Scribd
Upload
53 views3 pages

HW 03

This document contains 6 problems related to heat transfer through walls, cylinders, fins, and dust layers. Problem 1 involves calculating the heat flux required to maintain a chamber wall at 75C given internal and external heat transfer coefficients. Problem 2 gives an expression for the temperature distribution and heat flux in a heated shell wrapped around a rod. Problem 3 calculates the heat transfer rate from a copper cylinder connecting two surfaces. Problem 4 finds the maximum operating velocity for pulling silicon from molten silicon. Problem 5 determines the heat transfer rate for an aluminum fin array with varying fin density. Problem 6 calculates the heat transfer and thermal resistance for a fin array with a accumulating dust layer of varying thickness.

Uploaded by

Potatoes123
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
53 views3 pages

HW 03

This document contains 6 problems related to heat transfer through walls, cylinders, fins, and dust layers. Problem 1 involves calculating the heat flux required to maintain a chamber wall at 75C given internal and external heat transfer coefficients. Problem 2 gives an expression for the temperature distribution and heat flux in a heated shell wrapped around a rod. Problem 3 calculates the heat transfer rate from a copper cylinder connecting two surfaces. Problem 4 finds the maximum operating velocity for pulling silicon from molten silicon. Problem 5 determines the heat transfer rate for an aluminum fin array with varying fin density. Problem 6 calculates the heat transfer and thermal resistance for a fin array with a accumulating dust layer of varying thickness.

Uploaded by

Potatoes123
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 3

ME315 2019-F HW-03

1. A wall with heater (thickness of 0.2 m, thermal conductivity of 4 W/mK, and uniform volumetric
heat generation rate of 𝑞̇ = 1000W/m3 ) is used to maintain a temperature inside a chamber. The
ambient temperature is 25°C. The convection coefficients are hi = 20 W/m2K, and ho = 5 W/m2K,
respectively. To make sure the temperature inside the chamber is maintained at 75°C, an additional
thin-film heater is placed on the outer side of the wall, supplying a uniform areal heat flux qo”.

0 x L=200 mm

Wall, T∞,i, hi
T∞,o, ho
k, 𝑞̇

Thin film heater

(a) If no heat generated in the wall is lost to outside of the chamber, what’s the qo” the thin-film
heater needs to supply? Sketch the temperature distribution in the wall T – x, and evaluate surface
temperatures T(0) and T(L).
(b) When the volumetric heater within the wall is turned off, what are the surface temperatures at
steady state?
2. A rod with radius of ri, thermal conductivity ki, and with no heat generation, is wrapped by a
thick layer of electrically heated shell (thermal conductivity ko) that generates heat at a uniform
volumetric generation rate of 𝑞̇ (W/m3). The outer surface (radius of ro) is exposed to a fluid at T∞
and a convection coefficient h.
(a) Find an expression for the steady-state temperature distribution T(r) in the heater shell, in terms
of the given parameters ri, ro, 𝑞̇ , h, T∞, ki, and ko.
(b) Find an expression for the heat transfer per unit length at the outer surface, 𝑞′(𝑟0 ), in terms of
the given parameters.
3. A copper cylinder (D = 1 mm, L = 25 mm) connects two surfaces maintained at Ts,1 = 120°C,
Ts,2 = 20°C. The air, also at T∞ =20°C flows over both the base and the extended surface with heat
transfer coefficient h = 100 W/m2K.

1
(a) Calculate the heat transfer rate from the cylinder to the air.
(b) Consider bundle of cylinders installed every 4x4 mm, calculate the heat transfer rate per unit
area of the hot plane wall.
4. During silicon photovoltaics manufacturing processes, a thin sheet of silicon (W = 75 mm, t =
140 μm) is pulled continuously from the molten silicon at a very slow velocity in a very large
chamber. The free stream temperature of this process chamber is T∞ =450°C and the associated
convection coefficient around the silicon sheet is h = 5.7W/m2K. Calculate the maximum operation
velocity. (Latent heat of silicon fusion is hsl = 1.8x106 J/kg.)

5. Consider the aluminum rectangular fin array installed on a plane wall with height of 20 mm and
width of 20 mm. The fins have thickness, width, and length of 2 mm, 20mm, and 20 mm,
respectively. The temperature of the plane surface and ambient are Tb = 95°C and T∞ =20°C,
respectively. When more fins are installed, the air flow and the convection heat transfer are reduced.
This reduction can be described as h = hmax ×(1 – N/Nmax), where Nmax is the maximum number of fins
can be installed (i.e. when Nmax = 10 fin installed, 10×2mm=20 mm, there’s not spacing between fins).
Determine the total heat transfer rate for N = 0, 3, 6,9 when hmax = 50 W/m2K. Also, evaluate the fin
efficiency and effectiveness and comment which case is the best design.

2
6. An aluminum fin array (k = 175 W/mK, 14×17, cross section 1×1 mm, length 7 mm) is installed
on a chip (53 × 57 mm) to maintain the temperature of the chip below 75°C under air cooling h =
375 W/m2K at 25°C. Dust is collecting in the grooves between the separate fins during operation.
The thermal conductivity of the dust can be taken as 0.0032 W/mK. Calculate and plot the total
heat transfer rate and overall thermal resistance when the dust layer ranges from 0 ≤ Ld ≤ 5 mm.
(For simplicity, we can analyze the heat flow via the fin and the dust as two separate channels.)

You might also like