Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

2021 ◽  
Vol 86 (2) ◽  
pp. 39-49
Author(s):  
Sudi Mungkasi
Keyword(s):  
Steady State ◽  
Human Body ◽  
Diffusion Problem ◽  
State Condition ◽  
Unsteady State ◽  
Steady State Condition ◽  
Drug Diffusion ◽  
Dermal Layer ◽  
Drug Concentrations ◽  
Proposed Model

We consider the problem of drug diffusion in the dermal layer of human body. Two existing mathematical models of the drug diffusion problem are recalled. We obtain that the existing models lead to inconsistent equations for the steady state condition. We also obtain that solutions to the existing models are unrealistic for some cases of the unsteady state condition, because negative drug concentrations occur due to the inappropriate assumption of the model. Therefore, in this paper, we propose a modified mathematical model, so that the model is consistent, and the solution is nonnegative for both steady and unsteady state conditions of the drug diffusion problem in the dermal layer of human body. For the steady state condition, the exact solution to the proposed model is given. For unsteady state condition, we use a finite difference method for solving the models numerically, where the discretisation is centred in space and forward in time. Simulation results confirm that our proposed model and method preserve the non-negativity of the solution to the problem, so the solution is more realistic than that of the old model.

Heat transfer characteristics of a composite radiant wall under cooling/heating conditions

2019 ◽  
Vol 29 (8) ◽  
pp. 1155-1168
Author(s):  
S. Y. Qin ◽  
Y. A. Wang ◽  
S. Gao ◽  
D. G. Xu ◽  
X. Cui ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
State Condition ◽  
Ratio Model ◽  
Steady State Condition ◽  
Proposed Model ◽  
Heat Transfer Capacity ◽  
Large Heat ◽  
Temperature Heating ◽  
Indoor And Outdoor

The radiant wall composited with capillary tubes has been widely applied in heating or cooling systems due to its large heat transfer area, low-temperature heating and high-temperature cooling. In this study, a ratio model of heat transfer in steady-state condition was established, which explores heat transfer capacity from the capillary layer (active layer) towards the indoor and outdoor sides. The experimental data including the radiant surface temperature, the capillary layer temperature and the heat flux distribution were collected in cooling and heating conditions. The proposed ratio model was validated. The results show that the fluctuation of indoor air temperature is relatively small, suggesting that the radiant system possesses higher stability. Results showed that thermal resistances of the composite radiant wall in summer and winter conditions vary greatly due to different moisture contents. With the continuation of the system operation, the calculated values from the ratio model under the steady-state condition were more consistent with average values obtained from experiments under unsteady-state conditions, indicating that the overall heat transfer performance of the composite radiant wall could be properly evaluated by the proposed model in engineering applications.

Mathematical Simulation of Solid-Liquid Diffusion in Continuous Countercurrent Extraction Process, Part I - Modeling Development

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Waigoon Rittirut ◽  
Chakrit Thongurai ◽  
Chairat Siripatana
Keyword(s):  
Steady State ◽  
Numerical Method ◽  
Numerical Solutions ◽  
State Condition ◽  
Unsteady State ◽  
Countercurrent Extraction ◽  
Steady State Condition ◽  
Difference Formula ◽  
Continuous Countercurrent Extraction ◽  
Continuous Countercurrent

This work extends the development of backmixing-diffusion model by further removal of some assumptions from the previous works. The model covers for steady and unsteady state conditions in continuous countercurrent extraction and will be available for simulation purpose for reversing continuous countercurrent extractor (RCCE) in a more realistic ways, especially in beverage juice production. Solution of the modeling was carried out by numerical method, namely, an implicit finite difference. For the unsteady state condition, the Crank-Nicholson method was selected for calculation due to its stability; for the steady state one, the selected numerical method was center-difference formula with second order of magnitude of error, cooperated with Richardson’s extrapolation. Matrix inversions were done by Gauss Jordan method. Considerable verification was made by assuring the accuracy and stability of numerical method for both steady and unsteady state conditions in a practical range. It was found that the solution obtained from the developed model with aforementioned numerical method compared well with the well-established analytical solution whenever they are available. Generally, the numerical solutions gave high accuracy for the steady state condition, while still being acceptable for practical purpose.

Continuous determination of the volume of a space in a non steady state condition

1974 ◽  
Vol 36 (1) ◽  
pp. 59-66
Author(s):  
Oscar A. Gómez-Poviña ◽  
Carmen Sainz de Calatroni ◽  
Susana Orden de Puhl ◽  
Mariano J. Guerrero
Keyword(s):  
Steady State ◽  
State Condition ◽  
Steady State Condition ◽  
Continuous Determination

An Approach for Snaky Well Productivity under Steady-State Condition

2006 ◽  
Author(s):  
Zhilin Qi ◽  
Zhimin Du ◽  
Baosheng Liang ◽  
Yong Tang ◽  
Shouping Wang ◽  
...  
Keyword(s):  
Steady State ◽  
State Condition ◽  
Well Productivity ◽  
Steady State Condition

VIBRATIONS OF THE CLOSED FRAME STRUCTURES IN A STEADY-STATE CONDITION

Akustika ◽  
2021 ◽  
pp. 4-7
Author(s):  
Veronika Krutova ◽  
Besarion Meskhi
Keyword(s):  
Steady State ◽  
State Condition ◽  
Frame Structures ◽  
Steady State Condition ◽  
Load Bearing ◽  
Gantry Cranes

The load-bearing frames of the technological machinery of various functional purposes, such as bridge and gantry cranes, locomotives, motor locomotives, etc., are energetically closed rod systems [1-10].

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