Analytical Solution of the Transient Response of Gas-to-Gas Crossflow Heat Exchanger With Both Fluids Unmixed

1986 ◽  
Vol 108 (4) ◽  
pp. 722-727 ◽  
Author(s):  
D. D. Gvozdenac
Keyword(s):  
Heat Exchanger ◽  
Bessel Functions ◽  
Special Functions ◽  
Time Varying ◽  
Modified Bessel Functions ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Temperature Distributions ◽  
The Mean ◽  
Mixed Fluid

The dynamic response of a single-pass crossflow heat exchanger with both fluids unmixed to arbitrary time varying inlet temperatures of fluids is investigated analytically. The initial spatial temperature distribution of the heat exchanger core is arbitrary as well. Analytical solutions for temperature distributions of both fluids and the wall as well as the mean mixed fluid temperatures at the exit are presented. The solutions are found by using Laplace transform method and special functions in the form of series of modified Bessel functions.

scholarly journals Analytic approximations for special functions, applied to the modified Bessel functions I2(x) and I2/3(x)

2018 ◽  
Vol 11 ◽  
pp. 1028-1033 ◽  
Author(s):  
Pablo Martin ◽  
Jorge Olivares ◽  
Fernando Maass ◽  
Elvis Valero
Keyword(s):  
Bessel Functions ◽  
Special Functions ◽  
Modified Bessel Functions ◽  
Analytic Approximations

Special functions, infinite divisibility and transcendental equations

1979 ◽  
Vol 85 (3) ◽  
pp. 453-464 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
C. Ping May
Keyword(s):  
Bessel Functions ◽  
Special Functions ◽  
Infinite Divisibility ◽  
Probability Density Functions ◽  
Integral Representations ◽  
Density Functions ◽  
Modified Bessel Functions ◽  
Explicit Formulas ◽  
Linear Combinations ◽  
Transcendental Equations

AbstractWe establish integral representations for quotients of Tricomi ψ functions and of several quotients of modified Bessel functions and of linear combinations of them. These integral representations are used to prove the complete monotonicity of the functions considered and to prove the infinite divisibility of a three parameter probability distribution. Limiting cases of this distribution are the hitting time distributions considered recently by Kent and Wendel. We also derive explicit formulas for the Kent–Wendel probability density functions.

Effect of the Thermal Capacitance of Contained Fluid on Performance of Symmetric Regenerators

1987 ◽  
Vol 109 (3) ◽  
pp. 563-568 ◽  
Author(s):  
F. E. Romie
Keyword(s):  
Heat Exchanger ◽  
Laplace Transform ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Regenerative Heat ◽  
Regenerative Heat Exchanger ◽  
Thermal Capacitance ◽  
The Laplace Transform ◽  
System Equations ◽  
Usual Case

The operation of the symmetric counterflow regenerative heat exchanger is described for conditions under which the thermal capacitance of the contained fluid cannot, as is the usual case, be set equal to zero. The solution of the system equations is found by use of the Laplace transform method. The thermal effectiveness is presented for a range of parameters believed to cover most applications of the symmetric regenerator.

Calculating exit times for series Jackson networks

1987 ◽  
Vol 24 (1) ◽  
pp. 226-234 ◽  
Author(s):  
William A. Massey
Keyword(s):  
Bessel Functions ◽  
Transition Probabilities ◽  
Special Functions ◽  
Exit Time ◽  
Modified Bessel Functions ◽  
Exit Times ◽  
Jackson Network ◽  
Jackson Networks ◽  
Positive Orthant ◽  
New Family

We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N-dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M/M/1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jackson network with N nodes. These special functions allow us to derive asymptotic expansions for the taboo transition probabilities, as well as for the tail of the exit-time distribution.

Calculating exit times for series Jackson networks

1987 ◽  
Vol 24 (01) ◽  
pp. 226-234 ◽  
Author(s):  
William A. Massey
Keyword(s):  
Bessel Functions ◽  
Transition Probabilities ◽  
Special Functions ◽  
Exit Time ◽  
Modified Bessel Functions ◽  
Exit Times ◽  
Jackson Network ◽  
Jackson Networks ◽  
Positive Orthant ◽  
New Family

We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N-dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M/M/1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jackson network with N nodes. These special functions allow us to derive asymptotic expansions for the taboo transition probabilities, as well as for the tail of the exit-time distribution.

scholarly journals On Applications of Some Special Functions in Statistics

2020 ◽  
Vol 8 (6) ◽  
pp. 1902-1908
Keyword(s):  
Characteristic Function ◽  
Laplace Transform ◽  
Bessel Functions ◽  
Special Functions ◽  
Probability Distributions ◽  
Laguerre Polynomials ◽  
Real Life ◽  
Moment Generating Function ◽  
Cumulative Density Function ◽  
Modified Bessel Functions

In this paper we will introduce some probability distributions with help of some special functions like Gamma, kGamma functions, Beta, k-Beta functions, Bessel, modified Bessel functions and Laguerre polynomials and in mathematical analysis used Laplace transform. We will also obtain their cumulative density function, expected value, variance, Moment generating function and Characteristic function. Some characteristics and real life applications will be computed in tabulated for these distributions

A time-varying temperature model of mixing in the English Channel

1975 ◽  
Vol 55 (4) ◽  
pp. 975-992 ◽  
Author(s):  
R. D. Pingree ◽  
Linda Pennycuick ◽  
G. A. W. Battin
Keyword(s):  
Sea Surface ◽  
Time Varying ◽  
English Channel ◽  
Temperature Model ◽  
Satisfactory Explanation ◽  
Monthly Temperature ◽  
Temperature Distributions ◽  
The Mean ◽  
Surface Observations

The most comprehensive hydrographic work on the English Channel, even today, is that of Lumby (1935). Lumby used the surface observations of ships of opportunity (steamers on regular routes) that were gathered over a period of 25 years from 1903 to 1927. The number of observations gathered runs into tens of thousands and these were subdivided into convenient regions for the purpose of constructing an Atlas of sea surface temperature and salinity. The mean monthly values of temperature for each region from which the monthly contours were drawn can be considered as established to within ± 0.2 °C. Despite the fact that these data have been available for half a century no satisfactory explanation for these monthly temperature distributions has been offered. In this paper the role of horizontal turbulence in redistributing the net surface heating to produce these monthly temperature distributions is quantitatively examined.

Analytical Solution of Transient Response of Gas-to-Gas Parallel and Counterflow Heat Exchangers

1987 ◽  
Vol 109 (4) ◽  
pp. 848-855 ◽  
Author(s):  
D. D. Gvozdenac
Keyword(s):  
Transient Response ◽  
Heat Exchangers ◽  
Special Functions ◽  
Dynamic Responses ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Independent Variables ◽  
The Laplace Transform

This paper shows how the transient response of gas-to-gas parallel and counterflow heat exchangers may be calculated by an analytical method. Making the usual idealizations for analysis of dynamic responses of heat exchangers, the problem of finding the temperature distributions of both fluids and the separating wall as well as the outlet temperatures of fluids is reduced to the solution of an integral equation. This equation contains an unknown function depending on two independent variables, space and time. The solution is found by using the method of successive approximations, the Laplace transform method, and special functions defined in this paper.

scholarly journals Study of composite fractional relaxation differential equation using fractional operators with and without singular kernels and special functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Azhar Ali Zafar ◽  
Jan Awrejcewicz ◽  
Olga Mazur ◽  
Muhammad Bilal Riaz
Keyword(s):  
Differential Equation ◽  
Special Functions ◽  
Order Derivative ◽  
Laplace Transform Method ◽  
Derivative Operator ◽  
Transform Method ◽  
Integer Order ◽  
The Laplace Transform ◽  
Singular Kernels ◽  
Fractional Relaxation

AbstractOur aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of the non-integer order derivative operator $D_{t}^{\alpha }$ D t α , more specifically we employ the definitions of Caputo, Caputo–Fabrizio and Atangana–Baleanu of non-integer order derivative operators. We apply the Laplace transform method to solve the problem and express our solutions in terms of Lorenzo and Hartley’s generalised G function. Furthermore, the effects of the parameters involved in the model are graphically highlighted.

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