Analysis of Heat Transfer During Hydrair Cooling of Slab-Shaped Food Products—Part I: Theoretical Investigations

1980 ◽  
Vol 102 (4) ◽  
pp. 761-765 ◽  
Author(s):  
P. M. Abdul Majeed
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Reynolds Number ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Food Products ◽  
Air Cooling ◽  
Theoretical Investigations ◽  
Cooling Speed ◽  
Wetting Liquid

Hydrair cooling of perishable food products is expected to incorporate the advantages of both air cooling and hydrocooling processes. This technique consists of passing cold air over a product which is continuously wetted by a spray of chilled water. In this paper, a mathematical model for the hydrair cooling of slab-shaped food products is proposed. The set of differential equations for heat transfer through the product and the wetting liquid are solved simultaneously, using finite difference method. It is observed that the process of hydrair cooling is advantageous at lower values of the film Reynolds number for higher Biot number values. The cooling speed and the governing parameters are correlated.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

scholarly journals An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

2013 ◽  
Vol 23 (2) ◽  
pp. 357-372 ◽  
Author(s):  
Hasim A. Obaid ◽  
Rachid Ouifki ◽  
Kailash C. Patidar
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Hiv Transmission ◽  
Continuous Model ◽  
Unconditionally Stable ◽  
Theoretical Investigations ◽  
Epidemic Diseases ◽  
Nonstandard Finite Difference

We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.

HEAT TRANSFER IN LARGE RUBBER ELEMENTS THROUGH OF MODELING BY FINITE DIFFERENCE METHOD

2019 ◽  
Author(s):  
Lucas Peixoto ◽  
Ane Lis Marocki ◽  
Celso Vieira Junior ◽  
Viviana Mariani
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method

Parametric Optimization of Thermal Comfort in Extreme Weather Conditions

2019 ◽  
Vol 44 ◽  
pp. 75-90
Author(s):  
A. Oudrane ◽  
Benaoumeur Aour ◽  
Zeghmati Belkacem ◽  
Massaud Hamouda
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Building Materials ◽  
Parametric Optimization ◽  
Weather Conditions ◽  
Climatic Data ◽  
Hot Climate ◽  
Transfer Equations ◽  
The Finite Difference Method

This work focuses on the numerical investigation of different modes of heat exchangebetween the habitat and its environment in an extremely hot climate to optimize thermal comfort.Notably, to optimize habitable comfort, it is essential to model the solar flux and the temperatureabsorbed by the habitat walls. In this context, we have developed an analytical model to predict heatexchange for a habitat in the Adrar region. The heat transfer equations have been established in eachwall of the habitat. These equations were discretized by the finite difference method and solvedusing the Gauss algorithm. The models developed were validated with climatic data measured in theresearch unit ''URER'MS'' in Adrar. The results obtained showed that building materials andextreme weather conditions were the decisive parameters of unwanted overheating.

Heat Transfer During Air Cooling and Storing of Moist Food Products

1974 ◽  
Vol 17 (4) ◽  
pp. 0769-0773 ◽  
Author(s):  
S. Srinivasa Murthy ◽  
M. V. Krishna Murthy ◽  
A. Ramachandran
Keyword(s):  
Heat Transfer ◽  
Food Products ◽  
Air Cooling

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2009 ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Sparse Matrix ◽  
Complex Geometries ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.

Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Rectangular Channels

1987 ◽  
Vol 109 (4) ◽  
pp. 936-942 ◽  
Author(s):  
G. J. Hwang ◽  
F. C. Chou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Numerical Study ◽  
Fully Developed Flow ◽  
Rectangular Channels ◽  
Laminar Convection

This paper presents a numerical study of the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal rectangular channels with uniform heat input axially, In addition to the Prandtl number, the Grashof number Gr+, and the aspect ratio γ, a parameter Kp indicating the significance of wall conduction plays an important role in heat transfer. A finite-difference method utilizing a power-law scheme is employed to solve the system of governing partial differential equations coupled with the equation for wall conduction. The numerical solution covers the parameters: Pr = 7.2 and 0.73, γ = 0.5, 1, and 2, Kp = 10−4–104, and Gr+ = 0–1.37×105. The flow patterns and isotherms, the wall temperature distribution, the friction factor, and the Nusselt number are presented. The results show a significant effect of the conduction parameter Kp.

Study on a New Mathematical Model for Aggregate Air Cooling or Heating

2011 ◽  
Vol 374-377 ◽  
pp. 1882-1886
Author(s):  
Li Juan Wang ◽  
Yan Feng Liu ◽  
Jia Ping Liu ◽  
Fei Lu
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Hydraulic Structure ◽  
Surface Heat ◽  
Air Cooling ◽  
Foundation Engineering ◽  
Heating Capacity ◽  
Surface Heat Transfer Coefficient

Before the construction of hydraulic structure, aggregate must be cooled or heated by air (we call it aggregate air cooling or heating in this paper) or other technologies to the required temperature. Previous model of aggregate air cooling or heating cannot provide the center temperature of each aggregate. So a more accurate mathematical model is developed to determine the thermal performance of aggregate, and the surface heat transfer coefficient of wet aggregate is revised. This model can predict the center temperature of an aggregate and can accurately calculate the cold down time or temperature distribution of aggregate, so that the refrigeration or heating capacity can be reasonably supplied. It’s significant for foundation engineering of hydraulic structure.

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