Analytical Solutions to Coupled Partial Differential Equations Governing Heat and Mass Transfer During Food Drying

2013 ◽  
Vol 5 (5) ◽  
pp. 387-395
Author(s):  
Hongwei Zhang ◽  
Qingying Hu
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Partial Differential ◽  
Coupled Partial Differential Equations

scholarly journals Heat and Mass Transfer Effects on MHD Flow Past an Inclined Porous Plate in the Presence of Chemical Reaction

2020 ◽  
Vol 25 (3) ◽  
pp. 86-102
Author(s):  
A. Sandhya ◽  
G.V. Ramana Reddy ◽  
G.V.S.R. Deekshitulu
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Mhd Flow ◽  
Transfer Effects ◽  
Partial Differential ◽  
Flow Past

AbstractThe impact of heat and mass transfer effects on an MHD flow past an inclined porous plate in the presence of a chemical reaction is investigated in this study. An effort has been made to explain the Soret effect and the influence of an angle of inclination on the flow field, in the presence of the heat source, chemical reaction and thermal radiation. The momentum, energy and concentration equations are derived as coupled second order partial differential equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless partial differential equations can be solved by using a closed analytical method. Numerical results for pertaining parameters, such as the Soret number (Sr), Grashof number (Gr) for heat and mass transfer, the Schmidt number (Sc), Prandtl number (Pr), chemical reaction parameter (Kr), permeability parameter (K), magnetic parameter (M), skin friction (τ), Nusselt number (Nu) and Sherwood number (Sh) on the velocity, temperature and concentration profiles are presented graphically and discussed qualitatively.

MATHEMATICAL MODELLING OF SIMULTANEOUS HEAT AND MASS TRANSFER IN FLUIDIZED BED DRYING OF LARGE PARTICLES

1999 ◽  
Vol 23 (1B) ◽  
pp. 129-145 ◽  
Author(s):  
E. Hajidavaloo ◽  
F. Hamdullahpur
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Fluidized Bed ◽  
Solid Phase ◽  
Variable Mass ◽  
Partial Differential ◽  
Large Particles ◽  
Fluidized Bed Drying

A mathematical model for simulation of simultaneous unsteady heat and mass transfer in fluidized-bed drying of large particles is proposed. A set of coupled non-linear partial differential equations is employed to accurately model the process without using adjustable parameters. A three phase model representing a bubble (dilute) phase, interstitial gas phase and a solid phase is used to describe the thermal and hydrodynamic characteristics of the bed. The bubble and temperature distributions inside the solid phase is applied. The flow field is divided by an orthogonal grid to a finite number of control volumes to simulate the variation of the properties for the three phases in longitudinal direction. The Crank-Nicholson implicit numerical method is applied to solve the set of coupled nonlinear partial differential equations with variable mass and thermal diffusivity for a spherical-shape particle. A pilot-scaled fluidized bed dryer was built to test the results of proposed model with those obtained by experiments using wheat particles as a bed charge. A good agreement between the numerical and experimental results is observed.

scholarly journals A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ji Juan-Juan ◽  
Guo Ye-Cai ◽  
Zhang Lan-Fang ◽  
Zhang Chao-Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Table Lookup ◽  
Exact Analytical Solutions ◽  
Function Solution

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

Lie Group Analysis for a Mixed Convective Flow and Heat Mass Transfer Over a Permeable Stretching Surface with Soret and Dufour Effects

2013 ◽  
Vol 30 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Reda G. Abdel-Rahman ◽  
Ahmed M. Megahed
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Analysis ◽  
Group Method ◽  
Stretching Surface ◽  
Partial Differential ◽  
Soret And Dufour Effects

ABSTRACTThe Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL

2017 ◽  
Vol 59 (2) ◽  
pp. 167-182 ◽  
Author(s):  
H. Y. ALFIFI
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Partial Differential ◽  
Analytical Results ◽  
Transient Solutions ◽  
The Impact

Semi-analytical solutions are derived for the Brusselator system in one- and two-dimensional domains. The Galerkin method is processed to approximate the governing partial differential equations via a system of ordinary differential equations. Both steady-state concentrations and transient solutions are obtained. Semi-analytical results for the stability of the model are presented for the identified critical parameter value at which a Hopf bifurcation occurs. The impact of the diffusion coefficients on the system is also considered. The results show that diffusion acts to stabilize the systems better than the equivalent nondiffusive systems with the increasing critical value of the Hopf bifurcation. Comparison between the semi-analytical and numerical solutions shows an excellent agreement with the steady-state transient solutions and the parameter values at which the Hopf bifurcations occur. Examples of stable and unstable limit cycles are given, and Hopf bifurcation points are shown to confirm the results previously calculated in the Hopf bifurcation map. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document