PROBLEM 4.18
KNOWN: Power, size and shape of laser beam. Material properties. FIND: Maximum surface temperature for a Gaussian beam, maximum temperature for a flat beam, and average temperature for a flat beam. SCHEMATIC:
Gaussian q Flat
q
rb = 0.1 mm P =

PROBLEM 4.16
KNOWN: Thin-walled copper tube enclosed by an eccentric cylindrical shell; intervening space filled with insulation. FIND: Heat loss per unit length of tube; compare result with that of a concentric tube-shell arrangement. SCHEMATIC:
ASSUMPTI

PROBLEM 4.15 KNOWN: Dimensions and boundary temperatures of a steam pipe embedded in a concrete casing. FIND: Heat loss per unit length. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Negligible steam side convection resistance, pipe wall resist

PROBLEM 4.14
KNOWN: Tube embedded in the center plane of a concrete slab. FIND: The shape factor and heat transfer rate per unit length using the appropriate tabulated relation, SCHEMATIC:
ASSUMPTIONS: (1) Two-dimensional conduction, (2) Steady-state cond

PROBLEM 4.13 KNOWN: Surface temperatures of two parallel pipe lines buried in soil. FIND: Heat transfer per unit length between the pipe lines. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant properties, (

PROBLEM 4.12 KNOWN: Electrical heater of cylindrical shape inserted into a hole drilled normal to the surface of a large block of material with prescribed thermal conductivity. FIND: Temperature reached when heater dissipates 50 W with the block at 25C. S

PROBLEM 4.40
KNOWN: Nodal point on boundary between two materials. FIND: Finite-difference equation for steady-state conditions. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant properties, (4) No internal

PROBLEM 4.39
KNOWN: Nodal point configurations corresponding to a diagonal surface boundary subjected to a convection process and to the tip of a machine tool subjected to constant heat flux and convection cooling. FIND: Finite-difference equations for th

PROBLEM 4.38
KNOWN: Heat generation and thermal boundary conditions of bus bar. Finite-difference grid. FIND: Finite-difference equations for selected nodes. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant

PROBLEM 4.37
KNOWN: Two-dimensional cylindrical configuration with prescribed radial (r) and angular () spacings of nodes. FIND: Finite-difference equations for nodes 2, 3 and 1. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional con

PROBLEM 4.36
KNOWN: Conduction in a one-dimensional (radial) cylindrical coordinate system with volumetric generation. FIND: Finite-difference equation for (a) Interior node, m, and (b) Surface node, n, with convection. SCHEMATIC:
(a) Interior node, m (b)

PROBLEM 4.35
KNOWN: Boundary conditions that change from specified heat flux to convection. FIND: The finite difference equation for the node at the point where the boundary condition changes. SCHEMATIC:
q s
m -1,n y/2 y q1 q3 q5 x x m, n-1 m,n q2
h, T m

PROBLEM 4.34
KNOWN: External corner of a two-dimensional system whose boundaries are subjected to prescribed conditions. FIND: Finite-difference equations for these situations: (a) Upper boundary is perfectly insulated and side boundary is subjected to a

PROBLEM 4.33
KNOWN: Plane surface of two-dimensional system. FIND: The finite-difference equation for nodal point on this boundary when (a) insulated; compare result with Eq. 4.42, and when (b) subjected to a constant heat flux. SCHEMATIC:
ASSUMPTIONS: (1

PROBLEM 4.32
KNOWN: Internal corner of a two-dimensional system with prescribed convection boundary conditions. FIND: Finite-difference equations for these situations: (a) Horizontal boundary is perfectly insulated and vertical boundary is subjected to a

PROBLEM 4.31
KNOWN: Dimensions of chip array. Conductivity of substrate. Convection conditions. Contact resistance. Expression for resistance of spreader plate. Maximum chip temperature. FIND: Maximum chip heat rate. SCHEMATIC:
ASSUMPTIONS: (1) Steady-sta

PROBLEM 4.30
KNOWN: Dimensions and thermal conductivities of a heater and a finned sleeve. Convection conditions on the sleeve surface. FIND: (a) Heat rate per unit length, (b) Generation rate and centerline temperature of heater, (c) Effect of fin parame

PROBLEM 4.29
KNOWN: Dimensions and thermal conductivity of concrete duct. Convection conditions of ambient air. Inlet temperature of water flow through the duct. FIND: (a) Heat loss per duct length near inlet, (b) Minimum allowable flow rate corresponding

PROBLEM 4.28
KNOWN: Dimensions and surface temperatures of a square channel. Number of chips mounted on outer surface and chip thermal contact resistance. FIND: Heat dissipation per chip and chip temperature. SCHEMATIC:
ASSUMPTIONS: (1) Steady state, (2)

PROBLEM 4.27
KNOWN: Disc-shaped electronic devices dissipating 100 W mounted to aluminum alloy block with prescribed contact resistance. FIND: (a) Temperature device will reach when block is at 27C assuming all the power generated by the device is transfe

PROBLEM 4.25
KNOWN: Igloo constructed in hemispheric shape sits on ice cap; igloo wall thickness and inside/outside convection coefficients (hi, ho) are prescribed. FIND: (a) Inside air temperature T,i when outside air temperature is T,o = -40C assuming o

PROBLEM 4.24
KNOWN: Long fin of aluminum alloy with prescribed convection coefficient attached to different base materials (aluminum alloy or stainless steel) with and without thermal contact resistance R j at the t, junction. FIND: (a) Heat rate qf and j

PROBLEM 4.23
KNOWN: Dimensions, shape factor, and thermal conductivity of square rod with drilled interior hole. Interior and exterior convection conditions. FIND: Heat rate and surface temperatures. SCHEMATIC:
ASSUMPTIONS: (1) Steady-state, two-dimension

PROBLEM 4.22
KNOWN: Long constantan wire butt-welded to a large copper block forming a thermocouple junction on the surface of the block. FIND: (a) The measurement error (Tj - To) for the thermocouple for prescribed conditions, and (b) Compute and plot (T

PROBLEM 4.21 KNOWN: Platen heated by passage of hot fluid in poor thermal contact with cover plates exposed to cooler ambient air. FIND: (a) Heat rate per unit thickness from each channel, q , (b) Surface temperature of i cover plate, Ts, (c) q and Ts if

PROBLEM 4.19
KNOWN: Relation between maximum material temperature and its location, and scanning velocities. FIND: (a) Required laser power to achieve a desired operating temperature for given material, beam size and velocity, (b) Lag distance separating