d.b.)/min (within the first 10 min).Practical ApplicationsThis study employed numerical simulations to investigate the drying behavior of barley at both the particle scale and grain pile scale. The developed model was validated using experimental data from thin‐layer drying studies, confirming a significant agreement between the simulated and experimental values. Moreover, the study unveiled the impact of air temperature and relative humidity on the drying process. It was observed that regions with lower porosity within the grain pile experienced reduced rates of heat and moisture transfer. Notably, moisture transfer dominates the drying time. Additionally, the study emphasized the substantial influence of air temperature and relative humidity on the drying rates. These findings offer valuable insights for optimizing drying parameters, including air temperature and relative humidity, in order to enhance the efficiency and quality of the barley grain drying process.

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Mathematical Model of Preparing Process of Bulk Cargo for Transportation by Vessel

Polyvoda

Polyvoda²

2022

Lecture Notes in Data Engineering, Computational Intelligence, and Decision Making

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Analytical solution for the heat and mass transfer of spherical grains during drying

Cited by 8 publications

References 34 publications

Integration of recent developments in transient heat conduction and mass transfer for solid sphere into teaching

Integration of recent developments in transient heat conduction and mass transfer for solid sphere into teaching

Numerical study of heat and mass transfer during drying process of barley grain piles based on the pore scale

Mathematical Model of Preparing Process of Bulk Cargo for Transportation by Vessel

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