Question

A heat conductor has a shape of a pyramid. The base is square shaped, with sides 4 mm long, each. The
height of the pyramid is 12 mm. The pyramid has been placed on a heating element with constant
temperature 300°C. Heat is directed through the top of the pyramid so that the temperature at the height
of 10 mm is 100 °C. Assuming the heating power and heat conductivity of the material remaining constant,
compute the temperature of the pyramid at height of 6 mm. Hint: Check the heat conduction through
the pyramid using a differential form of Fourier’s law, layer by layer.
Is the model physical throughout the whole pyramid? Explain why.

Answer 1

Height pyramid Blement Hsag at base i's with 300°C At height IOmm T= (00 C At height 6m T-2 By difevential Jorm Foure the thermal dimeniconal form Conduction in one 0 -k dT dx material condustivitiy yEheat ylux dT: Temper ature change tial k mK yam1inal to height changelmm dx Case1 height T= 100°c Omm At Omm T=300°c From uatioń 0 T2-T h2-h 300 C- 100*C Omm 1omm Scanned with CamScanner

20 °C T: 2. Case 2 height 6nhm -- --+ T300 C Omm f again apply Same dr dx T2- TL -k. t4-tY 300°C-T Omm Yom beore So 20 OC yegut k 2 OC Mm 300°C-TI -6pam mm 120°C 300°C -Ti TI= 300 C |20°C cs Scaed ah CamScanner heig 6mm e have ht

80 C temperature AA height dayer, the layer by increases jemperature decreajs js physical yramid So this mndel Ahroughoutthe phole cs Scanned with CamScanner