How does transient heat transfer different from steady heat transfer? How does one-dimensional heat transfer different from two-dimensional?
The term steady implies no change with time at any point within the medium, while transient implies variation with time or time dependence. Therefore, the temperature or heat flux remains unchanged with time during steady heat transfer through a medium at any location.
2 dimensional: The temperature in a medium, in some cases, varies mainly in two primary directions, and the variation of temperature in the third direction (and thus heat transfer in that direction) is negligible. 1 dimensional:
temperature in the medium varies in one direction only and thus heat is transferred in one direction, and the variation of temperature and thus heat transfer in other directions are negligible or zero.
Write down one-dimensional translent heat conduction equation for a long cylinder with constant thermal conductivity and heat generation, and indicate what each variable represents.
$\frac{1}{r}\frac{d}{\text{dr}}\left( r\frac{\text{dT}}{\text{dr}} \right) + \frac{q}{k} = \frac{1}{\alpha}\frac{\text{dT}}{\text{dt}}$ q-density, C-specyfic heat, l-length, g-gravity acc, T-temp, t-time
Consider a medium in which the heat conduction equation is given in it’s simplest form as
$\frac{1}{r}\frac{d}{\text{dr}}\left( \text{kr}\frac{\text{dT}}{\text{dr}} \right) + \frac{d}{\text{dz}}\left( k\frac{\text{dT}}{\text{dz}} \right) + g = 0$ steady, two, variable
How is the boundary condition on an insulated surface expressed mathematically.
T(x,y,z,0)=f(x,y,z)
Explain how the fins enhance heat transfer from surface. Also, explain how the addition of fins may actually decrease heat transfer from a surface.
Fins enhance heat transfer from a surface by exposing a large surface area to convection and radiation. Revers connections of additional fins can reduce heat transfer and power.
What is the physical significance of the Prandtl number ? Does the value of the Prandtl number depends on the type of flow geometry? Does the Prandl number of air change with pressure and temp?
$Pr = \frac{\text{molecular\ diffusivity\ of\ monument}}{\text{molecular\ diffusivity\ of\ heat}} = \frac{v}{\alpha} = \frac{\text{μCp}}{k} = \frac{\text{μqCp}}{\text{gk}}$ Not depand of any types of flow, change with temp and pressure.
For steady two-dimensional flow, what are the boundary layer approximations?
Continuty $\frac{\text{du}}{\text{dx}} + \frac{\text{dv}}{\text{dy}} = 0\ $x-monumentum $q\left( u\frac{\text{du}}{\text{dx}} + v\frac{\text{du}}{\text{dy}} \right) = u\ \frac{d^{2}u}{uy^{2}} - \frac{\text{dP}}{dy^{2}}$ Energy
$\text{qCp}\left( u\frac{\text{dT}}{\text{dx}} + v\frac{\text{dT}}{\text{dy}} \right) = k\left( \frac{d^{2}T}{dx^{2}} + \frac{d^{2}T}{dy^{2}} \right) + u + \varnothing$
The Grashof number is a significant dimensionless parameter for forced convection and the Reynolds number is a significant dimensionless parameter for natural convection.
Consider turbulent forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?
Laminar $f = \frac{64u}{\text{qDVm}} = \frac{64}{\text{Re}}$ turbulent $P = \frac{f\frac{l}{D}\text{uV}m^{2}}{2}\ $
How is the hydrodynamic entry length defined for a flow in tube? Is the entry length longer in laminar or turbulent flow?
The length of region from the tube inlet to the point at which the boundary layer merges at the center line. Lh lam =0,05Re D Lh turb = 10 D
Consider two fluids, one with large coefficient of volume expansion and the other with a small one. In what fluid will a hot surface initiate stronger natural convection currents? Why? Assume the viscosity of the fluids to be the same.
$$\beta = \frac{1}{T}\left\lbrack K \right\rbrack\ \ Gr = \frac{\text{qB}\left( Ts - Tinf \right)Lc^{3}}{v^{2}}\ $$
Physically, what does the grashof number present? How does the grashof number differ from the Reynolds number?
$Gr = \frac{\text{qB}\left( Ts - Tinf \right)Lc^{3}}{v^{2}}$ $Re = \frac{\text{DhqV}}{\mu}$ The dimensionless parameter in the brackers represents the natural convection effects.
How does the Raylelgh number differ from the grashof number.
Ra = Gr*Pr
What does the effective conductivity of an enclosure reoresent? How is the ratio of the effective conductivity to thermal conductivity related to the nusselt number ?
$\mathbf{Q = hAs}\left( \mathbf{T}\mathbf{1 - T}\mathbf{2} \right)\mathbf{= kNuAs\ }\frac{\mathbf{T}\mathbf{1 - T}\mathbf{2}}{\mathbf{k}}$ $\mathbf{Qcond = kAs\ }\frac{\mathbf{T}\mathbf{1 - T}\mathbf{2}}{\mathbf{k}}$ kNu- effective thermal conductivity
Consider film condensation on a vertical plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?
Constant temp of Ts and tsat, heat trans across the liquid like is by pure conduction, velocity is low (or 0), laminar flow, properties of liquid is const, acceleration is negliglible.
When boiling a saturated liquid, one must be careful while increasing the heat flux to avoid burnout. Burnout occurs when the boiling transitions from nucleate to film or non of them.
Classify heat exchangers according to flow tyoe and explain the characteristic of each type.
Double pipe – one fluid is a double pipe heat exchangers flows through the smaller pipe whike the outer fluid flows through the ammuar space between two piipes.
Compact heat exchanger – specifically designed to realize a long heat transfer surface area per unit volume
Shell and tube – Contains a large amount of tubes packed in the shell with their axes parallel to that of the shell
Plate and frame – contains of a series of plates with corrugate flat flow passages
Under that conditions can the overall heat transfer coefficient of a heat exchanger be determined from U=$\left( \frac{\mathbf{1}}{\mathbf{h}\mathbf{1}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{h}\mathbf{0}} \right)^{\mathbf{- 1}}\mathbf{\ }$?
Thermal conduction of tube is high, Thermal resistance of tube is negli or Rwall = 0. Ai=A0=As
In the heat transfer relation Q=UAsΔTlm a heat exchanger what is ΔTlm called? How is it calculated for a parallel-flow and counter-flow heat exchanger?
ΔTlm- Log mean temperature, counter ΔTm=FΔTm, parallel: δ$\dot{Q = \dot{m}\text{CpldTl}}$
Explain how the LMTD method can be used to determine the heat transfer surface area of a multipass shell-and tube heat exchanger when all the necessary information, including the outlet temperature is given.
Select the type of heat exchanger, Determine any unknown inlet or outlet temp and heat transfer rate, Calculate the log mean temp difference ΔTlm, Obtain the value of the overall heat transfer coefficient u, Calculate the heat transfer surface area As.
What is a blackbody? Does a blackbody actually exist ?
Perfect emitter and absorber of radiation. At a specyfie temp and wave length, absorbs everything, no surface can emitate more energy, E=δT4
What is thermal radiation? How does it differ from the other forms of electromagnetic radiation?
Electromagnetic radiation generated nu the thermal motion of changed particules in matter. All mater with temp higher than 0 Kemits thermal radiation. Solar radiation, ultraviolet radiation, infrared radiation.
Define the properties emissivity and absorptivity. When are there two properties equal to each other?
Emiss- ration emitted by the surface of given temp compared to blackbody emiss, E<o:1> blackbody=1 , spectral directional emissivity – ratio of the intensity of radiation. Abser – the fraction of inradiation absorbed by the surface. Emits = absorbs $\alpha = \frac{\text{Gobs}}{G}$
What is the radiation shield? Why is it used ?
Shield which is design to absorb or reflect radiation. It’s use to diminish the quantity of radiation and protect us from unvisible radiation which influence on our health.
Define spectral transmissivity a medium of thickness L in terms of a) spectral intensities and b) the spectral absorbtion coefficient.
Eλ=πlλe Gλ = πlλ Iλi=πlλ e + r