Generally, Christians hold that the Holy Spirit dwells within the heart of man; man being body, soul and spirit. This indwelling is not physical but spiritual.
The heart consists of soul and spirit.
Hebrews 4:12 For the word of God [is] quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and [is] a discerner of the thoughts and intents of the heart.
The sending of the Holy Spirit was foretold within the Old Testament.
Ezekiel 36:26 A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh.
True circumcision is of the heart.
Romans2:28,29 For he is not a Jew, which is one outwardly; neither [is that] circumcision, which is outward in the flesh: But he [is] a Jew, which is one inwardly; and circumcision [is that] of the heart, in the spirit, [and] not in the letter; whose praise [is] not of men, but of God.
Our personal economy, our value system is established within the heart and our actions are derived within the heart.
Matthew 6:21 For where your treasure is, there will your heart be also.
Matthew 12:35 A good man out of the good treasure of the heart bringeth forth good things: and an evil man out of the evil treasure bringeth forth evil things
The “hidden man of the heart” is Jesus Christ born of the Holy Spirit, which resides within the heart of man.
1 Peter 3:4 But [let it be] the hidden man of the heart, in that which is not corruptible, [even the ornament] of a meek and quiet spirit, which is in the sight of God of great price.
Galatians 2:20 I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
Galatians4:6 And because ye are sons, God hath sent forth the Spirit of his Son into your hearts, crying, Abba, Father.