• 대한수학회지
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• 제55권6호
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• pp.1285-1303
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• 2018

This note is motivated by gradient estimates of Li-Yau, Hamilton, and Souplet-Zhang for heat equations. In this paper, our aim is to investigate Yamabe equations and a non linear heat equation arising from gradient Ricci soliton. We will apply Bochner technique and maximal principle to derive gradient estimates of the general non-linear heat equation on Riemannian manifolds. As their consequence, we give several applications to study heat equation and Yamabe equation such as Harnack type inequalities, gradient estimates, Liouville type results.

• 대한기계학회논문집
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• 제6권3호
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• pp.211-221
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• 1982

Numerical analysis has been made on the heat transfer of two dimensional turbulent channel with a slat type blockage. Especially the effects of the height of slat and Reynolds number on the heat transfer characteristics of channel wall have been investigated. The methods of accelerating the convergence of the numerical solution of governing differential equation have been also examined. Line-by-line iterative method shows higher convergence rate than point-by-point iterative method for solution of both momentum equation and energy equation. The results show that the ratio of heat transfer coefficient of the wall near the blockage to that of the fully developed flow increase with increasing the ratio of blockage to channel height and decreasing the Reynolds number. These trends of variation of heat transfer coefficient with respect to the height of slat and Reynolds number agree with those of Sparrow's experiment on the pipe flow with slat type blockage.

• 오토저널
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• 제4권2호
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• pp.58-68
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• 1982

It is well known to diesel engineers that the heat release pattern is one of the most important factors affecting engine performance. Thorough research in heat release pattern has materially helped the progress in high-speed diesel engine development . This paper is based on the research conducted at KAIST and Daewoo Heavy Industry last year. The purpose of this paper is to determine the heat release pattern in combustion chamber of MAN M type, the famous low-noise engine. Thermodynamic cycle simulation was performed using Whitehous-Way's heat release pattern with modified coefficients and Annand's heat transfer model. Instantaneous temperature and pressure of gas in cylinder could be determined by the numerical solution of simultaneous equation of mass conservation, equation of energy conservation, and state equation of ideal gas. Calculated results were compared with measured values in some details emphasizing upon the factors affecting rate of heat release. The agreement was fairly good and revealed why M type should have lower burning velocity at the early part of combustion in spite of high injection rate. Additional results by parametric studies were given in relation to fuel injection conditions for further application to engine development.

• Journal of Advanced Marine Engineering and Technology
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• 제40권5호
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• pp.389-396
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• 2016

The theory of Fourier heat conduction predicts accurately the temperature profiles of a system in a non-equilibrium steady state. However, in the case of transient states at the nanoscale, its applicability is significantly limited. The limitation of the classical Fourier's theory was overcome by C. Cattaneo and P. Vernotte who developed the theory of non-Fourier heat conduction in 1958. Although this new theory has been used in various thermal science areas, it requires considerable mathematical skills for calculating analytical solutions. The aim of this study was the identification of a newer and a simpler type of solution for the hyperbolic partial differential equations of the non-Fourier heat conduction. This constitutes the first trial in a series of planned studies. By inspecting each term included in the proposed solution, the theoretical feasibility of the solution was achieved. The new analytical solution for the non-Fourier heat conduction is a simple exponential function that is compared to the existing data for justification. Although the proposed solution partially satisfies the Cattaneo-Vernotte equation, it cannot simulate a thermal wave behavior. However, the results of this study indicate that it is possible to obtain the theoretical solution of the Cattaneo-Vernotte equation by improving the form of the proposed solution.

• 대한수학회지
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• 제44권3호
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• pp.585-603
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• 2007

The author studies the local $H\ddot{o}lder$ convergence of the solution to an evolution equation of p-Ginzburg-Landau type, to the heat flow of the p-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

• 대한설비공학회지:설비저널
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• 제7권1호
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• pp.13-19
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• 1978

An experiment has been performed of find a temperature distribution of the circulating fluid in a packed bed thermal storage system when the inlet fluid temperature is constant. The thermal storage system is a specific-heat type in which the circulating fluid, hot air, exchanges heat directly with the heat storage materials, glass balls, in a heat storage bin. An empirical equation which includes two dimensionless variables $t^*\;and\;T_f^*$, is obtained. Also, heat storage efficiency and heat storage capacity are calculated from this equation, The heat transfer coefficient calculated by the suggested equation was compared with the value determined by the existing empirical equation.

• 한국컴퓨터정보학회논문지
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• 제20권12호
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• pp.67-74
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• 2015

The heat conduction equation, a type of a Poisson equation which can be applied in various areas of engineering is calculating its value with the iteration method in general. The equation which had difference discretization of the heat conduction equation is the simultaneous equation, and each line has the characteristic of expressing in sparse matrix of the equivalent number of none-zero elements with neighboring grids. In this paper, we propose a data structure for sparse matrix that can calculate the value faster with less memory use calculate the heat conduction equation. To verify whether the proposed data structure efficiently calculates the value compared to the other sparse matrix representations, we apply the representative iteration method, CG (Conjugate Gradient), and presents experiment results of time consumed to get values, calculation time of each step and relevant time consumption ratio, and memory usage amount. The results of this experiment could be used to estimate main elements of calculating the value of the general heat conduction equation, such as time consumed, the memory usage amount.

• 대한수학회지
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• 제57권2호
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• pp.313-329
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• 2020

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.

• International Journal of Air-Conditioning and Refrigeration
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• 제13권2호
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• pp.83-88
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• 2005

This study investigates the air leakage and heat transfer characteristics of a commercially available rotary-type air-to-air heat exchanger with a fiber polyester matrix. Crossover leakage between the exhaust and supply air is measured using a tracer gas method for various ventilation rates and rotational speeds of the wheel. A correlation equation for the leakage is obtained by summing up pressure leakage and carryover leakage. The pressure leakage is observed to be a function of ventilation rate only, and the carryover leakage is found to be a linear function of wheel speed. The real efficiency of the heat exchanger can be obtained from its apparent efficiency by taking into account the leakage ratio. The heat recovery efficiency decreases, as the ventilation rate increases. As the wheel speed increases, however, the efficiency increases initially but reaches a constant value for the speeds over 10rpm.

• 설비공학논문집
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• 제16권12호
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• pp.1197-1203
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• 2004

This study investigates the air leakage and heat transfer characteristics of a rotary-type air-to-air heat exchanger with a fiber polyester matrix. The leakage airflow rate is measured using a tracer gas method for various ventilation rates and rotational speeds of the matrix wheel. A correlation equation for air leakage is obtained by combining the pressure leakage and the carryover leakage. The pressure leakage is observed to be a function of ventilation airflow rate only, and the carryover leakage is found to be a linear function of rotational speed. The real efficiency of the heat exchanger can be obtained from its apparent efficiencies by taking into account the air leakage ratio. As the ventilation rate increases, the heat recovery efficiency decreases. As the rotational speed of the matrix increases, the efficiency increases initially but reaches a constant value for the rotational speeds over 10 rpm.