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The heat transfer by conduction through a thick sphere is given by

A. $${\text{Q}} = \frac{{2\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$

B. $${\text{Q}} = \frac{{4\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$

C. $${\text{Q}} = \frac{{6\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$

D. $${\text{Q}} = \frac{{8\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}$$

Answer: Option B

Solution(By Examveda Team)

The heat transfer by conduction through a thick sphere is given by $${\text{Q}} = \frac{{4\pi {\text{k}}{{\text{r}}_1}{{\text{r}}_2}\left( {{{\text{T}}_1} - {{\text{T}}_2}} \right)}}{{{{\text{r}}_2} - {{\text{r}}_1}}}.$$

This Question Belongs to Mechanical Engineering >> Heat And Mass Transfer

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