6.Heat Transfer
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Heat transfer 2 3 Conduction—when heat transfer occurs through a substance without any mo ti on of th e sub stance, th en th e mod e of heat tr an sf er is ca ll ed conduction. Convection—if heat transfer through a substance is due to the movements of the substance, then it is called convection heat transfer. Radiation—when the heat is transferred without any medium, i.e. in the vacuum. Fourier’s law of heat conduction—it states that one-dimensional steady state fl ow of heat fl ow due to conduction per unit area is direct ly proportiona l to the temperature gradient. (i.e. dx dt α A Q ) Newton’s law of cooling—it states that the rate of heat transfer from a solid surface of area A, at a temperature t w to a fluid at a temperature t f , is giver by: Q = hA (t w - t f ) Critical insulation—the critical radius of the insulation is defined as the outer radius of insulation which gives maximum heat flow. Nusselt number: k hl N u = Prandtl number : k μ C P P r = Stefan Boltzman law—it states that the total emission from a black body per un it area per un it time is pr oport ion al to the four th po wer of the absolute temperature of the body. Mathematical expression for this law is E b = σ T 4 ; where σ=Stefan-Boltzman constant = 4.97*10 -8 Kirchhoff’s law—it states that the total emissive power for any body at a giv en temper ature is equal to its absorpt ivi ty mu ltip lied by the total emissive power of a perfect black body at the same temperature. Emissivity—it is defined as the ratio of the total emissive power of a body to the total emissive power of a black body. Thermoel ect ric phenomena—when two dissimilar metals or semicon du ctors are connected an d th e ju nc ti on hel d at dif fe rent temperature, five phenomena take place simultaneo usly: Seebeck e ffe ct—if E an d T ar e the emf outpu t and the temperature Δ Δ difference of the junction, then T E ∆ ∝ ∆ . The proportionality constant is denoted by, seebeck coefficient T E ab ∆ ∆ = ∝ Pel tier eff ect —if dir ect current is passed throu gh a pair of dis similar metals, there is heating at one junction, cooling at the other depending upon the material combinations. Peltier varied the current I and observed the heating and cooling rate Q for different sets of elements. It is found that: I Q ∝ Thomson effect—when a current passes through a single conductor having a temperature gradient, heat transfer is giving by: dx dT * I τ = dx dQ Short note on Mechanical Engineering Prepared by: Engr. Mohammad Ala Uddin
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Heattransfer
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Conduction—when heat transfer occurs through a substance without anymotion of the substance, then the mode of heat transfer is calledconduction.
Convection—if heat transfer through a substance is due to themovements of the substance, then it is called convection heat transfer.
Radiation—when the heat is transferred without any medium, i.e. in thevacuum.
Fourier’s law of heat conduction—it states that one-dimensional steadystate flow of heat flow due to conduction per unit area is directly
proportional to the temperature gradient. (i.e.dx
dtα
A
Q)
Newton’s law of cooling—it states that the rate of heat transfer from asolid surface of area A, at a temperature tw to a fluid at a temperature tf , isgiver by: Q = hA (tw- tf )
Critical insulation—the critical radius of the insulation is defined as theouter radius of insulation which gives maximum heat flow.
Nusselt number:k
hl N u =
Prandtl number:k
μC P
P r =
Stefan Boltzman law—it states that the total emission from a black bodyper unit area per unit time is proportional to the fourth power of theabsolute temperature of the body. Mathematical expression for this law isEb = σ T4; where σ=Stefan-Boltzman constant = 4.97*10-8
Kirchhoff’s law—it states that the total emissive power for any body at agiven temperature is equal to its absorptivity multiplied by the totalemissive power of a perfect black body at the same temperature.
Emissivity—it is defined as the ratio of the total emissive power of a bodyto the total emissive power of a black body.
Thermoelectric phenomena—when two dissimilar metals orsemiconductors are connected and the junction held at differenttemperature, five phenomena take place simultaneously:
Seebeck effect—if E and T are the emf output and the temperatureΔ Δ
difference of the junction, then T E ∆∝∆ .
The proportionality constant is denoted by, seebeck coefficient T
E ab
∆
∆=∝
Peltier effect—if direct current is passed through a pair of dissimilarmetals, there is heating at one junction, cooling at the other dependingupon the material combinations. Peltier varied the current I and observedthe heating and cooling rate Q for different sets of elements. It is found
that: I Q ∝
Thomson effect—when a current passes through a single conductor having
a temperature gradient, heat transfer is giving by: dx
dT*Iτ=dx
dQ
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Heattransfer
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Where is the Thomson coefficient and dQ/dx is the Thomson heatτ transfer per unit length.
Joule effect—when electrical current I flow through a conductor of resistance R, there is dissipation of electrical energy. This is well known
joule effect. The energy dissipated is given by: q j = I2R
Fourier effect—if the ends of any element are maintained at differenttemperatures, the heat transfer from the hot end to the cold end is relatedby: Qcond = U (Th-Tc) where, U=kA/L
The cooling and heating effects due to thermoelectric effects are given by:Qc = αab ITc;
Q
h = αab ITh
Short note on Mechanical Engineering Prepared by: Engr. Mohammad Ala Uddin
