Effect of heat transfer on the performance of a thermoelectric heat pump driven by a thermoelectric generator Lingen Chen*, Fankai Meng, and Fengrui Sun Postgraduate School, Naval University of Engineering, Wuhan 430033, P.R. China. Recibido el 13 de enero de 2009; aceptado el 9 de junio de 2009 A model of a thermoelectric heat pump driven by a thermoelectric generator with external heat transfer irreversibility is proposed. The performance of the combined thermoelectric heat pump device obeying Newton’s heat transfer law is analyzed using the combination of ﬁnite time thermodynamics and non-equilibrium thermodynamics. Two analytical formulae for heating load versus working electrical current, and the coefﬁcient of performance (COP) versus working electrical current, are derived. For a ﬁxed total heat transfer surface area of four heat exchangers, the allocations of the heat transfer surface area among the four heat exchangers are optimized for maximizing the heating load and the COP of the combined thermoelectric heat pump device. For a ﬁxed total number of thermoelectric elements, the ratio of the number of thermoelectric elements of the generator to the total number of thermoelectric elements is also optimized for maximizing both the heating load and the COP of the combined thermoelectric heat pump device. The inﬂuences of thermoelectric element allocation and heat transfer area allocation are analyzed by detailed numerical examples. The optimum working electrical currents for maximum heating load and maximum COP at different total numbers of thermoelectric elements and different total heat transfer areas are provided, respectively. Keywords: Combined thermoelectric device; thermoelectric generator; thermoelectric heat pump; heat transfer; ﬁnite-time thermodynamics; non-equilibrium thermodynamics. En el presente trabajo se propone un modelo de una bomba de calor termoel´ ctrica controlada por un generador termoel´ ctrico con transe e ferencia de calor externa irreversible. Se analiza el desempe˜ o de la bomba de calor combinada, la cual obedece a la ley de Newton de n transferencia de calor, usando la combinaci´ n de termodin´ mica de tiempo ﬁnito y termodin´ mica fuera de equilibrio. Se obtienen dos o a a f´ rmulas anal´ticas: para la carga de calor y para el coeﬁciente de desempe˜ o, ambas en funci´ n del trabajo de corriente el´ ctrica. Se realiza o ı n o e una optimizaci´ n de la posici´ n de la superﬁcie de transferencia de calor entre cuatro intercambiadores para maximizar la carga de calor y el o o coeﬁciente de desempe˜ o de la bomba de calor termoel´ ctrica combinada. Para este mismo ﬁn, se optimiza tambi´ n la raz´ n entre el n´ mero n e e o u de elementos termoel´ ctricos del generador y el total. Se analiza, mediante ejemplos num´ ricos detallados, la inﬂuencia entre las posiciones e e ´ del elemento termoel´ ctrico y del area de transferencia de calor. e Descriptores: Dispositivo termoel´ ctrico combinado; generador termoel´ ctrico; bomba de calor termoel´ ctrica; transferencia de calor; tere e e modin´ mica de tiempo ﬁnito; termodin´ mica fuera de equilibrio. a a PACS: 05.30-d; 05.70.-a; 05.60.Gg

1. Introduction
Semiconductor thermoelectric power generation, based on the Seebeck effect, and semiconductor thermoelectric cooling, based on the Peltier effect, have very interesting capabilities with respect to conventional power generation, cooling systems and heating systems [1-3]. The absence of moving components results in an increase in reliability, a reduction in maintenance, and an increase in system life; the modularity allows for application in a wide-scale range without significant losses in performance; the absence of a working ﬂuid prevents dangerous environmental leakage; and the noise reduction appears also to be an important feature. Thermoelectric generators, refrigerators, and heat pumps have been used in military, aerospace, instruments, and industrial or commercial products, as power...

...Mechanisms of HeatTransfer
Prepared by: Ms. Ana Antoniette C. Illahi
1
Conduction
• conduction (or heat conduction) is the transfer of thermal energy between regions of matter due to a temperature gradient. Heat spontaneously flows from a region of higher temperature to a region of lower temperature, and reduces temperature differences over time, approaching thermal equilibrium.
Prepared by: Ms. Ana Antoniette C. Illahi
2
(Heat Current in Conduction)
• • • • • • • • H - Heat Current dQ – Quantity of Heat dt – Time dQ/dt – the rate of heat flows A – Cross sectional area (TH - TC) – Temperature difference L – Length k – constant (thermal conductivity)
Prepared by: Ms. Ana Antoniette C. Illahi
H = dQ/dt = kA (TH - TC)/L
3
Conduction
H = dQ/dt = -kA (dT/ dx) H = A(TH - TC) / R R = L/ k R – thermal resistance
Prepared by: Ms. Ana Antoniette C. Illahi 4
Thermal Conductivities k (W/m oC)
Metals Aluminum Brass Copper Lead Mercury Silver Steel 205.0 109.0 385.0 34.7 8.3 406.0 50.2
Prepared by: Ms. Ana Antoniette C. Illahi 5
Solids (representative values) Brick. Insulating 0.15 Brick. red 0.6
Concrete 0.8
Cork Felt Fiberglass Glass Ice Rock wool Styrofoam Wood
0.04 0.04 0.04 0.8 1.6 0.04 0.01 0.12-0.04
Prepared by: Ms. Ana Antoniette C. Illahi 6
Gases Air Argon Helium Hydrogen Oxygen
0.024 0.016...

...HEATTRANSFERHeattransfer, also known as heat flow, heat exchange, or simply heat, is the transfer of thermal energy from one region of matter or a physical system to another. When an object is at a different temperature from its surroundings, heattransfer occurs so that the body and the surroundings reach the same temperature at thermal equilibrium. Such spontaneous heattransfer always occurs from a region of high temperature to another region of lower temperature, as required by the second law of thermodynamics.
In engineering, energy transfer by heat between objects is classified as occurring by heat conduction, also called diffusion, of two objects in contact; fluid convection, which is the mixing of hot and cold fluid regions; or thermal radiation, the transmission of electromagnetic radiation described by black body theory. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heattransfer.
II. THREE MODES OF HEATTRANSFER
1. Conduction
In heattransfer, conduction (or heat conduction) is the transfer of thermal energy between neighboring molecules in a substance...

...DEFINITION OF HEATTRANSFER |
Heattransfer is energy in transit due to temperature difference . Whenever there exists a temperature difference in a medium or between media, heattransfer must occur. The basic requirement for heattransfer is the presence of temperature difference . There can be no net heattransfer between two mediums that are at the same temperature. The temperature difference is the driving force for heattransfer, just as the voltage difference is the driving force for electric current flow and pressure difference is the driving force for fluid flow. The rate of heattransfer in a certain direction depends on the magnitude of the temperature gradient (the temperature difference per unit length or the rate of change of temperature) in that direction. The larger the temperature gradient, the higher the rate of heattransfer |
PHYSICAL ORIGINS AND RATE EQUATIONS:It is important to understand the physical mechanisms which underlie the heattransfer modes and that we are able to use the rate equations that quantify the amount of energy being transferred per unit time. Conduction:Conduction can be imagined as a atomic or molecular activity which involves the transfer of energy from the more...

...HeatTransfer Through Jacket
Objective
The objective of this example is to analyze heattransfer in a pilot plant using simulation models. The first step is to use pilot plant data to calculate heattransfer parameters. The second part involves using simulation models to examine the trade-off between jacket parameters and heating times.
Process Description
Assumptions: The stirred tank is assumed to be perfectly mixed. The contributions of agitator work, heat loss to environment, and evaporation to the energy and mass balances are assumed to be negligible.
Variables and Parameters: , Mass of bulk liquid; , heat capacity; , Temperature of bulk liquid; , flow rate of heattransfer fluid in jacket; , heat capacity of heattransfer fluid in jacket; , jacket inlet temperature; , jacket outlet temperature, , overall heattransfer coefficient times area.
Balance Equations:
where,
Pilot Plant Data: The following data relating bulk liquid temperatures to the jacket temperature is available from pilot plant tests.
We want to use this information to determine the UA values for the stirred tank and to study the impact of jacket parameters on heating times.
Process Parameters
The process parameters and initial conditions for...

...Set – 1 MEC301: HeatTransfer
Q.1 The slab shown in the figure is embedded on five sides in insulation materials. The sixth side is exposed to an ambient temperature through a heattransfer coefficient. Heat is generated in the slab at the rate of 1.0 kW/m3. The thermal conductivity of the slab is 0.2 W/m-K. (a) Solve for the temperature distribution in the slab, noting any assumptions you must make. Be careful to clearly identify the boundary conditions. (b) Evaluate T at the front and back faces of the slab. (c) Show that your solution gives the expected heat fluxes at the back and front faces.
Q.2
Compute overall heattransfer coefficient U for the slab shown in the figure.
Given: Ls = 2 mm = 0.002 m Lc = 3 mm = 0.003 m ks = 17 W/m-K kc = 372 W/m-K Q.3 A 4 mm diameter spherical ball at 50oC is covered by a 1 mm thick plastic insulation (k = 0.13 W/m-K). The ball is exposed to a medium at 15oC, with a combined convection and radiation heattransfer coefficient of 20 W/m2-K. Determine if the plastic insulation on the ball will help or hurt heattransfer from the ball. Q.4 Prove that if k varies linearly with T in a slab, and if heattransfer is one-dimensional and steady, then q may be evaluated precisely using k evaluated at the mean temperature in the slab.
Q.5...

...Heattransfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy and heat between physical systems. Heattransfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heattransfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.
Heat conduction, also called diffusion, is the direct microscopic exchange of kinetic energy of particles through the boundary between two systems. When an object is at a different temperature from another body or its surroundings, heat flows so that the body and the surroundings reach the same temperature, at which point they are in thermal equilibrium. Such spontaneous heattransfer always occurs from a region of high temperature to another region of lower temperature, as described by the second law of thermodynamics.
Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid. The flow of fluid may be forced by external processes, or sometimes (in...

...HeatTransfer by Convection
Ch.E. 324 Based on the lecture notes of Prof. Alberto Laurito
Learning Objectives
At the end of the discussion you should be able to: • differentiate convection from conduction • identify whether a heattransfer by convection is forced or natural • solve individual film coefficients(h) and overall heattransfer coefficients(U) in a double pipe heat exchanger.
Convection
- heat is transferred due to a mixing process between cold and hot portions of a fluid. Two Types of Convection 1. Forced convection - mixing is due to mechanical means such as pumps, compressors, agitators. 2. Natural convection - mixing is due to density difference arising from temperature gradient.
Convection
APPLICATIONS: 1. Double pipe heat exchanger* 2. Shell and tube heat exchanger 3. Bank of tubes 4. Film type condensation
Film Concept
Metal wall
Ti
Cold fluid Tb To Ta Hot fluid
• When a rapidly moving fluid comes in contact with a stationary phase, a thin film is formed.
q
Inner film
•The thin film acts as a boundary layer between the moving fluid and the wall.
•The thin film contributes an additional resistance to heat flow.
outer film
Temperature profile for heattransfer by
convection from one fluid to another
Film Concept
Metal wall Air...

...Unsteady State HeatTransfer laboratory were to study the rates of heattransfer for different materials of varying sizes, to develop an understanding of the concepts of forced and free convection and to determine the heattransfer coefficients for several rods. These objectives were met by heating several rods and allowing them to cool through free convection in air, free convection in water and forced convection in water- while monitoring their change in temperature over change in time.
Seven heattransfer coefficients were determined during the laboratory for various rods. A copper rod underwent free convection in air, free convection in water and forced convection in water. The measured heattransfer coefficients for the copper trials were 10.13 W/m2K, 438.43 W/m2K and 1715.69 W/m2K, respectively. These results supported theory that convection occurs for quickly in denser mediums and when it has a driving force. Two stainless steel rods underwent forced convection in water; the large rod had an experimental heattransfer coefficient of 1704.42 W/m2K while the small one had 1817.43 W/m2K. The smaller rod was expected to have the larger heattransfer coefficient since it has a smaller surface area. The results of the stainless steel rods therefore also supported theory....